Unit 3 AP Precalculus Practice Test 2025

Last Updated on February 4, 2025

Unit 3 AP Precalculus Practice Test 2025 Multiple Choice Questions Answers on Trigonometric and Polar Functions. This unit consists of Trigonometric Functions and Polar Functions.

There will be 17 MCQs in this free advanced placement (AP) Precalculus Unit 3 test. There will be no time limit. You can practice freely without any registration.

Before starting this test, it is crucial to understand the necessary background knowledge in trigonometry. It is reviewed in the Prior Knowledge section of this test. For example, Periodic behavior through trigonometric functions and How to solve trigonometric equations and inequalities.

Unit 3 AP Precalculus Practice Test 2025

AP Precalculus Practice Test UNIT 3

AP Precalculus Practice Test UNIT 3
Unit 3: Trigonometric and Polar Functions (30%–35%)
Total Items: 17

1 / 17

If cos x = $\frac{12} {13}$ , sin y = $\frac{4} {5}$ , and x and y are acute angles, what is the value of sin (x − y)?

(A)

\frac{72} {65}

(B)

\frac{56} {65}

\frac{16} {65}

(D) -

\frac{33} {65}

2 / 17

If f(x) = sin(cos−1 x), what is the value of f ( $\frac{1} {2}$ )?

(A) 1

(B)

\frac{1} {2}

(C)

\frac{ \sqrt 2} {2}

(D)

\frac{ \sqrt 3} {2}

3 / 17

At which value of x does the graph of f(θ) = (θ - $\frac{π} {4}$ ) tan have a vertical asymptote?

(A) -

\frac{π} {4}

)

(B) 0

(A)

\frac{π} {4}

)

(A)

\frac{π} {2}

)

4 / 17

Which of the following equations could represent the graph shown below?

(A) y = 3 sin 2x

(B) y = 2 sin 3x

(D) y = 2 sin 4x

5 / 17

Which of the following expressions is equivalent to sin θ?

(A) cos (θ + 1)

(B) cos (θ +

frac{π} {2}

)

frac{π} {2}

)

(D) cos (θ - 1)

6 / 17

The graph of which equation has an amplitude of $\frac{1} {2}$ and a period of π?

(A) y = 2 sin 2x

(B) y = 2 sin ½ x

(D) y =½ sin ½ x

7 / 17

If tan x = $\frac{ \sqrt3} {3}$ and cos x = − $\frac{ \sqrt3} {2}$ , find the measure of ∠x.

(A)

\frac{2Π} {3}

(B)

\frac{5Π} {6}

(C)

\frac{7Π} {6}

(D)

\frac{5Π} {3}

8 / 17

If x is a positive acute angle and cos x = a, which of the following is an expression for tan x in terms of a?

(A) $\frac{1-a} {a}$

(B) $\sqrt{1 - a^{2}}$

(A)

\frac{1-a} {a}

(B)

\sqrt{1 - a^{2}}

(C)

\frac {\sqrt{1 - a^{2}}} {a}

(D)

\frac{1} {1 - a}

9 / 17

If the terminal side of angle A in standard position is in Quadrant I and cos A = $\frac{35} {13}$ , what is the value of sin A · tan A?

(A)

\frac{144} {65}

(B)

\frac{60} {65}

(C)

\frac{144} {169}

(D)

\frac{60} {156}

10 / 17

Which of the following choices are equivalent to the expression cos α(secα − cos α) ?

(A) cos₂ α

(B) cos α − sin α

(D) cotα − 1

11 / 17

Find the average rate of change for the polar curve r = 2 + 4 cos θ in the interval $0, \frac{π} {2}$

(A)

- \frac{8} {π}

(B)

\frac{4} {π}

(C)

\frac{8} {π}

(D) 6

12 / 17

Which of the following polar equations represents the graph given below?

(A) r = 3 + sin θ

(B) r = 6 cos θ

(D) r = 3 + cos θ

13 / 17

Which of the following choices shows the point $-2- \frac{5π} {4}$ in polar coordinates plotted on the polar coordinate system?

(A)

(B)

(C)

(D)

14 / 17

Which of the following complex numbers cannot be written in polar form?

(A) −i

(B) 0

(D) −1

15 / 17

Which of the following choices is an equivalent polar form of the complex number 2 - 2i√3?

(A) 4 (cos

frac{π} {6}

+ sin

frac{π} {6}

)

(B) 4 (cos

frac{π} {3}

+ sin

frac{π} {3}

)

(- frac{π} {6}

) + sin (-

frac{π} {6}

))

(- frac{π} {3}

) + sin (-

frac{π} {3}

))

16 / 17

Which of the following choices represents the complex number k − ki, where k < 0, in polar form?

(A) k√2 (cos

\frac{3π} {4}

+ i sin

\frac{3π} {4}

)

(B) - k√2 (cos

\frac{3π} {4}

+ i sin

\frac{3π} {4}

)

\frac{7π} {4}

+ i sin

\frac{7π} {4}

)

(D) - k√2 (cos

\frac{7π} {4}

+ i sin

\frac{7π} {4}

)

17 / 17

Which of the following choices is equivalent to the complex number 2 (cos $\frac{π} {3}$ + i sin $\frac{π} {3}$ )?

(A) 1 + i√3

(B) (1, √3)

(D) (√3, 1)

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