Calculus 1 Practice Test
30 questions from 15 lessons · 90 minutes · percent score and grade · step-by-step answers
How it works
- 30 questions, about 90 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 7 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Calculus 1 formula sheet.
1 Question 1
Find the derivative of sin−1(x).Type the answer.
2 Question 2
Find the derivative of tan−1(3x + 2).Type the answer.
3 Question 3
Find the derivative of 32x.Type the answer.
4 Question 4
Find the derivative of 4log_3(2x + 1).Type the answer.
5 Question 5
Find the derivative of y = (x + 1)2 (x − 3)4 using logarithms.Type the answer.
6 Question 6
Find the derivative of y = (x + 1)2 (x + 3)3/(x + 2) using logarithms.Type the answer.
7 Question 7
Linear approximation of √x at x = 4Type the answer.
8 Question 8
Estimate sin(0.05) with a linear approximationType the answer.
9 Question 9
Find dy for y = x2 when x = 3 and dx = 0.1- A) 0.06
- B) 6
- C) 0.6
10 Question 10
The cube has side 10 cm, measured with a possible error of 0.1 cm. Estimate the percentage error in the volume.Type the answer.
11 Question 11
Absolute max and min of f(x) = x3 − 3x on [−2, 2]- A) 2 and x = 1
- B) −2 and x = 1
- C) 2 and x = −1
- D) −2
12 Question 12
Absolute maximum and minimum of f(x) = −x3 + 3x2 on [−1, 3]- A) 0 and x = −3
- B) 0 and x = 3
- C) x = 3
- D) 0
13 Question 13
Solve Rolle's theorem for f(x) = x2 − 4x on [0, 4]- A) c = 4
- B) c = 6
- C) c = 2
- D) c = 0
14 Question 14
Solve Rolle's theorem for f(x) = x3 − x on [0, 1]Type the answer.
15 Question 15
Concavity and inflection points of f(x) = x3 − 3x2Type the answer.
16 Question 16
Inflection points of f(x) = x4 + 4x3Type the answer.
17 Question 17
Two positive numbers multiply to 64. Find the smallest possible sum.- A) 16
- B) 1
- C) 64
18 Question 18
An open box with a square base must hold 108 cm³. Find the least material needed.Type the answer.
19 Question 19
Find the limit as x -> 0 of sin(x)/x.- A) 0
- B) −1
- C) 1
20 Question 20
Find the limit as x -> 0 of (1 − cos(2x))/x2.Type the answer.
21 Question 21
Use Newton's method on x2 − 2 = 0 starting at x = 1- A) root ≈ 14.1667
- B) root ≈ −1
- C) root ≈ 1.41667
- D) root ≈ 2
22 Question 22
Estimate √3 with Newton's method from x = 2, 3 stepsType the answer.
23 Question 23
f′(x) = 2x, f(0) = 4, find f(x)Type the answer.
24 Question 24
dy/dx = 6x2 − 6x + 5, y = 1 when x = 0, find yType the answer.
25 Question 25
Find d/dx ∫ from 1 to x of (t2 + 1) dtType the answer.
26 Question 26
Find d/dx ∫ from 0 to 2x of et dtType the answer.
27 Question 27
Find the average value of f(x) = 2x + 1 on [0, 4].Type the answer.
28 Question 28
Average value of f(x) = x2 on [0, 3], and find cType the answer.
29 Question 29
Water flows into a tank at r(t) = 4t + 5 litres per minute. How much flows in from t = 0 to t = 4?Type the answer.
30 Question 30
V(t) = t2 − 2t ms from t = 1 to t = 4. Find the displacement and the total distance.Type the answer.