Practice Test 1 - Practice tests

PSAT/NMSQT Prep 2019 - Princeton Review 2019


Practice Test 1
Practice tests

How to Score Your Practice Tests

For each subject area in the practice test, convert your raw score, or the number of questions you answered correctly, to a scaled score using the table below. To get your raw score for Evidence-Based Reading & Writing, add the total number of Reading questions you answered correctly to the total number of Writing questions you answered correctly; for Math, add the number of questions you answered correctly for the Math—No—Calculator and Math—Calculator sections.

Evidence-Based Reading and Writing

Math

TOTAL Raw Score

Scaled Score

Raw Score

Scaled Score

0

160

0

160

1

160

1

190

2

180

2

210

3

190

3

240

4

200

4

270

5

210

5

290

6

220

6

320

7

230

7

340

8

240

8

360

9

250

9

370

10

280

10

390

11

280

11

400

12

290

12

420

13

300

13

430

14

310

14

440

15

320

15

460

16

320

16

470

17

340

17

480

18

340

18

490

19

350

19

500

20

350

20

510

21

360

21

520

22

360

22

530

23

360

23

540

24

380

24

550

25

380

25

560

26

380

26

570

27

390

27

580

28

390

28

580

29

400

29

590

30

400

30

600

31

420

31

610

32

420

32

620

33

420

33

630

34

420

34

640

35

430

35

650

36

430

36

670

37

440

37

680

38

440

38

690

39

450

39

710

40

460

40

720

41

460

41

730

42

460

42

730

43

470

43

740

44

480

44

740

45

480

45

750

46

490

46

750

47

490

47

760

48

500

48

760

49

510



50

520



51

520



52

530



53

540



54

540



55

540



56

550



57

550



58

560



59

560



60

570



61

580



62

580



63

580



64

590



65

590



66

600



67

610



68

610



69

620



70

620



71

630



72

630



73

640



74

640



75

640



76

650



77

660



78

670



79

680



80

680



81

690



82

700



83

710



84

720



85

720



86

730



87

740



88

740



89

750



90

750



91

760



PSAT Practice Test 1 Answer Sheet

PSAT PRACTICE TEST 1

Reading Test

60 Minutes 47 Questions

This section corresponds to Section 1 of your answer sheet.

Directions

Read each passage or pair of passages, then answer the questions that follow. Choose your answers based on what the passage(s) and any accompanying graphics state or imply.

1.

1. Questions 1-10 are based on the following passage.

2. The following passage is adapted from Charles Dickens’s 1860 novel Great Expectations. In this scene, the narrator, a boy named Pip, eats breakfast with his older sister’s acquaintance, Mr. Pumblechook. Pumblechook has agreed to take Pip to see Miss Havisham, a wealthy woman who has requested this visit, although Pip has never met her.

Mr. Pumblechook and I breakfasted at eight o’clock in the parlor behind the shop, while the shopman took his mug of tea and hunch of bread and butter on a sack of peas in the front premises. I considered Mr. Pumblechook wretched company. Besides being possessed by my sister’s idea that a mortifying and penitential character ought to be imparted to my diet,1—besides giving me as much crumb as pos- sible in combination with as little butter, and putting such a quantity of warm water into my milk that it would have been more candid to have left the milk out altogether,—his conversation consisted of nothing but arithmetic. On my politely bidding him Good morning, he said, pompously, “Seven times nine, boy?” And how should I be able to answer, dodged in that way, in a strange place, on an empty stomach! I was hungry, but before I had swallowed a morsel, he began a running sum that lasted all through the breakfast. “Seven?” “And four?” “And eight?” … And so on. And after each figure was disposed of, it was as much as I could do to get a bite or a sup, before the next came; while he sat at his ease guessing nothing, and eating bacon and hot roll, in (if I may be allowed the expression) a gorging and gormandizing manner. For such reasons, I was very glad when ten o’clock came and we started for Miss Havisham’s; though I was not at all at my ease regarding the manner in which I should acquit myself under that lady’s roof. Within a quarter of an hour we came to Miss Havisham’s house, which was of old brick, and dismal, and had a great many iron bars to it. Some of the windows had been walled up; of those that remained, all the lower were rustily barred. There was a courtyard in front, and that was barred; so we had to wait, after ringing the bell, until some one should come to open it. While we waited at the gate, I peeped in (even then Mr. Pumblechook said, “And fourteen?” but I pretended not to hear him), and saw that at the side of the house there was a large brewery. No brewing was going on in it, and none seemed to have gone on for a long long time. A window was raised, and a clear voice demand- ed “What name?” To which my conductor replied, “Pumblechook.” The voice returned, “Quite right,” and the window was shut again, and a young lady came across the courtyard, with keys in her hand. “This,” said Mr. Pumblechook, “is Pip.” “This is Pip, is it?” returned the young lady, who was very pretty and seemed very proud; “come in, Pip.” Mr. Pumblechook was coming in also, when she stopped him with the gate. “Oh!” she said. “Did you wish to see Miss Havisham?” “If Miss Havisham wished to see me,” returned Mr. Pumblechook, discomfited. “Ah!” said the girl; “but you see she don’t.” She said it so finally, and in such an undiscussible way, that Mr. Pumblechook, though in a condition of ruffled dignity, could not protest. But he eyed me severely,—as if I had done anything to him!—and departed with the words reproachfully delivered: “Boy! Let your behavior here be a credit unto them which brought you up by hand!”2 I was not free from apprehension that he would come back to propound through the gate, “And sixteen?” But he didn’t.

1Pip’s sister indicated to Pumblechook that Pip should be grateful, even penitent (unreasonably so) for his help. 2Pumblechook is speaking of Pip’s sister, who often boasts that she raised him “by hand.”

1. According to the first paragraph, Pip’s breakfast with Mr. Pumblechook is

1. eaten on the run.

2. small and of poor quality.

3. better than Pip usually receives.

4. carefully cooked and served.

2. As used in line 5, “wretched” most nearly means

1. shameful.

2. deprived.

3. distressing.

4. heartbroken.

3. Based on the passage, it can be inferred that Mr. Pumblechook

1. has looked forward to his morning with Pip.

2. is as uncomfortable as Pip is during breakfast.

3. has known Pip and his sister for a very long time.

4. is indifferent to Pip’s discomfort during breakfast.

4. Which choice provides the best support for the answer to the previous question?

1. Lines 1—4 (“Mr. Pumblechook . . . premises”)

2. Lines 5—13 (“Besides . . . arithmetic”)

3. Lines 43—44 (“To which my . . . Pumblechook”)

4. Lines 57—60 (“She said . . . protest”)

5. What theme is communicated through the experiences of Pip, the narrator?

1. The world can be a puzzling and sometimes cruel place.

2. Young people are misunderstood by their elders.

3. Mean-spirited people deserve to be treated harshly.

4. The favors one receives in life should be reciprocated.

6. Which of the following is true when Mr. Pumblechook leaves Pip at Miss Havisham’s house?

1. Pip is excited to finally meet Miss Havisham.

2. Pip is nervous about being away from his sister for so long.

3. Pip is relieved to be away from Mr. Pumblechook.

4. Pip is anxious about spending time with the young lady who greets them.

7. Which choice provides the best support for the answer to the previous question?

1. Lines 1—4 (“Mr. Pumblechook . . . premises”)

2. Lines 42—43 (“A window . . . name”)

3. Lines 57—60 (“She said . . . protest”)

4. Lines 64—66 (“I was not . . . he didn’t”)

8. As used in line 59, “condition” most nearly means

1. illness.

2. prerequisite.

3. state.

4. limitation.

9. The function of the parenthetical comment in lines 23—24 is to reveal that

1. Pip is usually more polite in his references to others.

2. Mr. Pumblechook appreciates gourmet food.

3. Pip is very angered that his own breakfast is so meager.

4. Mr. Pumblechook has no qualms about overeating in public.

2.

9.  Questions 10—18 are based on the following passage.

10. This passage is adapted from Martin Luther King, Jr.’s “Letter from Birmingham Jail.”

…I think I should give the reason for my being in Birmingham, since you have been influenced by the argument of “outsiders coming in.” I have the honor of serving as president of the Southern Christian Leadership Conference, an organization operating in every Southern state with headquarters in Atlanta, Georgia. We have some eighty-five affiliate organizations all across the South, one being the Alabama Christian Movement for Human Rights. Whenever necessary and possible we share staff, educational, and financial resources with our affiliates. Several months ago our local af- filiate here in Birmingham invited us to be on call to engage in a nonviolent direct action program if such were deemed necessary. We readily consented and when the hour came we lived up to our promises. So I am here, along with several members of my staff, because we were invited here. I am here because I have basic organizational ties here. Beyond this, I am in Birmingham because injustice is here…. Moreover, I am cognizant of the interrelatedness of all communities and states. I cannot sit idly by in Atlanta and not be concerned about what happens in Birmingham. Injustice anywhere is a threat to justice everywhere. We are caught in an inescapable network of mutuality, tied in a single garment of destiny. Whatever affects one directly affects all indirectly. Never again can we afford to live with the narrow, provincial “outside agitator” idea. Anyone who lives inside the United States can never be considered an outsider anywhere in this country…. You may well ask, “Why direct action? Why sit-ins, marches, etc.? Isn’t negotiation a better path?” You are exactly right in your call for negotiation. Indeed, this is the purpose of direct action. Nonviolent direct action seeks to create such a crisis and establish such creative tension that a community that has constantly refused to negotiate is forced to confront the issue. It seeks so to dramatize the issue that it can no longer be ignored. I just referred to the creation of tension as a part of the work of the nonviolent resister. This may sound rather shocking. But I must confess that I am not afraid of the word tension. I have earnestly worked and preached against violent tension, but there is a type of constructive nonviolent tension that is necessary for growth. Just as Socrates felt that it was necessary to create a tension in the mind so that individuals could rise from the bondage of myths and half-truths to the unfettered realm of creative analysis and objective appraisal, we must see the need of having nonviolent gadflies to create the kind of tension in society that will help men rise from the dark depths of prejudice and racism to the majestic heights of understanding and brotherhood. So the purpose of the direct action is to create a situation so crisis-packed that it will inevitably open the door to negotiation. We, therefore, concur with you in your call for negotiation. Too long has our beloved Southland been bogged down in the tragic attempt to live in monologue rather than dialogue…. My friends, I must say to you that we have not made a single gain in civil rights without determined legal and nonviolent pressure. History is the long and tragic story of the fact that privileged groups seldom give up their privileges voluntarily. Individuals may see the moral light and voluntarily give up their unjust posture; but as Reinhold Niebuhr has reminded us, groups are more immoral than individuals. We know through painful experience that free- dom is never voluntarily given by the oppressor; it must be demanded by the oppressed…. For years now I have heard the word “Wait!” It rings in the ear of every African American with a piercing familiarity. This “wait” has almost always meant “never.” It has been a tranquilizing thalidomide, relieving the emotional stress for a moment, only to give birth to an ill-formed infant of frustra- tion. We must come to see with the distinguished jurist of yesterday that “justice too long delayed is justice denied.” We have waited for more than three hundred and forty years for our constitutional and God-given rights. The nations of Asia and Africa are moving with jet-like speed toward the goal of political independence, and we still creep at horse and buggy pace toward the gaining of a cup of cof- fee at a lunch counter….

10.King’s purpose for writing this letter is

1. to explain why he came to Birmingham to protest.

2. to launch a nonviolent protest movement in Birmingham.

3. to open an affiliate of the Southern Christian Leadership Conference in Birmingham.

4. to support fellow civil rights activists in Birmingham.

11.Which choice provides the best evidence for the answer to the previous question?

1. Lines 1—2 (“I think . . . in Birmingham”)

2. Lines 3—7 (“I have . . . Atlanta, Georgia”)

3. Lines 7—10 (“We have some . . . Rights”)

4. Lines 24—25 (“Injustice anywhere . . . everywhere”)

12.As used in lines 21—22, “interrelatedness of all communities and states” most nearly means that

1. King has personal connections to people in the town.

2. the Southern Christian Leadership Conference needs national support.

3. events in one part of the country affect everyone in the nation.

4. local civil rights groups operate independently of one another.

13.Based on paragraph 3, it can be reasonably inferred that King believed circumstances in Birmingham at the time

1. were unfair and wrong.

2. constituted an isolated event.

3. justified his arrest.

4. required federal intervention.

14.Which choice provides the best evidence for the answer to the previous question?

1. Lines 21—22 (“Moreover, . . . states”)

2. Lines 24—25 (“Injustice anywhere . . . everywhere”)

3. Lines 25—27 (“We are caught . . . destiny”)

4. Lines 28—30 (“Never again . . . idea”)

15.As used in line 40, “dramatize” most nearly means

1. to cast events in an appealing light.

2. to draw attention to significant events.

3. to exaggerate events to seem more important.

4. to turn events into a popular performance.

16.Which choice most clearly paraphrases a claim made by King in paragraph 3?

1. A failure to negotiate in the South has provoked secret action by civil rights activists.

2. A focus on dialogue blinds reformers to the necessity for direct action to promote change.

3. Direct action is necessary to motivate people to talk about prejudice and racism.

4. Nonviolent protest encourages a sense of brotherhood and understanding among citizens.

17.Paragraph 4 best supports the claims made in paragraph 3 by

1. arguing that nonviolent pressure is most likely to spur just action by individuals.

2. clarifying that throughout history, privileged classes have been reluctant to let go of privilege.

3. drawing a distinction between the morality of individuals and of groups.

4. pointing out that few gains in civil rights have been made without nonviolent pressure.

18.King refers to “the gaining of a cup of coffee at a lunch counter” (lines 87—88) primarily to

1. call attention to the sedative effect of delaying civil rights reform in the United States.

2. emphasize that white Americans will not willingly end oppression against black Americans.

3. describe the progress made toward the winning of equal rights in other countries.

4. underscore the contrast between progress made in other countries and the United States.

3.

18. Questions 19—28 are based on the following passages and supplementary material.

19. The idea of a World Bank became a reality in 1944, when delegates to the Bretton Woods Conference pledged to “outlaw practices which are agreed to be harmful to world prosperity.” Passage 1 discusses the benefits of the World Bank, while Passage 2 focuses on the limited lifespan of the Bretton Woods system.

Passage 1

In 1944, 730 delegates from forty-four Allied nations met in Bretton Woods, New Hampshire, just as World War II was ending. They were attend- ing an important conference. This mostly forgotten event shaped our modern world because delegates at the Bretton Woods Conference agreed on the establishment of an international banking system. To ensure that all nations would prosper, the United States and other allied nations set rules for a postwar international economy. The Bretton Woods system created the International Monetary Fund (IMF). The IMF was founded as a kind of global central bank from which member countries could borrow money. The countries needed money to pay for their war costs. Today, the IMF facilitates international trade by ensuring the stability of the international monetary and financial system. The Bretton Woods system also established the World Bank. Although the World Bank shares similarities with the IMF, the two institutions remain distinct. While the IMF maintains an orderly system of payments and receipts between nations, the World Bank is mainly a development institution. The World Bank initially gave loans to European countries dev- astated by World War II, and today it lends money and technical assistance specifically to economic projects in developing countries. For example, the World Bank might provide a low-interest loan to a country attempting to improve education or health. The goal of the World Bank is to “bridge the economic divide between poor and rich countries.” In short, the organizations differ in their purposes. The Bank promotes economic and social progress so people can live better lives, while the IMF represents the entire world in its goal to foster global monetary cooperation and financial stability. These two specific accomplishments of the Bretton Woods Conference were major. However, the Bretton Woods system particularly benefited the United States. It effectively established the U.S. dollar as a global currency. A global currency is one that countries worldwide accept for all trade, or international transactions of buying and selling. Because only the U.S. could print dollars, the United States became the primary power behind both the IMF and the World Bank. Today, global currencies include the U.S. dollar, the euro (European Union countries), and the yen (Japan). The years after Bretton Woods have been considered the golden age of the U.S. dollar. More importantly, the conference profoundly shaped foreign trade for decades to come.

