Calculus Readiness Test Preparation
University of San Francisco
Department of Mathematics and Statistics
The Calculus Readiness Test is used to place you into the appropriate calculus course at USF.
This is a 30-minute online test, with 24 multiple-choice questions. No calculators are permitted.
You may only take this test once; all subsequent scores will not be accepted. Below is a list of
topics on the exam, followed by a practice test to help you prepare.
Topics covered
1. Sim plification of algebraic expressions
2. Solving equations and inequalities
3. W orking w ith functions: Graphing functions, composition of functions, the inverse of a
function, etc.
4. Fam iliar fam ilies of functions: Lines, parabolas, exponential functions, logarithmic
functions, trigonometric functions and basic trigonometric identities.
5. M easurem ents: area, perimeter, volume, and other quantities
, Sample Test
1. (8)1/3 (81)−1/4 =
(A) 6
3
(B)
2
(C) (648)−1/12
2
(D) 3
2. If you know that 212 is approximately 4,000, then which of the following is the best
approximation for 224 ?
(A) 8,000
(B) 16,000
(C) 4 × 106
(D) 1.6 × 107
3. If log 4 (𝑥 + 3) = 2, then 𝑥 =
(A) -1
(B) 13
(C) 5
(D) 3
4. The line 𝑦 = 𝑥 + 1 and the parabola 𝑦 = 2𝑥 2 intersect when 𝑥 = 1 and when 𝑥 =
1
(A) 2
1
(B) −
2
(C) 2
(D) −2
5. The inequality |𝑥 − 3| ≤ 4 is equivalent to
(A) 𝑥 ≤ 7
(B) 𝑥 ≤ −1
(C) −1 ≤ 𝑥 ≤ 7
(D) −7 ≤ 𝑥 ≤ −7
6. Which of the following is a solution of log 2 (𝑥 + 1) − log 2(𝑥 − 2) = 2?
(A) 𝑥 =0
(B) 𝑥 =1
(C) 𝑥 =2
(D) 𝑥 =3
University of San Francisco
Department of Mathematics and Statistics
The Calculus Readiness Test is used to place you into the appropriate calculus course at USF.
This is a 30-minute online test, with 24 multiple-choice questions. No calculators are permitted.
You may only take this test once; all subsequent scores will not be accepted. Below is a list of
topics on the exam, followed by a practice test to help you prepare.
Topics covered
1. Sim plification of algebraic expressions
2. Solving equations and inequalities
3. W orking w ith functions: Graphing functions, composition of functions, the inverse of a
function, etc.
4. Fam iliar fam ilies of functions: Lines, parabolas, exponential functions, logarithmic
functions, trigonometric functions and basic trigonometric identities.
5. M easurem ents: area, perimeter, volume, and other quantities
, Sample Test
1. (8)1/3 (81)−1/4 =
(A) 6
3
(B)
2
(C) (648)−1/12
2
(D) 3
2. If you know that 212 is approximately 4,000, then which of the following is the best
approximation for 224 ?
(A) 8,000
(B) 16,000
(C) 4 × 106
(D) 1.6 × 107
3. If log 4 (𝑥 + 3) = 2, then 𝑥 =
(A) -1
(B) 13
(C) 5
(D) 3
4. The line 𝑦 = 𝑥 + 1 and the parabola 𝑦 = 2𝑥 2 intersect when 𝑥 = 1 and when 𝑥 =
1
(A) 2
1
(B) −
2
(C) 2
(D) −2
5. The inequality |𝑥 − 3| ≤ 4 is equivalent to
(A) 𝑥 ≤ 7
(B) 𝑥 ≤ −1
(C) −1 ≤ 𝑥 ≤ 7
(D) −7 ≤ 𝑥 ≤ −7
6. Which of the following is a solution of log 2 (𝑥 + 1) − log 2(𝑥 − 2) = 2?
(A) 𝑥 =0
(B) 𝑥 =1
(C) 𝑥 =2
(D) 𝑥 =3
