Free Printable Baldi's Math Quiz: 39. Calculus Summary

1.

a)

330

b)

165

c)

190

d)

255

2.

a)

9

b)

2

c)

3

d)

6

3.

a)

2

b)

3

c)

1

d)

4

4.

a)

{1/3,-1}

b)

{1/3,1}

c)

{-1/3,-1}

d)

{-1/3,1}

5.

a)

[0,1/2]u[1,infinity]

b)

[-1,1/2]u[1,infinity]

c)

[0,infinity]

d)

[-1/2,0]u[1,infinity]

6.

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50cm^3/min. When the thickness of the ice is 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is

a)

$\frac{1}{9\pi}$

b)

$\frac{1}{18\pi}$

c)

$\frac{1}{36\pi}$

d)

$\frac{5}{6\pi}$

7.

a)

6

b)

4

c)

2

d)

0

8.

a)

four rational numbers

b)

two irrational and two rational numbers

c)

four irrational numbers

d)

two irrational and one rational number

9.

a)

-1

b)

1

c)

5/2

d)

-5/2

10.

a)

(-1/5,1)

b)

(1/5,0)

c)

(1/5,-1)

d)

(-1/5,-1)

11.

a)

$-\pi$

b)

$-2\pi$

c)

$\pi$

d)

$2\pi$

12.

a)

( $\sqrt[]{-2}$ ,0 )

b)

( $\sqrt[]{2}$ ,0 )

c)

( $\sqrt[]{-2}$ ,0 )

d)

( $\sqrt[]{-2}$ , $\sqrt[]{2}$ )

13.

a)

3

b)

6

c)

9

d)

15

14.

a)

5

b)

4

c)

3

d)

2

15.

a)

1/4

b)

1/2

c)

1

d)

1/16

16.

a)

b)

c)

d)

17.

a)

b)

c)

d)

18.

The function f is continuous on the closed interval [0,6] and has values given in the table above. The trapezoidal approximation found with 3 subintervals is 52. What is the value of k?

a)

2

b)

6

c)

7

d)

10

19.

A particle moves along an axis so that at any time t>0, its velocity is given by v(t)=4-6t². If the particle is at position p=7 at t=1, what is the position of the particle at t=2?

a)

-10

b)

-5

c)

-3

d)

3

20.

a)

6

b)

ln 25

c)

2

d)

5+ 2/e

21.

a)

b)

c)

d)

22.

What is the area of the region enclosed by the graphs of f(x)=x-2x² and g(x)=-5x?

a)

7/3

b)

16/3

c)

20/3

d)

9

23.

The velocity of a particle moving along an axis is given by v(t)=2-t² for t>0, what is the average velocity of the particle from t=1 to t=3?

a)

-4

b)

-3

c)

8/3

d)

- 7/3

24.

a)

10

b)

20

c)

23

d)

35

25.

a)

b)

c)

d)

26.

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

a)

$x-\frac{1}{2}\sin2x+C$

b)

$x-\frac{1}{2}\cos2x+C$

c)

$\frac{x}{2}-\frac{1}{4}\sin2x+C$

d)

$\frac{x}{2}-\frac{1}{4}\cos2x+C$

27.

Using the substitution $u=\frac{1}{x}$ , what is the value of the definite integral $\int_{\frac{1}{2}}^1\ \frac{e^{\frac{1}{x^2}}}{x^3}\ dx$ ?

a)

$e\left(1-e\right)$

b)

$\frac{e\left(e^3-1\right)}{2}$

c)

$\frac{e^4-1}{4}$

d)

$\frac{e\left(e^2-1\right)}{4}$

28.

Using the substitution $u=x^3+4\ ,$ which of the following is the primitive of $\frac{x^2}{\sqrt[]{x^3+4}}$ ?

a)

$\frac{2}{3}x^2\sqrt[]{x^3+4}$

b)

$\frac{2}{3}\sqrt[]{x^3+4}$

c)

$\frac{2}{3\ \sqrt[]{x^3+4}}$

d)

$\frac{1}{6}\ \sqrt[]{x^3+4}$

29.