Passage 2

The financial system established at the 1944 Bretton Woods Conference endured for many years. Even after the United States abrogated agreements made at the conference, the nation continued to experience a powerful position in international trade by having other countries tie their currencies to the U.S. dollar. The world, however, is changing. In reality, the Bretton Woods system lasted only three decades. Then, in 1971, President Richard Nixon introduced a new economic policy by ending the convertibility of the dollar to gold. It marked the end of the Bretton Woods international monetary framework, and the action resulted in worldwide financial crisis. Two cornerstones of Bretton Woods, however, endured: the International Monetary Fund (IMF) and the World Bank. Since the collapse of the Bretton Woods system, IMF members have been trading using a flexible exchange system. Namely, countries allow their exchange rates to fluctuate in response to changing conditions. The exchange rate between two currencies, such as the Japanese yen and the U.S. dollar, for example, specifies how much one cur- rency is worth in terms of the other. An exchange rate of 120 yen to dollars means that 120 yen are worth the same as one dollar. Even so, the U.S. dollar has remained the most widely used money for international trade, and having one currency for all trade may be better than using a flexible exchange system. This seems to be the thinking of a powerful group of countries. The Group of Twenty (G20), which has called for a new Bretton Woods, consists of govern- ments and leaders from 20 of the world’s largest economies including China, the United States, and the European Union. In 2009, for example, the G20 announced plans to create a new global currency to replace the U.S. dollar’s role as the anchor currency. Many believe that China’s yuan, quickly climbing the financial ranks, is well on its way to becoming a major world reserve currency. In fact, an earlier 1988 article in The Economist stated, “30 years from now, Americans, Japanese, Europeans, and people in many other rich countries and some relatively poor ones will probably be paying for their shopping with the same currency.” The article predicted that the world supply of currency would be set by a new central bank of the IMF. This prediction seems to be coming to fruition since the G20 indicated that a “world cur- rency is in waiting.” For an international construct such as the original Bretton Woods to last some 26 years is nothing less than amazing. But move over Bretton Woods; a new world order in finance could be on the fast track.

Top 10 International Currencies

(Percent Shares of Average Daily Currency Trading)


2007

2010

2013


Share

Rank

Share

Rank

Share

Rank

U.S. Dollar (USD)

85.6%

1

84.9%

1

87.0%

1

Euro (EUR)

37.0%

2

39.1%

2

33.4%

2

Japanese Yen (JPY)

17.2%

3

19.0%

3

23.0%

3

UK Pound (GBP)

14.9%

4

12.9%

4

11.8%

4

Australian Dollar (AUD)

6.6%

6

7.6%

5

8.6%

5

Swiss Franc (CHF)

6.8%

5

6.3%

6

5.2%

6

Canadian Dollar (CAD)

4.3%

7

5.3%

7

4.6%

7

Mexican Peso (MXN)

1.3%

12

1.3%

14

2.5%

8

Chinese Yuan (CNY)

0.5%

20

0.9%

17

2.2%

9

New Zealand Dollar

1.9%

11

1.6%

10

2.0%

10

Adapted from Mauldin Economics; Bank for International Settlements, September 2013 Triennial Central Bank Survey.

19.Based on Passage 1, it can reasonably be inferred that

1. world leaders recognized the need for markets to function independently.

2. Bretton Woods increased U.S. economic influence around the world.

3. the IMF and the World Bank work closely together to ensure prosperity.

4. the conclusion of World War II had little influence on events at Bretton Woods.

20.Which choice provides the best evidence for the answer to the previous question?

1. Lines 8—10 (“To ensure . . . economy”)

2. Lines 10—12 (“The Bretton . . . Fund”)

3. Lines 44—46 (“Because only . . . World Bank”)

4. Lines 50—52 (“More importantly . . . to come”)

21.As used in line 35, “foster” most nearly means

1. publicize.

2. rear.

3. stabilize.

4. encourage.

22.Which statement best explains the difference between the purposes of the IMF and the World Bank?

1. The IMF provides money to pay for war costs, while the World Bank offers assistance to rebuild countries recovering from war across the globe.

2. The IMF encourages stability in the global financial system, while the World Bank promotes economic development in relatively poor nations.

3. The IMF supports the U.S. dollar in international markets, while the World Bank provides low-interest loans to many nations around the world.

4. The IMF offers governments advice about participation in global markets, while the World Bank encourages monetary cooperation between nations.

23.Based on the second paragraph in Passage 2, it can be reasonably inferred that

1. the United States did not support the goals of the IMF and the World Bank.

2. Bretton Woods was originally intended to last for three decades.

3. President Nixon acted to reinforce the decisions made at Bretton Woods.

4. some U.S. policy decisions differed from international consensus over Bretton Woods.

24.Which choice provides the best evidence for the answer to the previous question?

1. Lines 60—61 (“In reality . . . three decades”)

2. Lines 61—63 (“Then, in 1971 . . . to gold”)

3. Lines 66—68 (“Two cornerstones . . . World Bank”)

4. Lines 69—71 (“Since the collapse . . . exchange system”)

25.As used in line 90, “anchor” most nearly means

1. key.

2. fastening.

3. rigid.

4. supporting.

26.It can reasonably be inferred from both Passage 2 and the graphic that

1. international markets are increasingly comfortable using the yuan as trade currency.

2. the United States favors using the yuan as one of the world’s reserve currencies.

3. the G20 wants to replace the yuan and other currencies with a new global currency.

4. the IMF continues to support the yuan and other currencies in a flexible exchange system.

27.Which statement most effectively compares the authors’ purposes in both passages?

1. Passage 1’s purpose is to contrast the functions of the IMF and World Bank, while Passage 2’s purpose is to outline the benefits of a flexible trade system to the United States.

2. Passage 1’s purpose is to describe the history of international trade in the 20th century, while Passage 2’s purpose is to explain why the Bretton Woods system collapsed.

3. Passage 1’s purpose is to describe Bretton Woods’ effect on the global economy, while Passage 2’s purpose is to suggest that a new currency for global trade may soon be implemented.

4. Passage 1’s purpose is to promote the economic benefits of the IMF and World Bank, while Passage 2’s purpose is to encourage the reestablishment of the Bretton Woods system.

28.Both passages support which generalization about the global economy?

1. U.S. influence on global trade has continued under a flexible exchange system.

2. The purposes of the International Monetary Fund and the World Bank are indirectly related.

3. The Group of Twenty represents the financial interests of the world’s largest economies.

4. International institutions such as the IMF continue to influence economic trade and development.

4.

28. Questions 29—38 are based on the following passage.

29. This passage is adapted from an article about treating paralysis.

According to a study conducted by the Christopher and Dana Reeve Foundation, more than six million people in the United States suffer from debilitating paralysis. That’s close to one person in every fifty who suffers from a loss of the ability to move or feel in areas of his or her body. Paralysis is often caused by illnesses, such as stroke or multiple sclerosis, or injuries to the spinal cord. Research scientists have made advances in the treatment of paralysis, which means retraining affected individuals to become as independent as possible. Patients learn how to use wheelchairs and prevent complications that are caused by restricted movement. This retraining is key in main- taining paralytics’ quality of life; however, an actual cure for paralysis has remained elusive—until now. In 2014, surgeons in Poland collaborated with the University College London’s Institute of Neurology to treat a Polish man who was paralyzed from the chest down as a result of a spinal cord in- jury. The scientists chose this patient for their study because of the countless hours of physical therapy he had undergone with no signs of progress. Twenty-one months after their test subject’s initial spinal cord injury, his condition was considered complete as defined by the American Spinal Injury Association (ASIA)’s Impairment Scale. This meant that he experienced no sensory or motor function in the segments of his spinal cord nearest to his injury. The doctors used a technique refined during forty years of spinal cord research on rats. They removed one of two of the patient’s olfactory bulbs, which are structures found at the top of the human nose. From this structure, samples of olfactory ensheath- ing cells, responsible for a portion of the sense of smell, were harvested. These cells allow the olfactory system to renew its cells over the course of a human life. It is because of this constant regeneration that scientists chose these particular cells to implant into the patient’s spinal cord. After being harvested, the cells were reproduced in a culture. Then, the cells were injected into the patient’s spinal cord in 100 mini-injections above and below the location of his injury. Four strips of nerve tissue were then placed across a small gap in the spinal cord. After surgery, the patient underwent a tailor- made neurorehabilitation program. In the nineteen months following the operation, not only did the patient experience no adverse effects, but his condi- tion improved from ASIA’s class A to class C. Class C is considered an incomplete spinal cord injury, meaning that motor function is preserved to a certain extent and there is some muscle activity. The patient experienced increased stability in the trunk of his body, as well as partial recovery of voluntary movements in his lower extremities. As a result, he was able to increase the muscle mass in his thighs and regain sensation in those areas. In late 2014, he took his first steps with the support of only a walker. These exciting improvements suggest that the nerve grafts doctors placed in the patient’s spinal cord bridged the injured area and prompted the regenera- tion of fibers. This was the first-ever clinical study that showed beneficial effects of cells transplanted into the spinal cord. The same team of scientists plans to treat ten more patients using this “smell cell” transplant technique. If they have continued success, patients around the world can have both their mobility and their hope restored.

29.The passage is primarily concerned with

1. how various diseases and injuries can cause permanent paralysis.

2. ways in which doctors and therapists work to improve patients’ quality of life.

3. one treatment being developed to return mobility to patients suffering paralysis.

4. methods of physical therapy that can help patients with spinal cord injuries.

30.Based on the information in the passage, it can be inferred that the author

1. believes more research should be done before patients with paralysis are subjected to the treatment described in the passage.

2. feels that increased mobility will have a positive impact on patients suffering from all levels of paralysis.

3. thinks that more scientists should study paralysis and ways to improve the quality of life for patients with limited mobility.

4. was part of the research team that developed the new method of treating paralysis described in the passage.

31.Which choice provides the best support for the answer to the previous question?

1. Lines 6—8 (“Paralysis is . . . spinal cord”)

2. Lines 16—20 (“In 2014 . . . injury”)

3. Lines 53—56 (“The patient . . . extremities”)

4. Lines 67—69 (“If they . . . restored”)

32.As used in line 13, “restricted” most nearly means

1. confidential.

2. dependent.

3. increased.

4. limited.

33.In lines 46—47, the author’s use of the word “tailor-made” helps reinforce the idea that

1. the injected cells were from the patient and were therefore well-suited to work in his own body.

2. spinal cord cells were replaced during the transplant portion of the individualized treatment.

3. olfactory bulbs were removed from rats and placed in the patient’s spinal cord during surgery.

4. the method used by doctors to locate the damaged area required expertise and precision.

34.It can reasonably be inferred from the passage that

1. the patient’s treatment would have been more successful if scientists had used cells from another area of his body instead of from his olfactory bulbs.

2. cells from olfactory bulbs will be used to cure diseases that affect areas of the body other than the spinal cord.

3. the patient who received the experimental treatment using cells from olfactory bulbs would not have regained mobility without this treatment.

4. soon doctors will be able to treat spinal injuries without time-consuming and demanding physical therapy.

35.Which choice provides the best evidence for the answer to the previous question?

1. Lines 8—11 (“Research scientists . . . possible”)

2. Lines 20—22 (“The scientists . . . progress”)

3. Lines 31—33 (“They removed . . . nose”)

4. Lines 60—63 (“These exciting . . . fibers”)

36.As used in line 30, “refined” most nearly means

1. advanced.

2. improved.

3. experienced.

4. treated.

37.The success of the patient’s treatment was due in large part to

1. studies done on other patients.

2. research conducted by other doctors in Poland.

3. many experiments performed on rats.

4. multiple attempts on various types of animals.

38.The procedure described in which cells from olfactory bulbs are injected into a damaged area of the spinal cord is most analogous to which of the following?

1. Replacing a diseased organ in a patient with an organ from a donor who has the same tissue type

2. Giving a patient with a high fever an injection of medication to bring the core body temperature down

3. Placing a cast on a limb to hold the bone in place to encourage healing after suffering a break

4. Grafting skin from a healthy area of the body and transplanting it to an area that has suffered severe burns

5.

38. Questions 39—47 are based on the following passage and supplementary material.

39. The following passage is adapted from an essay about mercury in fish.

Mercury is an unusual element; it is a metal but is liquid at room temperature. It is also a neuro- toxin and a teratogen, as it causes nerve damage and birth defects. Mercury can be found just about everywhere; it is in soil, in air, in household items, and even in our food. Everyday objects, such as thermometers, light switches, and fluorescent light- bulbs, contain mercury in its elemental form. Bat- teries can also contain mercury, but they contain it in the form of the inorganic compound mercury chloride. Mercury can also exist as an organic compound, the most common of which is methyl- mercury. While we can take steps to avoid both elemental and inorganic mercury, it is much harder to avoid methylmercury. Most of the mercury in the environment comes from the emissions of coal-burning power plants; coal contains small amounts of mercury, which are released into the air when coal burns. The concen- tration of mercury in the air from power plants is very low, so it is not immediately dangerous. However, the mercury is then washed out of the air by rain- storms and eventually ends up in lakes and oceans. The mercury deposited in the water does not in- stantaneously get absorbed by fish, as elemental mer- cury does not easily diffuse through cell membranes. However, methylmercury diffuses into cells easily, and certain anaerobic bacteria in the water convert the elemental mercury to methylmercury as a by- product of their metabolic processes. Methylmer- cury released into the water by the bacteria diffuses into small single-celled organisms called plankton. Small shrimp and other small animals eat the plank- ton and absorb the methylmercury in the plankton during digestion. Small fish eat the shrimp and then larger fish eat the smaller fish; each time an animal preys on another animal, the predator absorbs the methylmercury. Because each animal excretes the methylmercury much more slowly than it absorbs it, methylmercury builds up in the animal over time and is passed on to whatever animal eats it, resulting in a process called bioaccumulation. As people became aware of the bioaccumulation of mercury in fish, many reacted by eliminating seafood from their diet. However, seafood contains certain omega-3 fatty acids that are important for good health. People who do not eat enough of these fatty acids, especially eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), are more likely to have heart attacks than people who have enough EPA and DHA in their diet. Because fish and shell- fish, along with some algae, are the only sources of these fatty acids, eliminating them from our diet might have worse health effects than consuming small amounts of mercury. Scientists have studied the effects of mercury by conducting tests on animals and by studying vari- ous human populations and recording the amount of mercury in their blood. By determining the lev- els of mercury consumption that cause any of the known symptoms of mercury poisoning, they were able to identify a safe level of mercury consump- tion. The current recommendation is for humans to take in less than 0.1 microgram of mercury for every kilogram of weight per day. This means that a 70-kilogram person (about 155 pounds) could safely consume 7 micrograms of mercury per day. Because haddock averages about 0.055 micrograms of mercury per gram, that person could safely eat 127 grams (about 4.5 ounces) of haddock per day. On the other hand, swordfish averages about 0.995 micrograms of mercury per gram of fish, so the 70-kilogram person could safely eat only about 7 grams (about one-quarter of an ounce) of swordfish per day. Nutritionists recommend that, rather than eliminate fish from our diet, we try to eat more of the low-mercury fish and less of the high-mercury fish. Low-mercury species tend to be smaller omnivorous fish while high-mercury species tend to be the largest carnivorous fish. Awareness of the particulars of this problem, accompanied by mindful eating habits, will keep us on the best course for healthy eating.

Species

Average Weight Range (grams)

Average Mercury Concentration (parts per billion)

Alaskan Pollock

227—1,000

31

Atlantic Haddock

900—1,800

55

Atlantic Herring

100—600

84

Chub Mackerel

100—750

88

Cod

800—4,000

111

Skipjack Tuna

2,000—10,000

144

Black-Striped Bass

6,820—15,900

152

Albacore Tuna

4,540—21,364

358

Marlin

180,000

485

39.The author of the passage would most likely agree with which of the following statements?

1. Mercury poisoning is only one of many concerns that should be considered when choosing which fish to add to one’s diet.

2. More should be done by scientists and nutritionists to inform people about the dangers of mercury poisoning.

3. Fish is an essential part of a healthy diet and can be eaten safely if recommendations for mercury consumption are kept in mind.

4. The mercury present in the air is more dangerous to people than the mercury consumed by eating fish with high mercury levels.

40.Which choice provides the best evidence for the answer to the previous question?

