Calculus Practice Test
40 questions from 20 lessons · 120 minutes · percent score and grade · step-by-step answers
How it works
- 40 questions, about 120 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 10 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 formula sheet.
1 Question 1
Find the limit of x2 − 4x − 2 as x -> 2 using a table.- A) 4.1
- B) 3.99
- C) 4
- D) 3.9
2 Question 2
Find the limit of x2 + 3x − 10x + 5 as x -> −5 using a table.Type the answer.
3 Question 3
Find lim x->3 (x2 + 2x − 1)Type the answer.
4 Question 4
Find the limit as x -> −2 of x2 + 5x + 6x2 − 4.Type the answer.
5 Question 5
Find lim x->4 √x − 2x − 4- A) 14
- B) 1
- C) −14
- D) 0
6 Question 6
Find lim x->6 (x − 6)/(2 − √(x − 2))Type the answer.
7 Question 7
Solve f(x) = x + 1 for x < 2, 5 − x for x >= 2, limit as x -> 2Type the answer.
8 Question 8
Solve f(x) = x2 + 2x for x < 1, 5 − 2x for x >= 1, limit as x -> 1Type the answer.
9 Question 9
Find the limit as x -> infinity of 3x2 + 1x2 − 4.- A) −3
- B) −14
- C) 3
10 Question 10
Find the limit as x -> infinity of 9x2 − 43x2 + 2x.Type the answer.
11 Question 11
Is f(x) = x2 − 3 continuous at x = 2- A) 1
- B) −2
- C) 2
12 Question 12
Solve f(x) = x2 + 2x for x < 1, x + 2 for x >= 1, continuous at x = 1Type the answer.
13 Question 13
Find the derivative of x2 from the definition.Type the answer.
14 Question 14
Find the derivative of 4x2 − 8x + 1 from the definition.Type the answer.
15 Question 15
Find the derivative of x5.Type the answer.
16 Question 16
Find the derivative of 2√x + 3x.Type the answer.
17 Question 17
Find the derivative of (x2 + 1)(3x − 2).- A) 9x2 + 4x + 3
- B) 6x
- C) 9x2 − 4x + 3
18 Question 18
Find the derivative of (5 − x)(x2 + 2).Type the answer.
19 Question 19
Find the derivative of (3x + 1)4.Type the answer.
20 Question 20
Find the derivative of 2/(x2 + 4).Type the answer.
21 Question 21
Find the derivative of ex + x2.Type the answer.
22 Question 22
Find the derivative of ln(2x + 5).Type the answer.
23 Question 23
x2 + y2 = 25, find dy/dxType the answer.
24 Question 24
Xy + y2 = 12, find dy/dxType the answer.
25 Question 25
A 10 ft ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?- A) 64 ft/s
- B) 0 ft/s
- C) 1.5 ft/s
- D) −1.5 ft/s
26 Question 26
A 20 m ladder leans against a wall. The bottom slides away at 1 m/s. How fast is the top sliding down when the bottom is 16 m from the wall?Type the answer.
27 Question 27
Tangent line to y = x2 at x = 1Type the answer.
28 Question 28
Tangent line to y = x2 + 3x − 1 at x = −1Type the answer.
29 Question 29
Turning points of f(x) = x3- A) Yes
- B) No
30 Question 30
Two numbers add up to 14. Find the largest product.- A) 0
- B) 14
- C) 7
- D) 49
31 Question 31
Integrate ∫ 3x2 dxType the answer.
32 Question 32
Integrate ∫ (2x5 − x2) dxType the answer.
33 Question 33
Evaluate ∫ from 1 to 3 of (2x + 1) dxType the answer.
34 Question 34
Find the area between y = −x2 + 4x and the x-axis.Type the answer.
35 Question 35
Integrate ∫ 2x(x2 + 1)3 dxType the answer.
36 Question 36
Integrate ∫ from 1 to 2 of 3x2(x3 − 1)2 dxType the answer.
37 Question 37
Estimate the area under y = x2 from x = 0 to x = 3 with 3 left rectangles- A) 4 square units
- B) 5 square units
- C) 1 square units
- D) 0 square units
38 Question 38
Estimate the area under y = 2x2 from x = 0 to x = 2 with 4 left rectanglesType the answer.
39 Question 39
Find the area between y = x2 − 4x and the x-axis.- A) area = 323 square units
- B) area = 0 square units
- C) area = 4 square units
- D) area = −323 square units
40 Question 40
Find the area between y = x2 − 5x + 4 and the x-axis from x = 1 to x = 3.Type the answer.