Unit 4 AP Precalculus Practice Test 2025

Last Updated on February 4, 2025

Unit 4 AP Precalculus Practice Test 2025 Multiple Choice Questions Answers on Functions Involving Parameters, Vectors, and Matrices (Not Assessed on the AP Exam). This unit consists of Parametric Functions, Vectors and Matrices.

There will be 17 MCQs in this free advanced placement (AP) Precalculus Unit 4 test. There will be no time limit. You can practice freely without any registration.

All the previous Units dealt with functions and graphs as defined by a single equation in two variables. In certain situations, however, these types of functions and graphs may not provide a complete picture of the real-world situation it is modeling.

A plane curve can be described by a function that uses three variables instead of two. The extra variable, typically represented by t or θ, is called the parameter and provides additional information about the process or function represented by the curve.

Unit 4 AP Precalculus Practice Test 2025

AP Precalculus Practice Test UNIT 4

AP Precalculus Practice Test UNIT 4
Unit 4: Functions Involving Parameters, Vectors, and Matrices (Not Assessed on the AP Exam)
Total Items: 17

1 / 17

Which of the following represents the parametric equation for the graph shown below?

(A) x = t² − 2, y = 3t

(B) y² = 9(x + 2)

(D) x² = 9(y + 2)

2 / 17

Which of the following represents the parameterization of the line through the points (−2, 5) and (4, 2)?

(A) x = −2 − 3t, y = 5 + 6t

(B) x = −2 + 6t, y = 5 − 3t

(D) x = -5 − 3t, y = −2 + 5t

3 / 17

Find the rectangular equation for the curve given by the parametric equations x = sin t, y = 1 − cos² t, 0 ≤ t ≤ π

(A) y = x

(B) y = x² + 1

(D) y = x² − 1

4 / 17

Find the rectangular equation for the curve given by the parametric equations x = t − 1, y = t2 − 1, − 2 ≤ t ≤ 4.

(A) y = x² + 2x

(B) y = x² − 2x

(D) y = x² − 2

5 / 17

Which of the following choices are pairs of parametric equations for the $\frac{(x + 3)^{5}} {25} - \frac{(y - 1)^{2}} {9} = 1 ?$

(A) x = 3 + 4 cos t, y = −2 + 7 sin t

(B) x = 4 cos t, y = 7 sin t

(D) x = 4 + 3 cos t, y = 7 − 2 sin t

6 / 17

Which of the following is a vector that has the opposite direction to ⟨−5, 12⟩ and has a length of 26?

(A) ⟨−10, −24⟩

(B) ⟨−10, 24)

(D) ⟨10, −24⟩

7 / 17

A particle moves on a plane curve so that at any time t > 0 its x- coordinate is t⁴ − 3t and its y-coordinate is (5t − 2)². Its velocity vector is $\vec{V}\$ = ⟨4t³ − 3, 10(5t − 2)⟩. What is the speed of the particle, to the nearest tenth, when t = 1?

(A) 5.6

(B) 14

(D) 62

8 / 17

Given the figure below where $\overline{\rm CP} = a, \overline{\rm JM} = c, and \overline{\rm KB} = d$ , which of the following is equivalent to $\overline{\rm CB}$

(A) a + d

(B) a − d

(D) −a − d

9 / 17

Given a particle whose velocity vector is $\vec{V}\$ = ⟨3 − t, −1 + 2t⟩ in meters per minute when t > 0, find the time, t, when the speed of the particle √10 is meters/minute.

(A) 0

(B) 2

(D) 10

10 / 17

Find the value of k such that are $\vec{c}\ = 3\vec{i}\ + 10\vec{k}\ and \vec{p} = k\vec{i} - 6\vec{j}$ are perpendicular.

(A) −7

(B) 1.8

(D) 20

11 / 17

If a particle moves in the xy-plane so that at time t > 0 its velocity vector is $\vec{V}\$ = ⟨t³ + 2t, t² + 1⟩, what is the speed of the particle at t = 2?

(A) √13

(B) √17

(D) 17

12 / 17

Consider the following three statements about an invertible n × n matrix

A.
I. A = A−1
II. AA = I
III. A−1 A−1 = I

Which of the statements are equivalent?

(A) I and II only

(B) II and III only

(D) I, II, and III

13 / 17

Which of the following is the correct geometric interpretation of the associated linear transformations for the standard matrix

(A) Rotates counterclockwise through π radians

(B) Rotates counterclockwise through Π/2 radians and doubles the length

(D) Rotates counterclockwise through Π/2 radians and quadruples the length

14 / 17

Let A = [−5 2] and B = [1 0]. Find 2A + 3B.

(A) [−10 4]

(B) [−9 4]

(D) [−2 2]

15 / 17

Calculate the area of the parallelogram with the given vertices C(0, 0), M(2, 6), π(11, 8), and J(9, 2).

(A) 100

(B) 52

(D) 49

16 / 17

A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there’s a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there’s a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50% chance of rising the next day and a 50% chance of falling. Which matrix is the transition matrix for this Markov chain if the states are listed in order of rising, falling, and constant?

(A)

(B)

(C)

(D)

17 / 17

Given that T : R³ → R², which of the following choices is not a linear transformation?

(A) T(x, y, z) = (x, x + y + z)

(B) T(x, y, z) = (1, 1)

(D) T(x, y, z) = (3x − 4y, 2x − 5z)

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