1. Lines 16—17 (“Most of . . . plants”)

2. Lines 30—32 (“Methylmercury released . . . plankton”)

3. Lines 56—59 (“Scientists . . . their blood”)

4. Lines 81—84 (“Awareness . . . eating”)

41.In addition to the levels of mercury in a specific species of fish, people should also consider which of the following when determining a safe level of consumption?

1. Their own body weight

2. Where the fish was caught

3. The other meats they are eating

4. What they ate the day before

42.As used in lines 19—20, “concentration” most nearly means

1. focus.

2. application.

3. density.

4. awareness.

43.The passage most strongly suggests which of the following statements is accurate?

1. It is not possible to completely avoid environmental exposure to mercury.

2. Inorganic mercury is more dangerous to humans than organic mercury.

3. Most of the exposure to mercury experienced by humans comes from fish consumption.

4. Mercury is one of the most abundant elements found in nature.

44.Which choice provides the best evidence for the answer to the previous question?

1. Lines 1—2 (“Mercury is an unusual . . . temperature”)

2. Lines 4—6 (“Mercury . . . our food”)

3. Lines 19—21 (“The concentration . . . dangerous”)

4. Lines 27—30 (“However, methylmercury . . . processes”)

45.Which of the following pieces of evidence would most strengthen the author’s line of reasoning?

1. More examples in paragraph 1 of places mercury is found

2. Details in paragraph 2 about the levels of mercury found in the air

3. An explanation in paragraph 4 of how to treat mercury poisoning

4. More examples in paragraph 5 of how many micrograms of mercury people of different weights could eat

46.As used in line 82, “particulars” most nearly means

1. data.

2. specifics.

3. points.

4. evidence.

47.Based on the information in the passage and the graphic, which of the following statements is true?

1. The fish with the lowest average weight is the safest to eat.

2. A person can safely eat more marlin than albacore tuna in one day.

3. Eating large fish carries a lower risk of mercury poisoning than eating small fish.

4. A person can safely eat more Alaskan pollock than black striped bass in one day.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

PSAT PRACTICE TEST 1

Writing and Language Test

35 Minutes 44 Questions

This section corresponds to Section 2 of your answer sheet.

Directions

Each passage in this section is followed by several questions. Some questions will reference an underlined portion in the passage; others will ask you to consider a part of a passage or the passage as a whole. For each question, choose the answer that reflects the best use of grammar, punctuation, and style. If a passage or question is accompanied by a graphic, take the graphic into account in choosing your response(s). Some questions will have “NO CHANGE” as a possible response. Choose that answer if you think the best choice is to leave the sentence as written.

1.

1. Questions 1—11 are based on the following passage and supplementary material.

2. The UN: Promoting World Peace

The United Nations (UN) is perhaps the most important political contribution of the 20th century. Some may argue that the work of the UN ; an international peacekeeping organization—has proven futile, given persisting global conflict. But the UN’s worldwide influence demands a closer look. This organization’s global impact is undeniable. The UN is a strong political organization determined to create opportunities for its member nations to enjoy a peaceful and productive world.

Decades ago, provoked by the events of World Wars I and II, world leaders began imagining a politically neutral force for international peace. The UN was born in 1945 with 51 participating nations. It was to be a collective political authority for global peace and security. Today, 193 nations are UN members. In keeping with the original hope, the UN still strives toward peaceful international relations.

Understandably, no single organization can perfectly solve the world’s countless, complex problems. But the UN has offered consistent relief for many of the past half-century’s most difficult disasters and conflicts. It also provides a safe space for international conversation. Moreover, it advocates for issues such as justice, trade, hunger relief, human rights, health, and gender equality, the UN also coordinates care for those displaced by disaster and conflict, dictates environmental protection, and works toward conflict reconciliation.

The UN’s budget, goals, and personnel count have significantly expanded to meet more needs. The year 2014 witnessed the UN peacekeeping force grow to over 100,000 strong. These uniformed, volunteer, civilian personnel represent 128 nations. The UN’s budget has also grown over the years to support an international court system, as well as countless agencies, committees, and centers addressing sociopolitical topics. Today’s UN does big things, and it functions with remarkable organization and efficiency. Critics highlight shortcomings to discount the UN’s effectiveness. But considering the countless disasters to which the UN has responded over its six decades of existence, today’s world might enjoy far less peace, freedom, and safety without the UN.

[1] From promoting overarching sociopolitical change to offering food and care for displaced groups, the UN serves to protect human rights. [2] Equally quotable are its initiatives to foster international collaboration, justice, and peace. [3] The UN provided aid to the Philippines after the disastrous 2013 typhoon. [4]Certainly, this work is not finished. [5] But no other organization compares with the work and influence of the UN. [6] This brave endeavor to insist on and strive for peace, whatever the obstacles, has indeed united hundreds of once-divided nations. [7] Today, with eleven Nobel Peace Prizes to its name, the UN is undoubtedly an irreplaceable and profoundly successful force for peace.

image

1.

1. NO CHANGE

2. —an international peacekeeping organization;

3. —an international peacekeeping organization—

4. ; an international peacekeeping organization,

2. Which choice would most clearly end the paragraph with a restatement of the author's claim?

1. The UN is an organization dedicated to advancing social and political justice around the world.

2. Those who argue otherwise are not well educated about geopolitical issues in the 20th century or today.

3. The UN has had its share of corruption over the years, but it has a well-earned reputation of effectively settling international disputes.

4. A better understanding of the UN suggests that the UN enables far greater peace in today’s world than could have been possible otherwise.

3.

1. NO CHANGE

2. Recently,

3. Consequently,

4. In other words,

4.

1. NO CHANGE

2. In having kept with the original hope, the UN still strives toward peaceful international relations.

3. In keeping with the original hope, the UN still strived toward peaceful international relations.

4. In keeping with the original hope, the UN still strove toward peaceful international relations.

5.

1. NO CHANGE

2. equality. The UN

3. equality: the UN

4. equality, The UN

6.

1. NO CHANGE

2. prefers

3. promotes

4. celebrates

7. Which choice provides the most logical introduction to the paragraph?

1. NO CHANGE

2. The UN has developed over the years, but critics charge it has met with limited success.

3. The responsibilities of the UN have expanded in recent years in response to challenging events.

4. The UN has maintained a quiet but effective voice on the world stage in spite of criticism.

8. Which choice best completes the sentence with accurate data based on the graphic?

1. NO CHANGE

2. The year 2010 led to an increase of approximately 100,000 in the UN peacekeeping force.

3. The year 2010 saw the UN peacekeeping force grow to approximately 100,000 strong.

4. The year 2010 saw the UN peacekeeping force decrease to just over 100,000 strong.

9.

1. NO CHANGE

2. considerably less peace, less freedom, and less safety

3. much less peace, less freedom, and less safety

4. significantly less peace and freedom, and less safety

10.

1. NO CHANGE

2. luminous

3. noteworthy

4. repeatable

11.Which sentence should be removed to improve the focus of the concluding paragraph?

1. Sentence 1

2. Sentence 3

3. Sentence 5

4. Sentence 6

2.

11. Questions 12—22 are based on the following passage.

12. DNA Analysis in a Day

Jane Saunders, a forensic DNA specialist, arrives at work and finds a request waiting for her: She needs to determine if the DNA of a fingernail with a few skin cells on it match any records in the criminal database.

“Human DNA is a long, double-stranded molecule; each strand consists of a complementary set of nucleotides,” she explains. “DNA has four nucleotides: adenine (A), thymine (T), guanine (G), and, cytosine (C). On each strand is a sequence of nucleotides that ’match,’ or pair up with the nucleotides on the other, or complementary, strand. On the other hand, when there is an adenine on one strand, there is a thymine on the complementary strand, and where there is guanine on one strand, there is cytosine on the complementary strand.”

She begins by moving the DNA from the rest of the sample, transferring it to a reaction tube. She adds a solution of primers, DNA polymerase, and nucleotides. Her goal is to separate the two strands of the DNA molecules and then make complementary copies of each strand.

The process of testing the DNA includes several steps and many changes in temperature. After mixing the primers, DNA polymerase, and nucleotides with the evidence DNA, Saunders closes the reaction tube and puts it in a thermocycler. It is programmed to raise the temperature to 94°C to separate the double strands into single strands, and then lower the temperature to 59°C to attach the primers to the single strands. Finally, it raises the temperature to 72°C for the DNA polymerase to build the complementary strands. The thermocycler holds each temperature for one minute and repeats the cycle of three temperatures for at least 30 cycles. At the end of each cycle, the number of DNA segments containing the sequence marked by the primers doubles. If the original sample contains only 100 DNA strands, the absolute final sample will have billions of segments.

[1] After a short lunch break, Saunders needs to separate and identify the copied DNA segments. [2] She had used primers that bind to 13 specific sites in human DNA called short tandem repeats, or STRs. [3] The 13 STRs are segments of four nucleotides that repeat, such as GATAGATAGATA. [4] “Now here’s where the real magic happens!” Saunders says excitedly. [5] “Most DNA is identical for all humans. [6] But STRs vary greatly. [7] The chances of any two humans—other than identical twins—having the same set of 13 STRs is less than one in one trillion.”

Saunders knows that the detectives will be prepared to hear her findings, so she sits down at her desk to compare her results with the criminal database in the hopes of finding a match. Is it possible that too much time is spent identifying DNA in cases that are relatively easy to solve?

12.

1. NO CHANGE

2. matches

3. has matched

4. will be matching

13.

1. NO CHANGE

2. molecule, each strand consists

3. molecule each strand consists

4. molecule but each strand consists

14.

1. NO CHANGE

2. adenine (A), thymine (T), guanine (G), and cytosine (C).

3. adenine (A), thymine (T) guanine (G) and cytosine (C).

4. adenine (A) thymine (T), guanine (G) and cytosine (C).

15.

1. NO CHANGE

2. Specifically,

3. However,

4. Similarly,

16.

1. NO CHANGE

2. reviewing

3. changing

4. detaching

17.Which choice most effectively combines the sentences at the underlined portion?

1. reaction tube since she adds

2. reaction tube, however, she adds

3. reaction tube, and adding

4. reaction tube, she adds

18.Which sentence most effectively establishes the central idea?

1. NO CHANGE

2. The object of testing the DNA is to re-create many strands of the DNA in question.

3. Saunders uses a variety of machines in order to analyze the DNA.

4. Saunders would be unable to identify the DNA without the thermocycler.

19.

1. NO CHANGE

2. absolutely the final sample

3. the final sample

4. the most final sample

20.Where should sentence 1 be placed to make the paragraph feel cohesive?

1. Where it is now

2. After sentence 2

3. After sentence 3

4. After sentence 4

21.

1. NO CHANGE

2. eager

3. impatient

4. conditioned

22.At this point, the writer wants to add a conclusion that best reflects Jane's feelings conveyed in the passage. Which choice accomplishes that?

1. NO CHANGE

2. It takes a good deal of work and expense to identify DNA in the world of modern forensics.

3. She takes pride in the fact that her scientific expertise plays such a key role in bringing criminals to justice.

4. She marvels at how far science has come in DNA analysis.

3.

22. Questions 23—33 are based on the following passage.

23. Will Your Start-Up Succeed?

According to research from Harvard Business School, the majority of small businesses fail in fact the success rate for a first-time company owner is a meager 18 percent. With odds so dismal, why would anyone become a business entrepreneur?

Many people desire the freedom of being their own boss, but to be successful, an entrepreneur must also be productive, persistent, and creative. Veteran entrepreneurs achieve a higher 30 percent success rate, so the most predictive factor for success appears to be the number of innovations that a person has “pushed out.” More specifically, the people who succeed at building a robust start-up are the ones who have previously tried. Finally, many entrepreneurs grab the idea for their business by solving practical problems, and it’s more than luck; 320 new entrepreneurs out of 100,000 do succeed by starting a company at the right time in the right industry.

Mitch Gomez is evidence of this data. He did graduate from college with a degree in accounting. “I quickly realized that I have too big of a personality to be content practicing accounting,” he laughs. He first built a successful insurance claims service, and next founded his own independent insurance agency. “I continually employ my accounting skills, but I’ve ascertained that I’m an even more effective salesperson.”

Similarly, Barbara Vital, the woman behind Vital Studio, explains, “I love spending as much time with my family as possible.” Vital saw an opportunity to launch a monogramming business when her two young sons started school, so she founded a company that offers monogrammed backpacks and water bottles for kids, as well as totes, rain boots; and baseball caps for college students. What is the secret to Vital’s success? “I’m always learning how to incorporate social media and add functionality to my product website to keep customers happy,” she says.

Finally, Chris Roth is an entrepreneur who can step out of his comfort zone. Always seeking a new challenge his company designed and manufactured technology to keep the nozzles of water misting systems clean. Roth has also established a corporate travel agency and a truck customization company, most recently claiming he has become an innovator who beat the odds by “striving to serve customers better than my competition.” Large companies often employ corporate travel agencies to arrange travel for their employees and clients.

Gomez, Vital, and Roth agrees that although being an entrepreneur can be a formidable challenge, exceptionally skillful entrepreneurs have important strategies for success, including stretching his personal boundaries and recovering from failures. “And nothing beats being your own boss,” adds Gomez.

23.

1. NO CHANGE

2. fail, in fact,

3. fail; in fact,

4. fail: in fact

24.Which sentence most effectively establishes the central idea?

1. NO CHANGE

2. The Small Business Administration defines a small business as one with fewer than 500 employees and less than $7 million in sales annually.

3. Many small businesses fail because company founders are not realistic about the amount of time it takes for a company to become profitable.

4. Running a small business can take up a lot more time than punching a clock for someone else and might not be enjoyable for everyone.

25.

1. NO CHANGE

2. derive

3. achieve

4. grasp

26.

1. NO CHANGE

2. has graduated

3. graduated

4. would have graduated

27.

1. NO CHANGE

2. service. And next

3. service and next

4. service; and next

28.

1. NO CHANGE

2. present

3. propel

4. impact

29.

1. NO CHANGE

2. totes; rain boots; and

3. totes, rain boots, and,

4. totes, rain boots, and

30.

1. NO CHANGE

2. challenge: his company

3. challenge; his company

4. challenge, his company

31.Which sentence would best support the central idea?

1. NO CHANGE

2. Savvy entrepreneurs know which risks are worth taking and which risks can tank their business before their doors open.

3. Now Roth’s small business installs water misters on restaurant patios and even sets up misting stations at outdoor music festivals.

4. Many new small businesses fail because company founders fail to do market research and identify the needs of their community.

32.

1. NO CHANGE

2. agree

3. should agree

4. had agreed

33.

1. NO CHANGE

2. their

3. our

4. her

4.

33. Questions 34—44 are based on the following passage and supplementary material.

34. Edgard Varèse’s Influence

Today’s music, from rock to jazz, has many influences. And perhaps none is as unique as the ideas from French composer Edgard Varèse. Called “the father of electronic music,” he approached compositions from a different theoretical perspective than classical composers such as Bartók and Debussy. He called his works “organized sound”; they did not endear melodies but waged assaults of percussion, piano, and human voices. He thought of sounds as having intelligence and treated music spatially, as “sound objects floating in space.”

His unique vision can be credited to his education in science. Born in 1883 in France, Varèse was raised by a great-uncle and grandfather in the Burgundy region. He was interested in classical music and composed his first opera as a teenager. While the family lived in Italy he studied engineering in Turin, where he learned math and science and was inspired by the work of the artist Leonardo da Vinci.

In 1903, he returned to France to study music at the Paris Conservatory. There, he composed the radical percussion performance piece Ionisation, which featured cymbals, snares, bass drum, xylophone, and sirens wailing. Later compositions were scored for the theremin, a new electronic instrument controlled by the player’s hands waving over its antennae, which sense their position. No composer had ever scored any music for the theremin before.

In his thirties, Varèse moved to New York City, where he played piano in a café and conducted other composers’ works until his own compositions gained success. His piece Amériques was performed in Philadelphia in 1926. Varèse went on to travel to the western United States, where he recorded, lectured, and collaborated with other musicians. By the 1950s, he was using tape recordings in contention with symphonic performance. His piece Déserts was aired on a radio program amid selections by Mozart and Tchaikovsky but was received by listeners with hostility.

