AP Precalculus — Practice Questions flashcards

6 of 55 questions free to study here · 3 topics · the whole deck is built into Willys

Multiple-choice practice questions, one best answer each, on polynomial, rational, exponential, logarithmic, trigonometric and polar functions, with rates of change and modeling.

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Practice deck · part of AP Precalculus · written against: College Board AP Precalculus Course and Exam Description (Units 1–3 (exam-assessed units)). Updated 2026-10-10.

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What is the average rate of change of $f(x) = x^3 - 4x$ over the interval $1 \le x \le 3$ ⁠?

A) 6
B) 18
C) 9
D) 7.5

C) 9

$f(3) = 15$ and $f(1) = -3$ ⁠, so the rate is $\frac{15 - (-3)}{3 - 1} = 9$ ⁠. Getting 18 means the change in output was not divided by the change in input.
Polynomial and Rational Functions › Rates of Change
A function $g$ has $g(0) = 2$ ⁠, $g(1) = 5$ ⁠, $g(2) = 7$ ⁠, $g(3) = 8$ and $g(4) = 8.5$ ⁠. Assuming the pattern in these values holds between them, which best describes $g$ on $0 \le x \le 4$ ⁠?

A) Decreasing and concave up
B) Increasing and concave down
C) Increasing and concave up
D) Decreasing and concave down

B) Increasing and concave down

The average rates of change over consecutive unit intervals are 3, 2, 1 and 0.5: all positive (increasing) but shrinking (concave down). Concave up would need those rates to grow.
Polynomial and Rational Functions › Rates of Change
A geometric sequence has $g_2 = 12$ and $g_5 = 96$ ⁠. Which expression gives $g_n$ ⁠?

A) $g_n = 3 \cdot 2^n$
B) $g_n = 1.5 \cdot 2^n$
C) $g_n = 12 \cdot 2^n$
D) $g_n = 6 \cdot 2^n$

A) $g_n = 3 \cdot 2^n$

Three steps multiply by $\frac{96}{12} = 8$ ⁠, so $r = 2$ ⁠, and $g_0 = \frac{12}{2^2} = 3$ ⁠. Using 12 as the starting value treats $g_2$ as if it were $g_0$ ⁠.
Exponential and Logarithmic Functions › Sequences
The first four terms of a sequence are 80, 60, 45 and 33.75. Which describes the sequence?

A) Arithmetic with common difference −15
B) Geometric with common ratio $\frac{4}{3}$
C) Geometric with common ratio $\frac{3}{4}$
D) Arithmetic with common difference −20

C) Geometric with common ratio $\frac{3}{4}$

Each term is $\frac{3}{4}$ of the one before ( $\frac{60}{80} = \frac{45}{60} = \frac{33.75}{45} = 0.75$ ⁠). The differences are −20, −15 and −11.25, which are not constant, so the sequence is not arithmetic.
Exponential and Logarithmic Functions › Sequences
A function $f$ has period 8, $f(3) = -2$ and $f(5) = 4$ ⁠. What is $f(29) - f(-13)$ ⁠?

A) −6
B) 2
C) 6
D) 0

C) 6

$29 = 5 + 3 \cdot 8$ ⁠, so $f(29) = 4$ ⁠; $-13 = 3 - 2 \cdot 8$ ⁠, so $f(-13) = -2$ ⁠. The difference is $4 - (-2) = 6$ ⁠; pairing 29 with 3 instead of 5 gives $-6$ ⁠.
Trigonometric and Polar Functions › Periodic Phenomena
In a circle of radius 4 cm, a central angle intercepts an arc 10 cm long. What is the angle's measure in radians?

A) 0.4
B) $2.5\pi$
C) 2.5
D) 40

C) 2.5

A radian measure counts how many radius-lengths fit along the arc: $\theta = \frac{10}{4} = 2.5$ ⁠. The value 0.4 divides the radius by the arc length instead.
Trigonometric and Polar Functions › Periodic Phenomena

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About these cards

Review status: Second-reader reviewed, with corrections applied.

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Topic outline follows the College Board AP Precalculus Course and Exam Description (effective Fall 2026), Units 1–3 (the AP name is used nominatively; no course or exam text reproduced).
OpenStax Precalculus 2e and OpenStax Calculus Volumes 1 and 2, consulted as references; no text copied.

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