Quiz about AB Calculus Practice Exam

Question 1

1. $$\int_{-1}^3(x^2-2x)dx=$$

Accepted Answer

$$\frac{4}{3}$$

Answer

$$-\frac{2}{3}$$

Answer

8

Answer

12

Question 2

If f(x) = $$e^{2x}\left(x^3+1\right)$$ , then f'(2) =

Accepted Answer

$$30e^4$$

Answer

$$6e^4$$

Answer

$$21e^4$$

Answer

$$24e^4$$

Question 3

Let f be a differentiable function such that $$f\left(2\right)=4$$ and $$f$$ What is the approximation for f(2.1) found by using the line tangent to the graph of f at x = 2?

Accepted Answer

3.95

Answer

2.95

Answer

4.05

Answer

4.1

Question 4

Let g be the function defined by g(x) = $$x^4 + 4x^3$$ . How many relative extrema does g have?

Accepted Answer

One

Answer

Zero

Answer

Two

Answer

Three

Question 5

The velocity of a particle moving along the x-axis is given by $$v(t) = 2 - t^2$$ for time t > 0. What is the average velocity of the particle from time t = 1 to time t = 3?

Accepted Answer

$$-\frac{7}{3}$$

Answer

-4

Answer

-3

Answer

$$\frac{7}{3}$$

Question 6

On a certain day, the rate at which material is deposited at a recycling center is modeled by the function R, where R(t) is measured in tons per hour and t is the number of hours since the center opened. Using a trapezoidal sum with the three subintervals indicated by the data in the table, what is the approximate number of tons of material deposited in the first 9 hours since the center opened?

Accepted Answer

68

Answer

70.5

Answer

85

Answer

136

Question 7

I DO

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 8

Let g be a continuous function. Using the substitution u = 2x - 1, the integral $$\int_2^3g(2x-1)dx$$ is equal to which of the following?

Accepted Answer

$$\frac{1}{2}\int_3^5g(u)du$$

Answer

$$\int_2^3g(u)du$$

Answer

$$\frac{1}{2}\int_2^3g(u)du$$

Answer

$$\int_3^5g(u)du$$

Question 9

The graph of y = f(x) consists of a semicircle with endpoints at (2, -6) and (12, -6) as shown in the figure. What is the value of $$\int_{2}^{12} f(x) dx$$ ?

Accepted Answer

-60 + $$\frac{25\pi}{2}$$

Answer

$$-\frac{25\pi}{2}$$

Answer

$$\frac{25\pi}{2}$$

Answer

60 - $$\frac{25\pi}{2}$$

Question 10

An object moves along a straight line so that at any time t its acceleration is given by a(t) = 6t. At time t = 0, the object's velocity is 10 and the object's position is 7. What is the object's position at time t = 2?

Accepted Answer

35

Answer

22

Answer

27

Answer

28

Question 11

If y = $$cos x - ln (2x)$$ , then $$\frac{d^3y}{dx^3}$$ = ?

Accepted Answer

$$sin x - \frac{2}{x^3}$$

Answer

$$-sin x - 2/x^3$$

Answer

sin x $$- \frac{1}{x^3}$$

Answer

$$-sin x - \frac{1}{x^3}$$

Question 12

Let f be the function defined above, where c is a constant. If f is continuous at x = 1, what is the value of c?

Accepted Answer

3

Answer

2

Answer

5

Answer

9

Question 13

Which of the following could be a slope field for the differential equation $$\frac{dy}{dx} = x^2 + y$$ ?

Accepted Answer

(D)

Answer

(A)

Answer

(B)

Answer

(C)

Question 14

I DO

The function y = $$\sin x$$ is a solution to which of the following differential equations?

Accepted Answer

y'' + y = 0

Answer

y'' - y' = 0

Answer

y'' - y = 0

Answer

y'' + y' = 0

Question 15

The function y = $$e^{3x}-5x+7$$ is a solution to which of the following differential equations?

Accepted Answer

y'' - 3y' - 15 = 0

Answer

y'' - 3y' + 15 = 0

Answer

y'' - y' - 5 = 0

Answer

y'' - y' + 5= 0

Question 16

If f(x) = $$sin^{-1} x$$ , then $$f$$ ?

Accepted Answer

2

Answer

$$\frac{\pi}{6}$$

Answer

$$\frac{\pi}{3}$$

Answer

$$\frac{4}{7}$$

Question 17

$$\lim_{x o e} \frac{(x^{20} - 3x) - (e^{20} - 3e)}{x - e}$$ is

Accepted Answer

$$20e^{19} - 3$$

Answer

0

Answer

$$e^{20} - 3e$$

Answer

nonexistent

Question 18

Let y = f(x) be a twice-differentiable function such that f(1) = 2 and $$\frac{dy}{dx} = y^3 + 3$$ . What is the value of $$\frac{d^2y}{dx^2}$$

Accepted Answer

132

Answer

12

Answer

66

Answer

165

Question 19

Let y = f(x) be the particular solution to the differential equation $$\frac{dy}{dx} = \frac{x+1}{y}$$ with the initial condition f(0) = -2. Which of the following is an expression for f(x)?

Accepted Answer

$$-\sqrt{x^2 + 2x + 4}$$

Answer

$$-2-\sqrt{x^2+2x}$$

Answer

$$-2+\sqrt{x^2+2x}$$

Answer

$$\sqrt{x^2 + 2x + 4}$$

Question 20

$$\lim_{x o 3} \frac{ an(x-3)}{3e^{x-3} - x}$$ is

Accepted Answer

$$\frac{1}{2}$$

Answer

0

Answer

$$\frac{1}{3}$$

Answer

nonexistent

Question 21

$$\int_{1}^{2} \frac{x^2 - x - 5}{x + 2} \, dx =$$

Accepted Answer

$$-\frac{3}{2}+\ln\frac{4}{3}$$

Answer

$$-\frac{25}{21}$$

Answer

$$\frac{5}{2} + 3 \ln \frac{3}{4}$$

Answer

$$\frac{23}{45}$$

Question 22

Which of the following limits is equal to $$\int_{2}^{5} x^2 \, dx$$ ?

Accepted Answer

$$\lim_{n o \infty} \sum_{k=1}^{n} \left[2 + \frac{3k}{n} ight]^2 \frac{3}{n}$$

Answer

$$\lim_{n o \infty} \sum_{k=1}^{n} \left[2 + \frac{k}{n} ight]^2 \frac{1}{n}$$

Answer

$$\lim_{n o \infty} \sum_{k=1}^{n} \left[2 + \frac{k}{n} ight]^2 \frac{3}{n}$$

Answer

$$\lim_{n o \infty} \sum_{k=1}^{n} \left[2 + \frac{3k}{n} ight]^2 \frac{1}{n}$$

AB Calculus Practice Exam

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