Varèse’s ideas were more forward-thinking than could be realized. One of his most ambitious scores, called Espace, was a choral symphony with multilingual lyrics, which was to be sung simultaneously by choirs in Paris, Moscow, Peking, and New York. He wanted the timing to be orchestrated by radio, but radio technology did not support worldwide transmission. If only Varèse had had the Internet!

Although many of their written compositions were lost in a fire in 1918, many modern musicians and composers have been influenced by Varèse, including Frank Zappa, John Luther Adams, and John Cage, who wrote that Varèse is “more relevant to present musical necessity than even the Viennese masters.”Despite being less famous than Stravinsky or Shostakovich, his impact is undeniable. Varèse’s love of science and mathematics is shown in his later compositions, but less so in his early works.

Composer

Number of Surviving Works

Edgard Varèse

14

Benjamin Britten

84

Charles Ives

106

Igor Stravinsky

129

Arnold Schoenberg

290

Dmitri Shostakovich

320

34.

1. NO CHANGE

2. influences, and perhaps none is as

3. influences, but perhaps none is as

4. influences. Or perhaps none is as

35.

1. NO CHANGE

2. works “organized sound”: They

3. works “organized sound”, they

4. works—“organized sound”—they

36.

1. NO CHANGE

2. amplify

3. deprive

4. employ

37.

1. NO CHANGE

2. in Italy, he studied engineering in Turin, where he

3. in Italy he studied engineering in Turin where he

4. in Italy, he studied engineering in Turin; where he

38.

1. NO CHANGE

2. the players’ hands

3. the players hands

4. the player’s hands’

39.

1. NO CHANGE

2. conjunction

3. appropriation

4. supplication

40.If added to the paragraph, which fact would best support the author’s claims?

1. The critical response to his 1926 performance in Philadelphia

2. The selections by Mozart and Tchaikovsky that were played on the radio

3. Which specific states he traveled to in the western United States

4. The cities in which the radio program was aired

41.

1. NO CHANGE

2. would have had

3. would have

4. have had

42.

1. NO CHANGE

2. its

3. our

4. his

43.Which choice most accurately and effectively represents the information in the graph?

1. NO CHANGE

2. Despite having fewer surviving works than his contemporaries, his impact is undeniable.

3. Even though he wrote pieces using a wider range of instruments than other composers, his impact is undeniable.

4. Even though far fewer of his works are now performed compared with those of his contemporaries, his impact is undeniable.

44.Which sentence best summarizes the central idea?

1. NO CHANGE

2. In contrast with his newfound popularity, Varèse’s early works have long been ignored due to increasing critical hostility.

3. Varèse and his innovative compositions became an inspiration for artists seeking to challenge traditional musical beliefs.

4. Though Varèse’s contemporary critics failed to call him a “Viennese master,” this distinction is changing.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

PSAT PRACTICE TEST 1

Math Test

25 Minutes 17 Questions

1.

1. NO-CALCULATOR SECTION

This section corresponds to Section 3 of your answer sheet.

Directions

For this section, solve each question and select the best answer choice. The available space on each page may be used for scratch work.

Notes:

1. Calculator use is NOT permitted.

2. All numbers used are real numbers, and all variables used represent real numbers, unless otherwise indicated.

3. Figures are drawn to scale and lie in a plane unless otherwise indicated.

4. Unless stated otherwise, the domain of any function f is assumed to be the set of all real numbers x, for which f(x) is a real number.

Information:

image

§ The sum of the degree measures of the angles in a triangle is 180.

§ The number of degrees of arc in a circle is 360.

§ The number of radians of arc in a circle is 2π.

1.

In the equation above, what is the value of n ?

1.

2.

3. There is no value of n that satisfies the equation.

4. There are infinitely many values of n that satisfy the equation.

2.

Which of the following is equivalent to the expression above?

1.

2.

3.

4.

3. image

The figure above shows the graph of f(x). For which value(s) of x does f(x) equal 0 ?

1. —3 and 3

2. —1 and 1

3. —1, 1, and 2

4. 2 only

4. Which of the following systems of inequalities has no solution?

1.

2.

3.

4.

5. At what value(s) of x do the graphs of y = −2x + 1 and y = 2x 2 + 5x + 4 intersect?

1.

2.

3.

4.

6. image

If line P shown in the graph is reflected over the x-axis and shifted up 3 units, what is the new y-intercept?

1. (0, —4)

2. (0, —2)

3. (0, 2)

4. (0, 4)

7. Which of the following are roots of the equation 3x 2 — 6x — 5 = 0 ?

1.

2.

3.

4.

8. If , where both m > 0 and n > 0, which of the following gives n in terms of m ?

1.

2.

3.

4.

9.

If (x, y) represents the solution to the system of equations shown above, what is the value of y ?

1. 10

2. 19

3. 29

4. 31

10.If , which of the following is not a possible value of d ?

1.

2.

3.

4.

11.Mae-Ling made 15 shots during a basketball game. Some were 3-pointers and others were worth 2 points each. If s shots were 3-pointers, which expression represents her total score?

1. 3s

2. s + 30

3. 3s + 2

4. 5s + 30

12.If , what is the value of 6x − 5y ?

1. 32

2. 80

3. 96

4. 160

13.If f(g(2)) = −1 and f(x) = x + 1, then which of the following could define g(x) ?

1. g(x) = x — 6

2. g(x) = x — 4

3. g(x) = x — 2

4. g(x) = x — 1

1. Directions

For questions 14—17, enter your responses into the appropriate grid on your answer sheet, in accordance with the following:

1. You will receive credit only if the circles are filled in correctly, but you may write your answers in the boxes above each grid to help you fill in the circles accurately.

2. Don’t mark more than one circle per column.

3. None of the questions with grid-in responses will have a negative solution.

4. Only grid in a single answer, even if there is more than one correct answer to a given question.

5. A mixed number must be gridded as a decimal or an improper fraction. For example, you would grid as 7.5 or .

(Were you to grid it as , this response would be read as .)

6. A decimal that has more digits than there are places on the grid may be either rounded or truncated, but every column in the grid must be filled in order to receive credit.

image

14.k(10x — 5) = 2(3 + x) — 7

If the equation above has infinitely many solutions and k is a constant, what is the value of k ?

15.A right triangle has leg lengths of 18 and 24 and a hypotenuse of 15n. What is the value of n ?

16.

If the expression above is combined into a single power of x with a positive exponent, what is that exponent?

17.image

If the equation of the parabola shown in the graph is written in standard quadratic form, y = ax2 + bx + c, and a = −1, then what is the value of b?

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

PSAT PRACTICE TEST 1

Math Test

45 Minutes 31 Questions

1.

1. CALCULATOR SECTION

This section corresponds to Section 4 of your answer sheet.

Directions

For this section, solve each question and select the best answer choice. The available space on each page may be used for scratch work.

Notes:

1. Calculator use is permitted.

2. All numbers used are real numbers, and all variables used represent real numbers, unless otherwise indicated.

3. Figures are drawn to scale and lie in a plane unless otherwise indicated.

4. Unless stated otherwise, the domain of any function f is assumed to be the set of all real numbers x, for which f(x) is a real number.

Information:

image

§ The sum of the degree measures of the angles in a triangle is 180.

§ The number of degrees of arc in a circle is 360.

§ The number of radians of arc in a circle is 2π.

1. image

The scatterplot above shows data collected from 10 major league baseball players comparing the average weekly time each one spent in batting practice and the number of home runs he hit in a single season. The line of best fit for the data is also shown. What does the slope of the line represent in this context?

1. The estimated time spent in batting practice by a player who hits 0 home runs

2. The estimated number of single-season home runs hit by a player who spends 0 hours in batting practice

3. The estimated increase in time that a player spends in batting practice for each home run that he hits in a single season

4. The estimated increase in the number of single-season home runs hit by a player for each hour he spends in batting practice

2. image

Where will the line shown in the graph above intersect the x-axis?

1. —5.5

2. —5

3. —4.5

4. —4

3. The function f(x) is defined as f(x) = −3g(x), where g(x) = x + 2. What is the value of f(5) ?

1. —21

2. —1

3. 4

4. 7

4. image

The graph above shows the average cost of back surgery followed by a hospital stay in the United States. The hospital charges for the surgery itself plus all the costs associated with recovery care for each night the patient remains in the hospital. Based on the graph, what is the average cost per night spent in the hospital?

1. $2,600

2. $4,000

3. $6,600

4. $8,000

5. image

The figure above represents a click-through rate curve, which shows the relationship between a search result position in a list of Internet search results and the number of people who clicked on advertisements on that result’s page. Which of the following regression types would be the best model for this data?

1. A linear function

2. A quadratic function

3. A polynomial function

4. An exponential function

6. Kudzu is a vine-like plant that grows indigenously in Asia. It was brought over to the United States in the early 20th century to help combat soil erosion. As can often happen when foreign species are introduced into a non-native habitat, kudzu growth exploded and it became invasive. In one area of Virginia, kudzu covered approximately 3,200 acres of a farmer’s cropland, so he tried a new herbicide. After two weeks of use, 2,800 acres of the farmer’s cropland were free of the kudzu. Based on these results, and assuming the same general conditions, how many of the 30,000 acres of kudzu-infested cropland in that region would still be covered if all the farmers in the entire region had used the herbicide?

1. 3,750

2. 4,000

3. 26,000

4. 26,250

7.

x

—2

—1

0

1

2

3

g(x)

5

3

1

—1

—3

—5

h(x)

—3

—2

—1

0

1

2

8. Several values for the functions g(x) and h(x) are shown in the table. What is the value of g(h(3)) ?

1. —5

2. —3

3. —1

4. 2

8. A business’s “break-even point” is the point at which revenue (sales) equals expenses. When a company breaks even, no profit is being made, but the company is not losing any money either. Suppose a manufacturer buys materials for producing a particular item at a cost of $4.85 per unit and has fixed monthly expenses of $11,625 related to this item. The manufacturer sells this particular item to several retailers for $9.50 per unit. How many units must the manufacturer sell per month to reach the break-even point for this item?

1. 810

2. 1,225

3. 2,100

4. 2,500

9. Crude oil is sold by the barrel, which refers to both the physical container and a unit of measure, abbreviated as bbl. One barrel holds 42 gallons and, consequently, 1 bbl = 42 gallons. An oil company is filling an order for 2,500 barrels. The machine the company uses to fill the barrels pumps at a rate of 37.5 gallons per minute. If the oil company has 8 machines working simultaneously, how long will it take to fill all the barrels in the order?

1. 5 hours and 50 minutes

2. 12 hours and 45 minutes

3. 28 hours and 30 minutes

4. 46 hours and 40 minutes

10.


Jan

Feb

Mar

April

Company A

54

146

238

330

Company B

15

30

60

120

12.Company A and Company B are selling two similar toys. The sales figures for each toy are recorded in the table above. The marketing department at Company A predicts that its monthly sales for this particular toy will continue to be higher than Company B’s through the end of the year. Based on the data in the table, and assuming that each company sustains the pattern of growth the data suggests, which company will sell more of this toy in December of that year and how much more?

1. Company A; 182

2. Company A; 978

3. Company B; 29,654

4. Company B; 60,282

11.image

Which symbol correctly completes the inequality whose solution is shown above?

1. <

2. >

3. ≤

4. ≥

1. Questions 12 and 13 refer to the following information.

2. A student is drawing the human skeleton to scale for a school assignment. The assignment permits the student to omit all bones under a certain size because they would be too small to draw. The longest bone in the human body is the femur, or thighbone, with an average length of 19.9 inches. The tenth longest bone is the sternum, or breastbone, with an average length of 6.7 inches.

12.If the scale factor of the drawing is one-eighth, about how long in inches should the student draw the femur?

1. 2

2. 2.5

3. 2.8

4. 3

13.The student draws the femur, but then realizes she drew it too long, at 3.5 inches. She doesn’t want to erase and start over, so she decides she will adjust the scale factor to match her current drawing instead. Based on the new scale factor, about how long in inches should she draw the sternum?

1. 0.8

2. 1

3. 1.2

4. 1.5

14.If a line that passes through the ordered pairs (4 — c, 2c) and (—c, —8) has a slope of , what is the value of c ?

1. —5

2. —3

3. —2

4. 2

15.

From

Distance to LHR

DCA

3,718

MIA

4,470

16.Two airplanes departed from different airports at 5:30 AM, both traveling nonstop to London Heathrow Airport (LHR). The distances the planes traveled are recorded in the table. The Washington, D.C. (DCA) flight flew through moderate cloud cover and as a result only averaged 338 mph. The flight from Miami (MIA) had good weather conditions for the first two-thirds of the trip and averaged 596 mph, but then encountered some turbulence and only averaged 447 mph for the last part of the trip. Which plane arrived first and how long was it at the London airport before the other plane arrived?

1. MIA; 2 hours, 40 minutes

2. MIA; 3 hours, 30 minutes

3. DCA; 1 hour, 20 minutes

4. DCA; 3 hours, 40 minutes

16.Which of the following quadratic equations has no solution?

1. 0 = −3(x + 1)(x — 8)

2. 0 = 3(x + 1)(x — 8)

3. 0 = −3(x + 1)2 + 8

4. 0 = 3(x + 1)2 + 8

17.image

A student looked at the graph above and determined based on the data that spending more money per student causes the gross domestic product (GDP) to increase. Which of the following statements is true?

1. The student is correct; the data shows that increased spending on students causes an increase in the GDP.

2. The student is incorrect; the data shows that having a higher GDP causes an increase in the amount of money a country spends on students.

3. The student is incorrect; there is no correlation and, therefore, no causation between GDP and expenditures on students.

4. The student is incorrect; the two variables are correlated, but changes in one do not necessarily cause changes in the other.

18.In chemistry, the combined gas law formula gives the relationship between the volumes, temperatures, and pressures for two fixed amounts of gas. Which of the following gives p2 in terms of the other variables?

1.

2.

3.

4.

19.An object’s weight is dependent upon the gravitational force being exerted upon the object. If 1 pound on Earth is equal to 0.377 pounds on Mars and 2.364 pounds on Jupiter, and 1 ton is equal to 2,000 pounds, how many more pounds does an object weighing 1.5 tons on Earth weigh on Jupiter than on Mars?

1. 1,131

2. 4,092

3. 5,961

4. 7,092

20.image

When a drug company wants to introduce a new drug, it must subject the drug to rigorous testing. The final stage of this testing is human clinical trials, in which progressively larger groups of volunteers are given the drug and carefully monitored. One aspect of this monitoring is keeping track of the frequency and severity of side effects. The figure above shows the results for the side effect of headaches for a certain drug. According to the trial guidelines, all moderate and severe headaches are considered to be adverse reactions. Which of the following best describes the data?

1. The data is symmetric with over 50% of participants having adverse reactions.

2. The data is skewed to the right with over 50% of participants having adverse reactions.

3. The data is skewed to the right with over 75% of participants failing to have adverse reactions.

4. The data is skewed to the right with approximately 50% of participants having no reaction at all.

21.In the legal field, “reciprocity” means that an attorney can take and pass a bar exam in one state and be allowed to practice law in a different state that permits such reciprocity. Each state bar association decides with which other states it will allow reciprocity. For example, Pennsylvania allows reciprocity with the District of Columbia. It costs $25 less than 3 times as much to take the bar in Pennsylvania than in D.C. If both bar exams together cost $775, how much less expensive is it to take the bar exam in D.C. than in Pennsylvania?

1. $200

2. $275

3. $375

4. $575

22.

Mr. Juno took his driver’s education class to the Department of Motor Vehicles to take their driver’s license test. The number of questions missed by each student in the class is recorded in the bar graph above. Which of the following statements is true?

1. More than half of the students missed 5 or more questions.

2. The mean number of questions missed was between 4 and 5.

3. More students missed 3 questions than any other number of questions.

4. Thirty-six students from Mr. Juno’s class took the driver’s license test that day.

23.If the graph of the equation y = ax 2 + bx + c passes through the points (0, 2), (—6, —7), and (8, —14), what is the value of a + b + c ?

