PSAT Math Questions and Answers

PSAT Math Questions and Answers Page

On this page, you will find links to our PSAT math practice questions and answers. Try the quizzes below to refresh your math skills.

Arithmetic, Statistics, and Probability Quiz

Algebra and Geometry Quiz

PSAT Math Sample Trigonometry Questions and Answers

In addition to the concepts in the quizzes above, you may also need to know basic trigonometry for your PSAT test.

Sine, Cosine, and Tangent

Question 1

∠A measures 58 and cos A = sin B.

What is the sum in degrees of ∠A + ∠B ?

A) 30

B) 32

C) 45

D) 90

Tips:

Remember these important trigonometric formulas for the exam:

cos A = sin (90° − A)

sin A = cos (90° − A)

cos² A + sin² A = 1

cos² A = 1 − sin² A

sin² A = 1 − cos² A

tan A = sin A ÷ cos A

tan A × cos A = sin A

Answer:

The correct answer is D. You will recall from the formulas that sin A = cos (90° − A). If sin B = cos A, as in this problem, then B = 90° − A and A + B = 90°

Question 2

If x represents a real number, what is the greatest possible value of:

4 × cos 2x?

A) 2

B) 3

C) 4

D) 6

Tip:

The greatest possible value of cosine is 1. Therefore, cos 2x must be less than or equal to 1.

Answer:

The correct answer is C. Since the greatest possible value of cosine is 1, cos 2x must be less than or equal to 1. So, the greatest possible value of cos 2x is represented by the following formula: cos 2x = 1. Now, multiply each side of the equation by 4 in order to get 4 × cos 2x.

cos 2x = 1

4 × cos 2x = 1 × 4

4 × cos 2x = 4

So, the greatest possible value is 4.

Question 3

If cos A = 9/15 and tan A = 12/9 then sin A = ?

A) 12/9

B) 9/12

C) 12/15

D) 15/12

Tip:

To calculate the sine, cosine, and tangent of any given angle A, which is the 90 degree angle in a right triangle, use the following formulas:

sine A = opposite / hypotenuse

cosine A = adjacent / hypotenuse

tangent A = opposite / adjacent

Answer:

The correct answer is C. From the trig formulas, we know that cos A = adjacent over hypotenuse and tan A = opposite over adjacent. For our problem cos A = 9/15 so the adjacent side is 9 and the hypotenuse is 15. Furthermore, tan A = 12/9 so the opposite side is 12. Now substitute the values for sine. For our problem, the opposite side is 12 and the hypotenuse is 15.

sine A = opposite / hypotenuse, so for our question, sin A = 12/15

Question 4

The cosine of angle Z is 0.78801075 and the tangent of angle Z is 0.7812856. What is the sine of angle Z?

A) 1 – 0.61566148

B) 0.61566148

C) 0.7812856

D) 0.78801075

Tip:

Refer to the trigonometry concepts after question 1 above.

Answer:

The correct answer is B. The trig formulas state that tan A × cos A = sin A. In this question, the cosine of angle Z is 0.78801075 and the tangent of angle Z is 0.7812856, so put the values into the formula to solve.

tan A × cos A = sin A

0.7812856 × 0.78801075 = sin A

0.61566148 = sin A

Question 5

The sine of a 41 degree angle is equal to which of the following?

A) 45° – 41°

B) the cosine of 49°

C) the tangent of 41°

D) (0.75470958)²

Tip:

Refer to the trigonometry concepts after question 1 above again.

Answer:

The correct answer is B. The trig formulas state that cos A°= sin(90° – A°). This is a 41 degree angle, so sin 41° = cos(90° – 41°) = cos 49°. The sine of a 41 degree angle is 0.656059, and the cosine of a 49 degree angle is also 0.656059.

What’s on the PSAT Math Test?

There are 48 questions on the math section of the PSAT exam. You will be allowed 70 minutes to take the math part of the test. The test assesses your knowledge of arithmetic, algebra, and geometry.

Multiple choice questions

Of the 48 questions on the exam, 40 of those will be multiple choice questions. These will have choices A to D as possible correct answers.

Free-response questions

The other eight questions on the PSAT math test are in the “free-response” format. This means that you will have to come up with the correct answer on your own. The free-response questions are usually provided at the end of the section.

Do I need to memorize math formulas?

You will need to know math formulas for the test. But more importantly, you will need to know how to use and apply the formulas to solve real-life problems.

Can I use a calculator on the PSAT math exam?

There will be a calculator section and a no calculator section on the test. There will be some some multiple choice and some free-response questions in each section.

PSAT Math Strategies

You can do the questions on the PSAT in any order you like, so do the easy questions first and save the more difficult ones for later.

Each question is worth the same number of points, so you won’t get more credit for answering a really difficult question correctly.

Remember that you will have to answer 48 questions in 70 minutes – that’s about 70 seconds for each question. And many students are unable to complete all of the questions in the allotted time.

So it will pay off to know which type of questions you find easy and which type you find hard. Because when you get to the test, you will be able to skip over the ones you know are hard for you.

You have to complete the “non calculator section” before you go on the the section where you can use the calculator. So identify the hard questions in each section and plan accordingly.

There is no penalty for guessing, so if you know that you are just going to waste time on a question, mark an answer at random on your answer sheet and move on.