1. —19

2. —2

3. 1.75

4. 2.25

24.A bakery sells three sizes of muffins—mini, regular, and jumbo. The baker plans daily muffin counts based on the size of his pans and how they fit in the oven, which results in the following ratios: mini to regular equals 5 to 2, and regular to jumbo equals 5 to 4. When the bakery caters events, it usually offers only the regular size, but it recently decided to offer a mix of mini and jumbo instead of regular. If the baker wants to keep the sizes in the same ratio as his daily counts, what ratio of mini to jumbo should he use?

1. 1:1

2. 4:2

3. 5:2

4. 25:8

25.

If the system of linear equations shown above has no solution, and k is a constant, what is the value of k ?

1.

2.

3.

4. 3

26.What is the value of ?

1. 9 60

2. 9 120

3. 9 150

4. 9 210

27.If a right cone is three times as wide at its base as it is tall, and the volume of the cone is 384π cubic inches, what is the diameter in inches of the base of the cone?

1. 8

2. 12

3. 16

4. 24

1. Directions

For questions 28—31, enter your responses into the appropriate grid on your answer sheet, in accordance with the following:

1. You will receive credit only if the circles are filled in correctly, but you may write your answers in the boxes above each grid to help you fill in the circles accurately.

2. Don’t mark more than one circle per column.

3. None of the questions with grid-in responses will have a negative solution.

4. Only grid in a single answer, even if there is more than one correct answer to a given question.

5. A mixed number must be gridded as a decimal or an improper fraction. For example, you would grid as 7.5 or .

(Were you to grid it as , this response would be read as .)

6. A decimal that has more digits than there are places on the grid may be either rounded or truncated, but every column in the grid must be filled in order to receive credit.

image

28.

Nine data points were used to generate the scatterplot shown above. Assuming all whole number values for the data points, what is the maximum value in the range of the data?

29.If Ax + By = C is the standard form of the line that passes through the points (—4, 1) and (3, —2), where A is an integer greater than 1, what is the value of B ?

1. Questions 30 and 31 refer to the following information.

2. The Great Depression began in 1929 and lasted until 1939. It was a period of extreme poverty, marked by low prices and high unemployment. The main catalytic event to the Great Depression was the Wall Street Crash (stock market crash). The Dow, which measures the health of the stock market, started Black Thursday (October 24, 1929) at approximately 306 points.

30.The stock market had been in steady decline since its record high the month before. If the market had declined by 19.5% between its record high and opening on Black Thursday, what was the approximate value of the Dow at its record high? Round your answer to the nearest whole point.

31.By the end of business on Black Thursday, the Dow had dropped by 2%. Over the course of Friday and the half-day Saturday session, there was no significant change. Unfortunately, the market lost 13% on Black Monday, followed by another 12% on Black Tuesday. What was the total percent decrease from opening on Black Thursday to closing on Black Tuesday? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

PSAT PRACTICE TEST

Answer key

READING TEST

1. B

2. C

3. D

4. B

5. A

6. C

7. D

8. C

9. A

10.A

11.A

12.C

13.A

14.B

15.B

16.C

17.D

18.D

19.B

20.C

21.D

22.B

23.D

24.B

25.A

26.A

27.C

28.D

29.C

30.B

31.D

32.D

33.A

34.C

35.B

36.B

37.C

38.D

39.C

40.D

41.A

42.C

43.A

44.B

45.D

46.B

47.D

PSAT PRACTICE TEST

Answer key

WRITING AND LANGUAGE TEST

1. C

2. D

3. A

4. A

5. B

6. C

7. A

8. C

9. A

10.C

11.B

12.B

13.A

14.B

15.B

16.D

17.C

18.A

19.C

20.A

21.B

22.C

23.C

24.A

25.B

26.C

27.C

28.A

29.D

30.D

31.C

32.B

33.B

34.C

35.A

36.D

37.B

38.A

39.B

40.A

41.A

42.D

43.B

44.C

PSAT PRACTICE TEST

Answer key

MATH TEST: NO-CALCULATOR

1. A

2. C

3. B

4. C

5. B

6. D

7. D

8. A

9. C

10.A

11.B

12.D

13.B

14.1/5 or .2

15.2

16.3

17.6

PSAT PRACTICE TEST

Answer key

MATH TEST: CALCULATOR

1. D

2. B

3. A

4. B

5. D

6. A

7. B

8. D

9. A

10.C

11.A

12.B

13.C

14.B

15.A

16.D

17.D

18.C

19.C

20.C

21.C

22.B

23.C

24.D

25.A

26.D

27.D

28.85

29.7

30.380

31.25

PSAT PRACTICE TEST 1

Answers and explanations

READING TEST

1. Great Expectations

Suggested Passage Map notes:

o ¶1: Pip eating paltry breakfast, Mr. P making him do math while he eats, Pip does not like Mr. P

o ¶2: Pip visiting Miss H, Miss H’s house in disrepair

o ¶3-9: lady let’s in Pip, makes Mr. P go away

o ¶10: Pip happy to be rid of Mr. P for now

1. B/Difficulty: Easy

Category: Detail

Getting to the Answer: Examine the description of breakfast in the first paragraph before choosing the correct answer. In lines 8-9, Pip uses “crumb” and “little butter” to describe what he ate, and he also says in line 10 that “a quantity of warm water” had been added to his milk. Therefore, it’s clear that Pip’s breakfast with Mr. Pumblechook is (B), “small and of poor quality.”

2. C/Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Eliminate answer choices that might be synonyms of “wretched” but don’t make sense in the context of the passage. When Pip describes Mr. Pumblechook’s company to be “wretched,” he means “distressing,” or causing misery. Choice (C) is the correct answer.

3. D/Difficulty: Medium

Category: Inference

Getting to the Answer: Review the passage for details that reveal Mr. Pumblechook’s attitude. By his actions, you can infer that Mr. Pumblechook is indifferent to Pip’s discomfort. Choice (D) is the correct answer.

4. B/Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Find each answer choice in the passage. Think about your answer for the previous question, and determine which lines provide the strongest support for that answer. In the first paragraph, Pip describes how Mr. Pumblechook offers him a meager breakfast and quizzes him on arithmetic during their meal rather than making conversation. Choice (B) is the correct answer.

5. A/Difficulty: Hard

Category: Global

Getting to the Answer: Study the answer choices. Eliminate any that go too far in their interpretation of characters and events in the passage. Though B seems to reflect what might be true of Pip and Mr. Pumblechook’s relationship, and one might believe that C and D are true, the correct answer is (A). This theme most clearly reflects the message conveyed through Pip’s experiences in this passage.

6. C/Difficulty: Medium

Category: Inference

Getting to the Answer: Think about details in the passage that relate to the characters’ relationships. What do they reveal about how Pip probably feels at the end of the passage? It is reasonable to infer that Pip is relieved when he is no longer in Mr. Pumblechook’s company. Therefore, (C) is the correct answer.

7. D/Difficulty: Hard

Category: Command of Evidence

Getting to the Answer: Locate each answer in the passage, and decide which one provides the best support for the answer to the previous question. At the end of the passage, Pip “was not free from apprehension” (line 64) that Mr. Pumblechook would return but then tells the reader that no return took place. Choice (D) best supports the idea that Pip is relieved to be away from Mr. Pumblechook.

8. C/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Substitute each answer choice for “condition.” The correct answer will not change the meaning of the sentence. Choice (C) is the correct answer. The narrator says that Mr. Pumblechook is “in a condition of ruffled dignity” (line 59). In this context, “state” means the same as “condition.”

9. A/Difficulty: Medium

Category: Rhetoric

Getting to the Answer: Think of what the parenthetical comment by Pip tells you about his personality. In a sense, Pip is apologizing for what he is about to say of Mr. Pumblechook. The parenthetical comment reveals that Pip is usually more polite in his references to others. Choice (A) is the correct answer.

10.“Letter from Birmingham Jail”

Suggested Passage Map notes:

o ¶1: MLK states why he is in Birmingham, history of SCLC, in Birmingham due to injustice

o ¶2: MLK cannot let injustice continue, we are one people

o ¶3: MLK explains why peaceful protests are needed, benefits of tension to open negotiations

o ¶4: nonviolent pressure only way to enact change

o ¶5: justice must be demanded by the oppressed

10.A/Difficulty: Medium

Category: Rhetoric

Getting to the Answer: Avoid answer choices that deal with related issues but do not address the main purpose of the letter. The passage as a whole addresses why King came to Birmingham, and then builds on his explanation for being in Birmingham to explore his cause. Choice (A) is correct.

11.A/Difficulty: Easy

Category: Command of Evidence

Getting to the Answer: Choose the answer that relates directly to the purpose you identified in the previous question. King begins the letter by stating, “I think I should give the reason for my being in Birmingham,” which clearly explains his purpose for writing the letter from the jail. Choice (A) is correct.

12.C/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Read the complete sentence and the surrounding paragraph to best understand the meaning of the phrase within its greater context. In the paragraph, King goes on to explain that events in Birmingham must necessarily concern him. He states that an injustice in one place threatens justice everywhere, and even writes, “Whatever affects one directly affects all indirectly” (lines 27-28). This suggests that events in Birmingham affect people throughout the nation. Choice (C) is correct, as it explains that the “interrelatedness of all communities and states” refers to the idea that events in one part of the country affect the entire nation.

13.A/Difficulty: Easy

Category: Inference

Getting to the Answer: Predict King’s opinions before reviewing the answer choices. The correct answer can be inferred directly from King’s views as expressed in the paragraph. In this paragraph, King refers specifically to injustice and how it affects people everywhere. From this, you can most clearly infer that King considered circumstances in Birmingham to be unfair and wrong. Choice (A) is correct.

14.B/Difficulty: Easy

Category: Command of Evidence

Getting to the Answer: Review the answer to the previous question. Read the answer choices to identify the one whose rhetoric provides clear support for the inference. Although the entire paragraph provides general support and context for the inference, only (B) suggests that circumstances in Birmingham were unjust, that is, unfair and wrong.

15.B/Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Before viewing the answer choices, think about the purpose of the word in the sentence, and form an alternate explanation of the word. Then identify the answer choice that best reflects that meaning and intent. King says that direct action in Birmingham aims to “dramatize the issue that it can no longer be ignored.” This suggests that the issue, or events, in Birmingham are of great significance and demand attention that they have not received. Therefore, (B) is correct.

16.C/Difficulty: Hard

Category: Rhetoric

Getting to the Answer: Consider the overall thrust of King’s argument in this paragraph. Choose the answer that encapsulates this idea. In paragraph 3, King responds to charges that activists should focus on negotiation, not direct action. He argues that direct action is needed to spur negotiations. King reasons that nonviolent protests create the tension between forces in society needed to bring people to the table to discuss the relevant issues of prejudice and racism. His claim in the paragraph is that direct action is needed to spur negotiation, making choice (C) correct.

17.D/Difficulty: Hard

Category: Rhetoric

Getting to the Answer: Identify an idea in paragraph 4 that provides clear support to the claim made in the previous paragraph. In paragraph 3, King claims that nonviolent direct action is needed to prompt negotiations on civil rights. In paragraph 4, he supports that argument by explaining that no gains have been made in civil rights without such nonviolent action, as choice (D) states.

18.D/Difficulty: Medium

Category: Rhetoric

Getting to the Answer: Read the complete paragraph to best understand the context and purpose of the cited line. The correct answer will identify what the phrase helps achieve in the paragraph. At the start of the paragraph, King argues that oppressors do not willingly give more freedom to the people whom they oppress. He goes on to explain the delay tactics that have kept African Americans from winning equal rights, and concludes that oppressed peoples in other nations are winning independence while ­African Americans still cannot get a cup of coffee at a lunch counter. The phrase helps King underscore the contrast between these two scenarios, so (D) is the correct answer.

19.Paired Passages—Bretton Woods

Suggested Passage Map notes:

Passage 1

o ¶1: background of Bretton Woods

o ¶2: created IMF to facilitate international trade

o ¶3: created World Bank to give loans to war affected countries, bridge rich and poor countries

o ¶4: BW made U.S. dollar global currency

o ¶5: shaped foreign trade

o ¶6: BW made U.S. powerful

Passage 2

o ¶1: BW only lasted 3 decades, Nixon changed economic policy

o ¶2: BW collapsed, IMF began flexible exchange system for currency

o ¶3: U.S. dollar still widely used

o ¶4: G20 wants to create global currency

o ¶5-6: predicts worldwide currency, new world order in finance coming

19.B/Difficulty: Medium

Category: Reading / Inference

Getting to the Answer: Remember that you are being asked to choose an inference suggested by Passage 1, not a statement of fact. The passage notes that the U.S. dollar became a global currency that nations around the world accept for trade, leaving the United States in a stronger position to influence international markets. Choice (B) is the correct answer.

20.C/Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: The correct choice should support your answer to the previous question. Consider which choice best shows a clear relationship with your answer to the item above. Choice (C) explicitly states the United States became the “primary power” behind the institutions established at Bretton Woods.

21.D/Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Predict an answer based on the context of the passage. The correct answer should not alter the meaning of the sentence in the passage. Then choose the option that best fits your prediction. The passage states that the IMF gives loans to member countries to ensure their continued stability. Choice (D) is correct because it most closely reflects the IMF’s goals of proactively promoting global economic growth and stability.

22.B/Difficulty: Medium

Category: Connections

Getting to the Answer: Locate information in the passage that accurately summarizes the purposes of both institutions. Then ask yourself how these purposes differ. Both institutions encourage economic growth. However, Passage 1 notes that the IMF maintains payments and receipts between nations. The World Bank, on the other hand, focuses on “economic and social progress” (line 33) in individual countries. Choice (B) is the correct answer.

23.D/Difficulty: Hard

Category: Inference

Getting to the Answer: Eliminate any answer choices that are not suggested in the passage. Choice (D) is correct. The paragraph states that President Nixon’s decision broke with the Bretton Woods framework. It can be reasonably inferred that the decision differed from the consensus of other nations, given the fact that many nations had agreed to Bretton Woods.

24.B/Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: The answer choice should support your answer to the previous question. The paragraph states that President Nixon’s decision “marked the end” of the Bretton Woods framework, which best supports the inference that the United States did not have the support of other nations. The correct answer is (B).

25.A/Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Reread the sentence in which the word appears and decide which meaning makes the most sense in context. The sentence is referring to a new global currency that might take the place of the U.S. dollar as the major, or key, currency. Therefore, (A) is the correct definition of “anchor” in this context.

26.A/Difficulty: Hard

Category: Synthesis

Getting to the Answer: Study the yuan’s percent share of use in daily trading relative to other currencies in the graphic over time. What does this suggest about global views of the yuan? Passage 2 explicitly states that the yuan is “becoming a major world reserve currency” (lines 92-93). This is supported by the data in the chart, which shows the yuan’s percent share of use in daily trading climbing from 0.5% in 2007 to 2.2% in 2013. Choice (A) is correct.

27.C/Difficulty: Medium

Category: Synthesis

Getting to the Answer: Identify the overall purpose of each passage. Then consider which answer choice accurately describes these purposes. Choice (C) is the correct answer. Passage 1 focuses on the effects of Bretton Woods, while Passage 2 focuses on the reasons why the international economy may transition to a new global currency.

28.D/Difficulty: Medium

Category: Synthesis

Getting to the Answer: Keep in mind that the correct answer will be a statement that is evident in both passages. The role of the IMF is mentioned prominently in both passages. Therefore, (D) is the correct answer.

29.Treatment for Paralysis Passage

Suggested Passage Map notes:

o ¶1: six million U.S. people paralyzed; causes of paralysis

o ¶2: patient in Poland became subject of study

o ¶3: spinal cord research on rats, now used to develop treatment

o ¶4: patient responded well to treatment

o ¶5: future benefits of treatment

29.C/Difficulty: Easy

Category: Global

Getting to the Answer: Keep in mind that the correct answer will be supported by all of the information in the text rather than just a few details. The passage is concerned with one experimental treatment that doctors are exploring to help paralyzed patients regain mobility. Choice (C) is the correct answer.

30.B/Difficulty: Medium

Category: Inference

Getting to the Answer: Consider the main points the author makes throughout the passage. The correct answer will be directly related to these points, even if it is not directly stated in the passage. Choice (B) is the correct answer. It can be inferred that the author feels that increased mobility will have a positive impact on patients suffering from all levels of paralysis.

31.D/Difficulty: Easy

Category: Command of Evidence

Getting to the Answer: Locate each answer choice in the passage. Decide which one provides the best support for the answer to the previous question. In the last line of the passage, the author says that paralyzed patients “can have both their mobility and their hope restored” (lines 68-69). This answer, (D), offers the strongest support for the answer to the previous question.

32.D/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: The correct answer will not only be a synonym for “restricted” but will also make sense in the context of the sentence in the passage. Eliminate answers, such as A, that are synonyms for “restricted” but do not make sense in context. Here, the author is explaining that patients in wheelchairs must learn to prevent complications from restricted movement. In this context, “restricted” most nearly means “limited,” answer choice (D).

33.A/Difficulty: Hard

Category: Rhetoric

Getting to the Answer: Locate lines 46-47 in the passage, and then read the paragraph that comes before it. This will help you identify why the author chose “tailor-made” to describe the patient’s treatment. The patient received his own cells during the treatment, meaning that the treatment was tailored to his own body. Choice (A) fits this situation and is therefore the correct answer.

34.C/Difficulty: Hard

Category: Inference

Getting to the Answer: Remember that when a question is asking you to infer something, the answer is not stated explicitly in the passage. In paragraph 2, the author explains that the patient who received the experimental treatment had not seen an increase in mobility despite “countless hours” (line 21) of physical therapy. Therefore, it is logical to infer that the patient would not have regained mobility without this experimental treatment. Choice (C) is the correct answer.

35.B/Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Think about how you selected the correct answer for the previous question. Use that information to help you choose the correct answer to this question. In paragraph 2, the author explains that the patient selected for the experimental treatment had not regained mobility despite intensive physical therapy. This provides the strongest support for the answer to the previous question, so (B) is correct.

36.B/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Substitute each of the answer choices for “refined.” Select the one that makes the most sense in context and does not change the meaning of the sentence. In this context, “refined” most nearly means “improved.” Choice (B) is the correct answer.

37.C/Difficulty: Easy

Category: Inference

Getting to the Answer: Skim the passage and look for details about how doctors came to use the treatment described. In paragraph 3, the author explains that the doctors used a technique that was developed during years of research on rats. Therefore, (C) is the correct answer.

38.D/Difficulty: Medium

Category: Connections

Getting to the Answer: Compare and contrast each answer choice with the procedure described in the passage. As in the procedure described in the passage, skin transplants for burn victims involve taking tissue containing healthy cells from one area of the body and using it to repair damage done to another area. Choice (D) is the correct answer.

39.Mercury in Fish Passage

Suggested Passage Map notes:

o ¶1: what mercury is, uses for mercury

o ¶2: causes of mercury pollution

o ¶3: water affected by mercury, issue for many organisms

o ¶4: consumption of mercury-laden seafood, risks and benefits

o ¶5: explanation of safe levels of mercury based on bodyweight and fish type

o ¶6: nutritionists’ recommendations

39.C/Difficulty: Medium

Category: Inference

Getting to the Answer: The correct answer will be directly supported by the evidence in the passage. Avoid answers like A and B that go beyond what can logically be inferred about the author. The author explains how mercury gets into the fish that humans eat and goes on to say that it is possible to eat fish that contain mercury without getting mercury poisoning. Choice (C) is the correct answer because it is directly supported by the evidence in the passage.

40.D/Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: The correct answer will provide direct support for the answer to the previous question. Avoid answers like B that include relevant details but do not provide direct support. In the last paragraph, the author says that nutritionists recommend eating low-mercury fish instead of eliminating fish altogether, adding that an awareness of the issues with mercury can help us make healthy eating choices. This statement supports the answer to the previous question, so (D) is the correct answer.

41.A/Difficulty: Easy

Category: Detail

Getting to the Answer: Review the details provided in the passage about how to determine a safe level of mercury consumption. In paragraph 5, the author explains that humans should consume less than 0.1 microgram of mercury for every kilogram of their own weight. Therefore, (A) is the correct answer.

42.C/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Eliminate answer choices that are synonyms for “concentration” but do not make sense in context. In this sentence, the author is describing the amount of mercury in the air from power plants. “Concentration” most nearly means “density” in this context, so (C) is the correct answer.

43.A/Difficulty: Medium

Category: Inference

Getting to the Answer: Eliminate any answer choices that are not directly supported by information in the passage. The passage strongly suggests that it is impossible to avoid exposure to mercury completely. Therefore, (A) is the correct answer.

44.B/Difficulty: Easy

Category: Command of Evidence

Getting to the Answer: Locate each of the answer choices in the passage. The correct answer should provide support for the answer to the previous question. In paragraph 1, the author explains that mercury can be found in many places. This supports the conclusion that it is impossible to avoid mercury completely. Choice (B) is the correct answer.

45.D/Difficulty: Hard

Category: Rhetoric

Getting to the Answer: Consider one of the central ideas of the passage. The correct answer would help provide additional support for this idea. One central idea in the passage is that people can eat fish if they know what mercury levels are safe for human consumption. The author states that scientists have determined safe mercury levels by studying at what point symptoms of mercury poisoning occur. However, the author only provides one example weight of how many micrograms of mercury a person could eat. Therefore, (D) is the correct answer.

46.B/Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Reread the sentence and replace “particulars” with each answer choice. Though the answer choices are similar in meaning to a certain degree, one of them makes the most sense when substituted for “particulars.” In this context, “particulars” most nearly means “specifics”; therefore, (B) is the correct answer.

47.D/Difficulty: Hard

Category: Synthesis

Getting to the Answer: Remember that the correct answer will be supported by information in both the passage and the graphic. Refer to the passage to draw conclusions about the information in the graphic. The passage states that it is safe to eat fish that contain mercury as long as certain guidelines are followed regarding daily consumption. The graphic shows that Alaskan ­pollock has the lowest concentration of mercury of the fish listed. Therefore, (D) is the correct answer; a person can safely eat more Alaskan pollock than black-striped bass in one day.

PSAT PRACTICE TEST 1

Answers and explanations

WRITING AND LANGUAGE TEST

The UN: Promoting World Peace

1. C/Difficulty: Medium

Category: Punctuation

Getting to the Answer: Examine the passage to determine whether the current punctuation is incorrect. Then consider which set of punctuation marks correctly emphasizes the selected part of the sentence. The dashes provide emphasis for the idea that the UN is a peacekeeping organization; the dashes help set off this part of the sentence from the remaining content. The correct answer is (C).

2. D/Difficulty: Hard

Category: Development

Getting to the Answer: Review the main points made so far. The correct answer should touch on or summarize previous ideas in the paragraph. Choice (D) is correct. This concluding sentence effectively summarizes the ideas that compose the paragraph’s main claim.

3. A/Difficulty: Medium

Category: Organization

Getting to the Answer: Read the previous paragraph and identify the word or phrase that is the best transition between the two paragraphs. The previous paragraph describes the UN today, and the paragraph beginning with the phrase in question explains the origins of the UN in the 1940s. Choice (A) indicates the correct shift in time period and provides the most effective transition between paragraphs.

4. A/Difficulty: Medium

Category: Usage

Getting to the Answer: Pay close attention to the context of the previous sentence to help you establish the correct verb tense for this particular sentence. The correct answer is (A). It uses the present tense to logically follow the previous sentence that refers to the UN in the present tense, as well.

5. B/Difficulty: Easy

Category: Punctuation

Getting to the Answer: Watch out for choices that may create a run-on sentence. The correct choice is (B), which provides a clear separation between one complete sentence and the next.

6. C/Difficulty: Easy

Category: Effective Language Use

Getting to the Answer: Substitute each choice in the complete paragraph. The correct answer will most appropriately fit within the context of the sentence and the paragraph. The correct answer is (C). The UN encourages, or promotes, environmental protection.

7. A/Difficulty: Medium

Category: Development

Getting to the Answer: The correct choice should introduce a central idea that is supported by subsequent sentences in the paragraph. The correct answer is (A). The expansion of the UN’s budget, goals, and personnel number connects to specific evidence in the rest of the paragraph.

8. C/Difficulty: Medium

Category: Quantitative

Getting to the Answer: Notice that the graphic gives specific information about the increases and decreases in the UN peacekeeping force over a period of time. Study the answer choices to find the one that best relates to the paragraph while using accurate information from the graphic. The graphic shows data through the year 2010 and does not indicate that personnel levels rose above 100,000. Choice (C) is the correct answer.

9. A/Difficulty: Medium

Category: Effective Language Use

Getting to the Answer: Watch out for unnecessarily wordy choices like B. The correct answer is (A) because it effectively communicates an idea without additional words that distract from the content.

10.C/Difficulty: Easy

Category: Effective Language Use

Getting to the Answer: Look at the context of the sentence in which the word appears as well as the paragraph itself to choose the answer that works best. Choice (C), “noteworthy,” is synonymous with “worth mentioning,” which clearly fits within the context of the paragraph and the author’s intent to highlight the accomplishments of the UN.

11.B/Difficulty: Medium

Category: Development

Getting to the Answer: Read the entire paragraph. Identify the sentence that is least relevant to the paragraph’s topic and purpose. The purpose of this paragraph is to sum up the central ideas of the passage. Choice (B) introduces a detail that, while important, does not summarize the central ideas of the passage and therefore detracts from the paragraph’s focus.

DNA Analysis in a Day

12.B/Difficulty: Easy

Category: Usage

Getting to the Answer: Read the sentence and notice that the verb in question is in a clause with intervening prepositional phrases that come between the subject and the verb. Check to see what the subject is and whether the verb agrees with the subject. The verb “match” is in a plural form, but the subject is “DNA,” not one of the other nouns in the prepositional phrases. “DNA” is singular. Choice (B) is the correct answer because it is the singular form of the verb “to match.”

13.A/Difficulty: Medium

Category: Punctuation

Getting to the Answer: Read the sentence to determine whether the two clauses separated by the semicolon are independent or not. If they are both independent, a semicolon is the appropriate punctuation. Be careful of answer choices with inappropriate transition words. A semicolon is the correct way to separate two independent but related clauses, so (A) is the correct answer.

14.B/Difficulty: Easy

Category: Punctuation

Getting to the Answer: Study the words in a series and see where a comma might need to be inserted or eliminated. Choice (B) is correct.

15.B/Difficulty: Hard

Category: Organization

Getting to the Answer: When you see an underlined transition, identify how the sentence relates to the previous one to determine what kind of transition is appropriate. Choice (B) is correct because the sentence to which the transition belongs provides more detail about a general statement that preceded it.

16.D/Difficulty: Easy

Category: Effective Language Use

Getting to the Answer: Imagine that the sentence has a blank where the word in question is. Read the entire paragraph for context and predict what word could complete the blank. Review the answer choices to find the word closest in meaning to your prediction. The paragraph later states that Jane Saunders’s goal is to separate the two strands of DNA. Only answer choice (D) has the correct connotation and fits within the context of the sentence.

17.C/Difficulty: Medium

Category: Effective Language Use

Getting to the Answer: It is important to combine sentences in order to vary sentence structures. But the correct choice should not only be the most effective way to combine the two sentences; it must also be in parallel construction with the first sentence. Watch out for choices that may have incorrect transition words as well. Choice (C) is the correct answer. It joins the sentences concisely and correctly because the verb “adding” is in parallel construction with the earlier verbs “detaching” and “transferring.” The subject in both sentences is the same, “she,” so it can be dropped when combining the two sentences.

18.A/Difficulty: Medium

Category: Development

Getting to the Answer: Read the entire paragraph and then put each answer choice at the beginning. Choose the one that makes the most sense and is further explained by subsequent details in the ­paragraph. The paragraph discusses the process of identifying DNA, which is lengthy and involves changing the temperature of the DNA several times. Choice (A) is closest to this summation of what is to follow and is the correct answer.

19.C/Difficulty: Easy

Category: Effective Language Use

Getting to the Answer: Watch out for choices that are wordy or redundant. Choice (C) is the most concise and effective way of stating the information in the passage.

20.A/Difficulty: Medium

Category: Organization

Getting to the Answer: Consider the function of this sentence. At what point in the paragraph should this function be employed? The sentence is setting the scene, so it should be placed where it is now, at the beginning of the paragraph. To place it later would make the meaning of the paragraph unclear. Choice (A) is the correct answer.

21.B/Difficulty: Easy

Category: Effective Language Use

Getting to the Answer: Think about the connotations of each answer choice, and be sure to pick the one that fits with the context of the sentence. Substitute each answer choice for the word to see which word works best. “Eager” best reflects how the detectives would be feeling while waiting for important test results. They would be eagerly anticipating this important information and would want it as quickly as possible. Choice (B) is the correct answer.

22.C/Difficulty: Hard

Category: Development

Getting to the Answer: Decide which sentence sounds like the most appropriate way to conclude the passage. The rhetorical question currently in the passage (choice A) introduces an opinion that the passage never reveals; there is no sign that Jane Saunders would feel this way. Likewise, there is no indication in the passage of how expensive modern DNA analysis is (choice B), nor that Saunders marvels about how far science has come in DNA analysis (choice D). Choice (C) is the correct answer; it presents a fairly natural way for Saunders to feel given her accomplishments for the day.

Will Your Start-Up Succeed?

23.C/Difficulty: Medium

Category: Sentence Formation

Getting to the Answer: Check to see whether there are two independent clauses within this sentence. Two independent clauses without punctuation indicate a run-on sentence. As written, this is a run-on sentence. Choice (C) is the correct answer because it separates the two complete but related thoughts with a semicolon.

24.A/Difficulty: Medium

Category: Development

Getting to the Answer: Eliminate answers that might contain details related to the central idea but do not properly express the central idea. This paragraph is mostly about the characteristics of people who are successful entrepreneurs. Choice (A) is the correct answer because it introduces the main idea by summarizing the traits people must have to achieve success as a business owner.

25.B/Difficulty: Hard

Category: Effective Language Use

Getting to the Answer: Eliminate answers such as D that mean nearly the same thing as “grab” but do not clarify the meaning of the sentence. In this context, “derive” best clarifies the meaning of the sentence, which explains how entrepreneurs get ideas for their businesses. Choice (B) is the correct answer.

26.C/Difficulty: Easy

Category: Usage

Getting to the Answer: Read the rest of the paragraph and pay attention to the verb tense used. The verbs in the rest of this paragraph are in past tense. “Graduated” is the past tense of the verb “to graduate”; therefore, (C) is the correct answer.

27.C/Difficulty: Medium

Category: Punctuation

Getting to the Answer: Examine the structure of the whole sentence. Consider whether the punctuation is correct or even necessary. The subject of this sentence is “he,” and it is followed by a compound predicate containing the verbs “built” and “founded.” When a compound predicate contains only two items, a comma should not separate either verb from the subject. No punctuation is necessary, so (C) is the correct answer.

28.A/Difficulty: Medium

Category: Effective Language Use

Getting to the Answer: Replace the underlined word with each answer choice. Consider which word makes the most sense in context and conveys the clearest meaning. The sentence discusses how Vital began her own business. In this context, “launch” conveys the most precise meaning because it connotes the start of a major endeavor. Choice (A) is the correct answer because no change is needed.

29.D/Difficulty: Easy

Category: Punctuation

Getting to the Answer: This sentence contains a list of items in a series. Think about the rules of punctuation for items in a series. Items in a series should be separated by commas, with a comma following each word except the last item in the series. The word “and” is not an item in the series and, therefore, should not be followed by a comma. Therefore, (D) is the correct answer.

30.D/Difficulty: Easy

Category: Punctuation

Getting to the Answer: Identify the main elements of this sentence, such as the subject, predicate, and any restrictive or nonrestrictive clauses. Remember that a nonrestrictive clause should be set off with a comma. The clause “always seeking a new challenge” is nonrestrictive and should be set off from the rest of the sentence with a comma. Choice (D) is the correct answer.

31.C/Difficulty: Hard

Category: Development

Getting to the Answer: Identify the central idea of the paragraph. Read each answer choice and consider which sentence could be added to the paragraph to provide support for the central idea you identified. This paragraph is mostly about Chris Roth, an entrepreneur who now has several companies. (C) is the correct answer because it provides specific details about one of the companies Roth owns.

32.B/Difficulty: Easy

Category: Usage

Getting to the Answer: Read the entire sentence. Identify the subject and determine whether it is plural or singular. Determine the correct verb tense for the sentence. The subject of this sentence is plural (Gomez, Vital, and Roth), so the verb must be plural, as well. (B) is the correct answer because “agree” is the plural present tense of the verb “to agree.”

33.B/Difficulty: Easy

Category: Usage

Getting to the Answer: Read the entire sentence and identify the antecedent for the underlined pronoun. The correct answer will be the pronoun that is in agreement with the antecedent. In this sentence, the antecedent is “entrepreneurs,” which requires a third-person plural pronoun. Therefore, (B) is the correct answer.

34.C/Difficulty: Medium

Category: Sentence Formation

Getting to the Answer: Read the two sentences connected by the underlined portion and decide which answer choice creates a grammatically correct and logical sentence. Choice (C) is correct. Using the coordinating conjunction “but” with a comma to combine the sentences shows that the second portion, which mentions Varèse as being unique, stands in contrast to the first portion, which mentions many influential artists. The other options, featuring “and” and “or,” do not show this necessary contrast.

35.A/Difficulty: Hard

Category: Punctuation

Getting to the Answer: Reread the entire sentence to assess how the punctuation in the answer choices affects how each portion of the sentence relates to one another. The correct answer is (A). The semicolon correctly links the two independent clauses that have a direct relationship with one another.

36.D/Difficulty: Medium

Category: Effective Language Use

Getting to the Answer: Read the sentence for context clues, and think about the author’s intention. Then determine which answer provides the most appropriate word choice. “Employ” is the only word that matches the meaning of the sentence, which states that Varèse did not use traditional melodies. Thus, choice (D) is correct.

37.B/Difficulty: Medium

Category: Punctuation

Getting to the Answer: Reread the sentence to determine how each portion relates to the others. Then examine how the punctuation in the answer choices affects these relationships. The portion of the sentence discussing the family’s move to Italy is an introductory element and needs a comma to offset it from the rest of the sentence. The portion discussing what Varèse learned in Turin is a parenthetical element and also requires a comma. Therefore, choice (B) is correct.

38.A/Difficulty: Medium

Category: Punctuation

Getting to the Answer: Review the sentence for context clues and to assess the subject’s ownership of the objects in the sentence. Then determine which form of the possessive noun correctly reflects this ownership. The hands in the sentence belong to a single player using a single theremin; therefore, the correct answer will use the singular possessive noun “player’s.” Choice (A) is correct.

39.B/Difficulty: Medium

Category: Effective Language Use

Getting to the Answer: Read the sentence for context clues. Decide on the answer choice that makes the sentence’s meaning precise and clear. “Conjunction” is the only word that relates to two things occurring at the same time to create a single outcome, which is the intended meaning of the sentence. Choice (B) is correct.

40.A/Difficulty: Hard

Category: Development

Getting to the Answer: Assess the central idea of the introductory sentence in the paragraph, and determine which additional fact noted in the answer choices would have the greatest benefit to the reader. The introductory sentence states that Varèse worked in New York until he secured his first success. Describing the critical reaction to the next event mentioned would help strengthen the idea that the Philadelphia performance was a successful event in Varèse’s career. Choice (A) is the correct answer.

41.A/Difficulty: Hard

Category: Usage

Getting to the Answer: Consider what kind of situation the author is presenting here, and decide which tense of the verb “has” creates a grammatically correct sentence that reflects this meaning. Keep in mind the time of the events in the sentence. The sentence imagines a situation in which Varèse had been able to use the Internet, an unrealistic action. The double “had had” is correct; it describes past-tense actions that might have occurred in the past but didn’t. Choice (A) is correct.

42.D/Difficulty: Easy

Category: Usage

Getting to the Answer: Read the entire sentence to figure out who is the owner of the burned compositions. Then select the proper personal pronoun for this antecedent. Choice (D) is the correct singular possessive pronoun because the burned compositions belonged to Varèse, one person, and not a group of artists.

43.B/Difficulty: Medium

Category: Quantitative

Getting to the Answer: Study the information in the graphic to determine which answer choice most accurately finishes the sentence. Choice (B) is correct because it accurately reflects information included in the graphic.

44.C/Difficulty: Medium

Category: Development

Getting to the Answer: After reading the final paragraph, examine each answer choice to determine which best summarizes the paragraph’s overall message. Choice (C) is correct. It is the one sentence that sets up the idea that Varèse’s challenging work has been an inspiration to many later artists, an idea supported by the rest of the paragraph.

PSAT PRACTICE TEST 1

Answers and explanations

MATH TEST: NO-CALCULATOR

1. A/Difficulty: MediumEasy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: You could start by cross-multiplying to get rid of the denominators, but simplifying the numerators first will make the calculations easier. Don’t forget to distribute the negative to both terms in the parentheses on the right-hand side of the equation.

Choice (A) is correct.

2. C/Difficulty: Easy

Category: Passport to Advanced Math / Exponents

Getting to the Answer: Don’t be tempted—you can’t simply cancel one term when a polynomial is divided by a monomial. You can, however, split the expression into three terms, each with a denominator of 9x 2, and simplify. You could also use polynomial long division to answer the question. Use whichever method gets you to the answer more quickly on Test Day.

Choice (C) is correct.

3. B/Difficulty: Easy

Category: Passport to Advanced Math / Functions

Getting to the Answer: When using function notation, f(x) is simply another way of saying y, so this question is asking you to find the value(s) of x for which y = 0, or in other words, where the graph crosses the x-axis. Don’t be tempted by the flat parts of the graph—they have a slope of 0, but the function itself does not equal 0 here (it equals —4). The graph crosses the x-axis at the points (—1, 0) and (1, 0), so the values of x for which f(x) = 0 are —1 and 1, (B).

4. C/Difficulty: Medium

Category: Heart of Algebra / Inequalities

Getting to the Answer: You don’t need to use algebra to answer this question, and you also don’t need to graph each system. Instead, think about how the graphs would look. The only time a system of linear inequalities has no solution is when it consists of two parallel lines shaded in opposite directions. All the inequalities are written in slope-intercept form, so look for parallel lines (two lines that have the same slope but different y-intercepts). The slopes in A are different (m = 1 and m = 2), so eliminate this choice. The same is true for B (m = 1 and m = —1) and D (m = —1 and m = 1). This means (C) must be correct (m = 1 and m = 1, b = 1 and b = —1). The graph of the system is shown here:

Because the shading never overlaps, the system has no solution.

5. B/Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: Although this question asks where the graphs intersect, it is not necessary to actually graph them. The point(s) at which the two graphs intersect are the points where the two equations are equal to each other. So, set the equations equal and use algebra to solve for x. Because the question only asks for the x-values, you don’t need to substitute the results back into the equations to solve for y:

Now that the equation is factored, use the Zero-Product Property to solve for x:

Choice (B) is correct.

6. D/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: You can approach this question conceptually or concretely. When dealing with simple transformations, drawing a quick sketch is most likely the safest approach. You are only concerned about the y-intercept, so keep your focus there. When the graph is reflected over the x-axis, the y-intercept will go from (0, —1) to (0, 1). Next, the line is shifted up 3 units, which adds 3 to the y-coordinates of all the points on the line, making the new y-intercept (0, 4). Choice (D) is correct. A sketch is provided here:

7. D/Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: The roots of an equation are the same as its solutions. Take a peek at the answer choices—they contain radicals, which tells you that the equation can’t be factored. Instead, either complete the square or solve the equation using the quadratic formula, whichever you are most comfortable with. The equation is already written in the form y = ax2 + bx + c and the coefficients are fairly small, so using the quadratic formula is probably the quickest method. Jot down the values that you’ll need: a = 3, b = —6, and c = —5. Then, substitute these values into the quadratic formula and simplify:

This is not one of the answer choices, so simplify the radical. To do this, look for a perfect square that divides into 96 and take its square root. Then, if possible, cancel any factors that are common to the numerator and the denominator:

Choice (D) is correct. Be careful—you can’t simplify the answer any further because you cannot divide the square root of 6 by 3.

8. A/Difficulty: Medium

Category: Passport to Advanced Math / Exponents

Getting to the Answer: When you write an equation in terms of a specific variable, you are simply solving the equation for that variable. To do this, you'll need to use the property that raising a quantity to the one-fourth power is the same as taking its fourth root and that applying a negative exponent to a quantity is the same as writing its reciprocal. Rewrite the equation using these properties, and then solve for n using inverse operations. Note that the inverse of taking a fourth root of a quantity is raising the quantity to the fourth power:

Choice (A) is correct.

9. C/Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: When a system consists of two equations already written in terms of y, the quickest way to solve the system is to set the equations equal to each other and then use inverse operations. Don’t let the fraction intimidate you—you can write the first equation as a fraction over 1 and use cross-multiplication:

Don’t let A fool you—the question is asking for the value of y, not the value of x. To find y, substitute 10 for x in either equation and simplify:

Choice (C) is correct.

10.A/Difficulty: Medium

Category: Heart of Algebra / Inequalities

Getting to the Answer: You don’t need to separate this compound inequality into pieces. Just remember, whatever you do to one piece, you must do to all three pieces. The fractions in this question make it look more complicated than it really is, so start by clearing them. To do this, multiply everything by the least common denominator, 10:

Now, read the inequality symbols carefully. The value of d is between —2 and not including —2 because of the < symbol, so (A) is the correct answer. Don’t let C fool you—you can’t have a 0 denominator in a rational expression, but in this expression, the variable is in the numerator, so it can equal 0.

11.B/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: The key to answering this type of question is determining how many results fit in each category. Here, you need to know how many shots were 3-pointers and how many were 2-pointers. Mae-Ling successfully made 15 shots total and s were 3-pointers, so the rest, or 15 — s, must have been 2-pointers. Write the expression in words first: points per 3-pointers (3) times number of shots that were 3-pointers (s), plus points per regular goal (2) times number of regular goals (15 — s). Now, translate from English into math: 3s + 2(15 — s). This is not one of the answer choices, so simplify the expression by distributing the 2 and then combining like terms: 3s + 2(15 — s) = 3s + 30 — 2s = s + 30. This matches (B).

12.D/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: There is only one equation given and it has two variables. This means that you don’t have enough information to solve for either variable. Instead, look for the relationship between the left side of the equation and the other expression that you are trying to find. The expression you are trying to find (6x — 5y) has the x-term first and then the y-term, so start by reversing the order of the terms on the left side of the given equation. Also, notice that the x term in 6x — 5y is not negative, so multiply the equation by —1:

Finally, there are no fractions in the desired expression, so clear the fractions by multiplying both sides of the equation by 10. This yields the expression that you are looking for, so no further work is required—just read the value on the right-hand side of the equation, which is 160:

Choice (D) is correct.

13.B/Difficulty: Medium

Category: Passport to Advanced Math / Functions

Getting to the Answer: Understanding the language of functions will make questions that seem complicated much more doable. When you know the output of a function (or in this question, a composition of two functions), you can work backward to find the input. Because g(x) is the inside function for this composition, its output becomes the input for f(x). Unfortunately, you don’t have any information about g yet. You do know, however, that f of some number, g(2), is —1, so set f(x) equal to —1 and solve for x:

You now know that f(—2) = —1. In the equation for the composition, g(2) represents x, so you also know that g(2) must be —2. Your only option now is to use brute force to determine which equation for g, when evaluated at 2, results in —2.

Choice A: g(2) = 2 — 6 = —4 (not —2), so eliminate.

Choice B: g(2) = 2 — 4 = —2

You don’t need to go any further; (B) is correct.

You could check your answer by working forward, starting with g(2):

14.1/5 or .2 Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: There are two variables but only one equation, so you can’t actually solve the equation for k. Instead, recall that an equation has infinitely many solutions when the left side is identical to the right side. When this happens, everything cancels out and you get 0 = 0, which is always true. Start by simplifying the right-hand side of the equation. Don’t simplify the left side because k is already in a good position:

Next, compare the left side of the equation to the right side. Rather than distributing the k, notice that 2x is a fifth of 10x and —1 is a fifth of —5, so if k were (or 0.2), then both sides of the equation would equal 2x — 1, and it would therefore have infinitely many solutions. Thus, k is or .2.

15.2 Difficulty: Medium

Category: Additional Topics in Math / Geometry

Getting to the Answer: You could use the Pythagorean theorem to solve this, but it will save valuable time on Test Day if you recognize that this question is testing your knowledge of Pythagorean triples. The triangle is a right triangle with leg lengths of 18 and 24, which, when divided by 6, are in the proportion 3:4. This means that the triangle is a scaled up 3:4:5 right triangle with a scale factor of 6. To keep the same proportion, the hypotenuse must be 5 × 6 = 30. For 15n to equal 30, n must be 2.

16.3 Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Getting to the Answer: You need to use rules of exponents to simplify the expression. Before you can do that, you must rewrite the radicals as fraction exponents. Use the phrase “power over root” to help you convert the radicals: and . Then use rules of exponents to simplify the expression. Add the exponents of the factors that are being multiplied and subtract the exponent of the factor that is being divided:

The exponent of the simplified expression is 3.

17.6 Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: When you are given the graph of a parabola, try to use what you know about intercepts, the vertex, and the axis of symmetry to answer the question. Here, you could try to use points from the graph to find its equation, but this is not necessary because the question only asks for the value of b. As a shortcut, recall that you can find the vertex of a parabola using the formula (the quadratic formula without the radical part). You are given that a = —1. Now look at the graph—the vertex of the parabola is (3, 8), so substitute 3 for x, —1 for a, and solve for b:

As an alternate method, you could plug the value of a and the vertex (from the graph) into vertex form of a quadratic equation and simplify:

The coefficient of x is b, so b = 6.

PSAT PRACTICE TEST

Answers and explanations

MATH TEST: CALCULATOR

1. D/Difficulty: Easy

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: You don’t need to know the slope of the line of best fit to answer the question, so don’t waste valuable time trying to find it. Instead, use the labels on the axes to determine the meaning of the slope.

Getting to the Answer: Graphically, slope is the ratio of the change in the y-values (rise) to the change in the x-values (run). In a real-world scenario, this is the same as the unit rate. In this context, the rise describes the change in the number of home runs hit in a single season, and the run describes the change in the number of hours a player spends in batting practice. Thus, the unit rate, or slope, represents the estimated increase (since the data trends upward) in the number of single-season home runs hit by a player for each hour he spends in batting practice.

2. B/Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Finding an x-intercept is easy when you know the equation of the line—it’s the value of x when y is 0. Notice that the answer choices are very close together. This means you shouldn’t just estimate visually. Take the time to do the math. Everything you need to write the equation is shown on the graph—just pay careful attention to how the Per webster’s, grid line is two words are labeled. The y-intercept is 10 and the line rises 2 units and runs 1 unit from one point to the next, so the slope is This means the equation of the line, in slope-intercept form, is y = 2x + 10. Now, set the equation equal to zero and solve for x:

The line will intersect the x-axis at —5, which is (B).

3. A/Difficulty: Easy

Category: Passport to Advanced Math / Functions

Getting to the Answer: When you see an expression like f(x), it means to substitute the given value for x in the function’s equation. When there is more than one function involved, pay careful attention to which function should be evaluated first. You are looking for the value of f(x) at x = 5. Because f(x) is defined in terms of g(x), evaluate g(5) first by substituting 5 for x in the expression x + 2:

This means (A) is correct.

4. B/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: The cost per night in the hospital is the same as the unit rate, which is represented by the slope of the line. Use the grid lines and the axis labels to count the rise and the run from the y-intercept of the line (0, 26,000) to the next point that hits an intersection of two grid lines, (2, 34,000). Pay careful attention to how the grid lines are marked (by 2s on the x-axis and by 2,000s on the y-axis). The line rises 8,000 units and runs 2 units, so the slope is , which means it costs an average of $4,000 per night to stay in the hospital. Note that you could also use the slope formula and the two points to find the slope:

Choice (B) is correct.

5. D/Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Getting to the Answer: You aren’t given much information to go on except the shape of the graph, so you’ll need to think about what the shape means. Remember, linear functions increase at a constant rate, exponential functions increase at either an increasing or decreasing rate, gradually at first and then more quickly or vice versa, and quadratics and polynomials reverse direction one or more times. The graph begins by decreasing extremely quickly, but then it almost (but not quite) levels off. Therefore, it can’t be linear and because it doesn’t change direction, an exponential function, (D), would be the best model for the data.

6. A/Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: This is a science crossover question. Read the first three sentences quickly—they are simply describing the context. The second half of the paragraph poses the question, so read that more carefully. In the sample, 2,800 out of 3,200 acres were free of kudzu after applying the herbicide. This is of the area. For the whole region, assuming the same general conditions, 0.875(30,000) = 26,250 acres should be free of the kudzu. Be careful—this is not the answer. The question asks how much of the cropland would still be covered by kudzu, so subtract to get 30,000 — 26,250 = 3,750 acres, (A).

7. B/Difficulty: Medium

Category: Passport to Advanced Math / Functions

Getting to the Answer: The notation g(h(x)) indicates a composition of two functions, which can be read “g of h of x.” It means that the output when x is substituted in h(x) becomes the input for g(x). First, use the top and bottom rows of the table to find that h(3) is 2. This is your new input. Now, use the top and middle rows of the table to find g(2), which is —3, (B).

8. D/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Assign a variable to the unknown, and then create an equation that represents the scenario. Let n be the number of units the manufacturer sells in a month. Sales must equal expenses for the manufacturer to break even (sales = expenses). The sales are equal to the selling price ($9.50) times the number of units sold (n), so write 9.5n on one side of the equal sign. The monthly expenses are the fixed expenses ($11,625) plus the amount paid for the materials needed to produce one unit ($4.85) times the number of units (n), so write 11,625 + 4.85n on the other side of the equal sign. Then, solve for n:

Choice (D) is correct.

9. A/Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Let the units in this question guide you to the answer. You can do one conversion at a time or all of them at once. Just be sure to line up the units so they’ll cancel correctly. The company uses 8 machines, each of which pumps at a rate of 37.5 gallons per minute, so the rate is actually 8 × 37.5 = 300 gallons per minute. Find the total number of gallons needed, and then use the rate to find the time:

The answers are given in hours and minutes, so change 350 minutes to 350 ÷ 60 = 5.833 hours, which is 5 hours and 50 minutes, (A).

10.C/Difficulty: Medium

Category: Problem Solving and Data Analysis / Functions

Getting to the Answer: Look for a pattern for the sales of each company. Then apply that pattern to see which one will sell more in the last month of the year. Writing a function that represents each pattern will also help, but you have to be careful that you evaluate the function at the correct input value. Company A’s sales can be represented by a linear function because each month the company sells 92 more of the toy than the month before, which is a constant difference. The sales can be represented by the function f(t) = 92t + 54, where t is the number of months after January. December is 11 months (not 12) after January, so during the last month of the year Company A should sell f(11) = 92(11) + 54 = 1,066 of the toy. Company B’s sales can be represented by an exponential function because the sales are doubling each month, which is a constant ratio (2 for doubling). The function is g(t) = 15(2)t, where t is again the number of months after January. In December, Company B should sell g(11) = 15(2)11 = 30,720. This means that in December, Company B should sell 30,720 — 1,066 = 29,654 more of the toy than Company A. Choice (C) is correct.

11.A/Difficulty: Medium

Category: Heart of Algebra / Inequalities

Getting to the Answer: Apply logic to this question first, and then algebra. The dot at the beginning of the shaded portion is an open dot, so —2 is not included in the solution set of the inequality. This means you can eliminate C and D because those symbols would include the endpoint. Don’t immediately choose B just because the arrow is pointing to the right, which typically indicates greater than. When dealing with an inequality, if you multiply or divide by a negative number, you must flip the symbol, so the answer is not necessarily what you might think. Because you were able to eliminate two of the choices, the quickest approach is to pick one of the remaining symbols, plug it in, and see if it works. If it does, choose that answer. If it doesn’t, then it must be the other symbol. Try (A):

The resulting inequality, x > —2, means all the values on the number line greater than (or to the right of) —2, so the initial inequality symbol must have been <. Choice (A) is correct.

12.B/Difficulty: Easy

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: When a question involves scale factors, set up a proportion and solve for the missing value:

Choice (B) is correct.

13.C/Difficulty: Easy

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: Don’t make this question harder than it actually is. You don’t need to find the new scale factor. Instead, use the length that the student drew the femur and the actual length to set up and solve a new proportion:

Choice (C) is correct.

14.B/Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Given two points (even when the coordinates are variables), the slope of the line between the points can be found using the formula . You are given a numerical value for the slope and a pair of ordered pairs that have variables in them. To find the value of c, plug the points into the slope formula, and then solve for c. Be careful of all the negative signs:

Choice (B) is correct.

15.A/Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: Questions that involve distance, rate, and time can almost always be solved using the formula Distance = rate × time. Break the question into short steps (first part of trip, second part of trip). Start with the plane from DCA. Use the speed, or rate, of the plane, 338 mph, and its distance from London, 3,718 miles, to determine when it arrived. You don’t know the time, so call it t:

It took the DCA flight 11 hours. Now determine how long it took the plane from MIA. You’ll need to find the distance for each part of the trip—the question only tells you the total distance. Then, use the formula to find how long the plane flew at 596 mph and how long it flew at 447 mph:

First part of trip:

Second part of trip:

This means it took the MIA flight 5 hours + 3 hours, 20 minutes = 8 hours, 20 minutes. So, the plane from MIA arrived first. It arrived 11 hours — 8 hours, 20 minutes = 2 hours, 40 minutes before the plane from DCA, making (A) correct.

16.D/Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: The graph of every quadratic equation is a parabola, which may or may not cross the x-axis, depending on where its vertex is and which way it opens. When an equation has no solution, its graph does not cross the x-axis, so try to envision the graph of each of the answer choices (or you could graph each one in your graphing calculator, but this will probably take longer). Don’t forget—if the equation is written in vertex form, y = a(xh)2 + k, then the vertex is (h, k) and the value of a tells you which way the parabola opens. When a quadratic equation is written in factored form, the factors tell you the x-intercepts, which means A and B (which are factored) must cross the x-axis, so eliminate them. Now, imagine the graph of the equation in C: The vertex is (—1, 8) and a is negative, so the parabola opens downward and consequently must cross the x-axis. This means (D) must be correct. The vertex is also (—1, 8), but a is positive, so the graph opens up and does not cross the x-axis.

17.D/Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: The two variables are certainly correlated—as one goes up, the other goes up. A linear regression model would fit the data fairly well, so you can eliminate C. The spending is graphed on the x-axis, so it is the independent variable and therefore does not depend on the GDP, graphed on the y-axis, so you can eliminate B as well. The data does show that as spending on students increases, so does the GDP, but this is simply correlation, not causation. Without additional data, no statements can be made about whether spending more on students is the reason for the increased GDP, so (D) is correct.

18.C/Difficulty: Easy

Category: Passport to Advanced Math / Exponents

Getting to the Answer: Focus on the question at the very end—it’s just asking you to solve the equation for p2. Multiply both sides by T2 to get rid of the denominator on the right-hand side of the equation. Then divide by V2 to isolate p2:

Stop here! You cannot cancel the V’s and T’s because the subscripts indicate that they are not the same variable. In math, subscripts do not behave the same way superscripts (exponents) do. Choice (C) is correct.

19.C/Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: The factor-label method (canceling units) is a great strategy for this question. You’re starting with tons, so work from that unit, arranging conversions so that units cancel. To keep units straight, use an E for Earth, an M for Mars, and a J for Jupiter:

The object weighs 1,131 pounds on Mars and 7,092 pounds on Jupiter, so it weighs 7,092 — 1,131 = 5,961 more pounds on Jupiter, (C).

20.C/Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: Examine the shape of the data and familiarize yourself with the title and the axis labels on the graph. Data is symmetric if it is fairly evenly spread out, and it is skewed if it has a long tail on either side. Notice that the data is skewed to the right, so you can immediately eliminate A. Choices B, (C), and D all describe the data as skewed to the right, so you’ll need to examine those statements more closely. For B, “adverse reactions” include the last four bars, which represent 89 + 41 + 22 + 8 = 160 participants total, which is not even close to 50% of 900, so eliminate B. Note that you don’t need to add all the bar heights to find that there were 900 participants—the title of the graph tells you that. Now look at C—“failed to have adverse reactions” means “None” or “Mild” (the first three bars), which represent 900 — 160 = 740 of the 900 participants. 75% of 900 = 675, and 740 is more than 675, so (C) is correct. For D, the “None” column contains 320 participants, which does not equal approximately 50% of 900, so it too is incorrect.

21.C/Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: Use the Kaplan Method for Translating English into Math. Write a system of equations with p = the cost in dollars of the Pennsylvania bar exam and d = the cost of the D.C. bar exam. The Pennsylvania bar exam (p) costs $25 less (— 25) than 3 times as much (3d) as the D.C. bar exam, or p = 3d — 25. Together, both bar exams cost $775, so d + p = 775. The system is:

The top equation is already solved for p, so substitute 3d — 25 into the second equation for p, and solve for d:

Be careful—that’s not the answer. The D.C. bar exam costs $200, which means the Pennsylvania bar exam costs $775 — $200 = $575. This means the D.C. bar exam is $575 — $200 = $375 less expensive than the Pennsylvania bar exam. Choice (C) is correct.

22.B/Difficulty: Medium

Category: Problem Solving and Data Analysis / ­Statistics and Probability

Getting to the Answer: Always read the axis labels carefully when a question involves a chart or graph. Frequency, which is plotted along the vertical axis, tells you how many students missed the number of questions indicated under each bar. Evaluate each statement as quickly as you can.

Choice A: Add the bar heights (frequencies) that represent students that missed 5 or more questions: 7 + 3 + 3 + 2 = 15. Then, find the total number of students represented, which is the number that missed less than 5 questions plus the 15 you just found: 2 + 3 + 4 + 6 = 15, plus the 15 you already found, for a total of 30 students. The statement is not true because 15 is exactly half (not more than half) of 30.

Choice (B): This calculation will take a bit of time so skip it for now.

Choice C: The tallest bar tells you which number of questions was missed most often, which was 5 questions, not 3 questions, so this statement is not true.

Choice D: The number of students from Mr. Juno’s class who took the test that day is the sum of the heights of the bars, which you already know is 30, not 36.

This means (B) must be correct. Mark it and move on to the next question. (In case you're curious, find the mean by multiplying each number of questions missed by the corresponding frequency, adding all the products, and dividing by the total number of students, which you already know is 30:

The mean is indeed between 4 and 5.)

23.C/Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: Writing quadratic equations can be tricky and time-consuming. If you know the roots, you can use factors to write the equation. If you don’t know the roots, you need to create a system of equations to find the coefficients of the variable terms. You don’t know the roots of this equation, so start with the point that has the nicest values (0, 2) and substitute them into the equation, y = ax 2 + bx + c, to get 2 = a(0)2 + b(0) + c, or 2 = c. Now your equation looks like y = ax 2 + bx + 2. Next, use the other two points to create a system of two equations in two variables:

(−6, −7) → −7 = a(−6)2 + b(−6) + 2 → −9 = 36a − 6b

(8, −14) → −14 = a(8)2 + b(8) + 2 → −16 = 64a + 8b

You now have a system of equations to solve. If you multiply the top equation by 4 and the bottom equation by 3, and then add the equations, the b terms will eliminate each other:

Now, find b by substituting a = —0.25 into either of the original equations. Using the top equation, you get:

The value of a + b + c is (—0.25) + 0 + 2 = 1.75, (C).

24.D/Difficulty: Hard

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Read the question, organizing important information as you go. You need to find the ratio of mini muffins to jumbo muffins. You’re given two ratios: mini to regular and regular to jumbo. Both of the given ratios contain regular muffin size units, but the regular amounts (2 and 5) are not identical. To directly compare them, find a common multiple (10). Multiply each ratio by the factor that will make the number of regular muffins equal to 10:

Mini to regular: (5:2) × (5:5) = 25:10

Regular to jumbo: (5:4) × (2:2) = 10:8

Now that the number of regular muffins is the same in both ratios (10), you can merge the two ratios to compare mini to jumbo directly: 25:10:8. So, the proper ratio of mini muffins to jumbo muffins is 25:8, which is (D).

25.A/Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: Graphically, a system of linear equations that has no solution indicates two parallel lines, or in other words, two lines that have the same slope. So, write each of the equations in slope-intercept form (y = mx + b) and set their slopes (m) equal to each other to solve for k. Before finding the slopes, multiply the top equation by 6 to make it easier to manipulate:

The slope of the first line is , and the slope of the second line is . Set them equal and solve for k:

Choice (A) is correct.

26.D/Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Getting to the Answer: The numbers in some questions are simply too large to use a calculator (you get an “overflow” error message). Instead, you’ll have to rely on rules of exponents. Notice that all of the base numbers have 3 as a factor, so rewrite everything in terms of 3. This will allow you to use the rules of exponents. Because 27 is the cube of 3, you can rewrite 27 90 as a power of 3:

Now the product should read: 3 90 × 3 270, which is equal to 3 90 + 270 = 3 360. Repeat this process for the quantity that is being divided:

Finally, use rules of exponents one more time to simplify the new expression:

All the answer choices are given as powers of 9, so rewrite your answer as a power of 9:

Choice (D) is correct.

27.D/Difficulty: Hard

Category: Additional Topics in Math / Geometry

Getting to the Answer: If needed, don’t forget to check the formulas provided for you at the beginning of each math section. The volume of a right cone is given by . Here, you only know the value of one of the variables, V, so you’ll need to use the information in the question to somehow write r and h in terms of just one variable. If the cone is three times as wide at the base as it is tall, then call the diameter 3x and the height of the cone one-third of that, or x. The volume formula calls for the radius, which is half the diameter, or . Substitute these values into the formula and solve for x:

The question asks for the diameter of the base, which is 3x = 3(8) = 24, choice (D).

28.85 Difficulty: Easy

Category: Problem Solving and Data Analysis / Scatterplots

Getting to the Answer: The range of a set of data points is the set of outputs, which correspond to the y-­values of the data points on the graph. To find the maximum value in the range of the data, look for the highest point on the graph, which is (250, 85). The y-value is 85, so 85 is the maximum value in the range.

29.7 Difficulty: Hard

Category: Heart of Algebra / Linear Equations

Getting to the Answer: To write the equation of a line, you need two things: the slope and the y-intercept. Start by finding these, substituting them into slope-­intercept form of a line (y = mx + b), and then manipulate the equation so that it is written in standard form. Use the given points, (—4, 1) and (3, —2), and the slope formula to find m:

Next, find the y-intercept, b, using the slope and one of the points:

Write the equation in slope-intercept form: .

Now, rewrite the equation in the form Ax + By = C, making sure that A is a positive integer (a whole number greater than 0):

The question asks for the value of B (the coefficient of y), so the correct answer is 7.

30.380 Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: You can use the formula Percent × whole = part to solve this problem, but you will first need to think conceptually about what the question is asking. The question is asking for the Dow value before the 19.5% decrease to 306. This means that 306 represents 100 — 19.5 = 80.5% of what the stock market was at its record high. Fill these amounts into the equation and solve for the original whole, the record high Dow value:

Rounded to the nearest whole point, the record high was approximately 380 points.

31.25 Difficulty: Hard

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percents

Getting to the Answer: Percent change is given by the ratio . To find the total percent change, you’ll need to work your way through each of the days, and then use the ratio. Jot down the Dow value at the end of each day as you go. Do not round until you reach your final answer. First, calculate the value of the Dow at closing on Black Thursday: It opened at 306 and decreased by 2%, which means the value at the end of the day was 100 − 2 = 98% of the starting amount, or 306 × 0.98 = 299.88. Then, it decreased again on Monday by 13% to close at 100 − 13 = 87% of the opening amount, or 299.88 × 0.87 = 260.8956. Finally, it decreased on Tuesday by another 12% to end at 100 − 12 = 88% of the starting amount, or 260.8956 × 0.88 = 229.588. Now use the percent change formula to calculate the percent decrease from opening on Black Thursday (306) to closing on Black Tuesday (229.588):

The Dow had a total percent decrease of approximately 25% between opening on Black Thursday and closing on Black Tuesday.