Using the substitution $u=\ln x\ ,$ which of the following is a primitive of $\frac{\left(\ln x\right)^2}{x}$ ?

a)

$\frac{x\left(\ln x\right)^3}{3}$

b)

$\frac{\left(\ln x\right)^3}{3x}$

c)

$\left(\ln x\right)^3$

d)

$\frac{\left(\ln x\right)^3}{3}$

30.

What is the integral $\int_1^2\ x\ \sqrt[]{2-x}\ dx$ transformed to by the substitution $u=\sqrt[]{2-x}$ ?

a)

$\int_1^2\left(2u-u^3\right)\ du$

b)

$\int_1^0\left(2u-u^3\right)\ du$

c)

$\int_1^2\left(4u^2-2u^4\right)\ du$

d)

$\int_0^1\left(4u^2-2u^4\right)\ du$

31.

What is the integral $\int_0^1\ \frac{1}{\left(4-x^2\right)^{\frac{3}{2}}}\ dx$ transformed to by the substitution $x=2\sin\theta$ ?

a)

$\int_0^{\frac{\pi}{3}}\sec^2\theta\ d\theta$

b)

$\frac{1}{2}\int_0^{\frac{\pi}{6}}\sec^3\theta\ d\theta$

c)

$\frac{1}{4}\int_0^{\frac{\pi}{6}}\sec^2\theta\ d\theta$

d)

$\frac{1}{8}\int_0^{\frac{\pi}{3}}\sec^3\theta\ d\theta$

32.

What is the exact area of the region bounded by the curve $y=\frac{\cos x}{1+\sin^2x}\ ,$ the line $x=0$ and the line $x=\frac{\pi}{2}$ ? (Use the substitution $u=\sin x$ )

a)

$\frac{\pi}{4}$ square units

b)

$\frac{\pi}{2}$ square units

c)

$\pi$ square units

d)

$1$ square unit

33.

The region between the curve $y=e^{2x}$ and the x-axis from $x=0$ to $x=1$ is rotated about the x-axis. What is the volume of the solid generated?

a)

$\frac{\pi}{2}\left(e^2-1\right)$ cubic units

b)

$\frac{\pi}{4}\left(e^2-1\right)$ cubic units

c)

$\frac{\pi}{2}\left(e^4-1\right)$ cubic units

d)

$\frac{\pi}{4}\left(e^4-1\right)$ cubic units

34.

A champagne flute is designed by rotating the curve $y=2+2\sin\frac{x}{2}$ from $x=\pi$ to $x=3\pi$ about the x-axis. What is the capacity of the flute?

a)

$12\pi$ cubic units

b)

$12\pi^2$ cubic units

c)

$24\pi$ cubic units

d)

$24\pi^2$ cubic units

35.

A rubber washer is generated by rotating the region between the curve $y=\log_e2x\ ,$ the x-axis and the line $x=2$ about the y-axis.

What is the exact volume of the washer?

a)

$\frac{\pi}{2}\left(8\log_e4-11\right)$ cubic units

b)

$\frac{\pi}{4}\left(16\log_e4-11\right)$ cubic units

c)

$\frac{\pi}{8}\left(32\log_e4-15\right)$ cubic units

d)

$\frac{\pi}{16}\left(64\log_e4-15\right)$ cubic units

36.

Find the gradient of the tangent to $y=\frac{x^3}{x^2-1}$ at x = 2.

a)

$\frac{3}{5}$

b)

$\frac{4}{9}$

c)

$\frac{1}{3}$

d)

$\frac{2}{9}$

37.

Find the derivative of $y=\log_2x+\log_3\left(x^3\right)$

a)

$\frac{\ln24}{x\ln2\ln3}$

b)

$\frac{1}{x\ln2}$

c)

$\frac{\ln2}{x\ln2\ln3}$

d)

$\frac{3}{x\ln3}$

38.

Consider $g\left(x\right)=3-2\cos2x$ . Find $g'\left(x\right)$ .

a)

4sinx

b)

3sin2x

c)

4sin2x

d)

3sinx

39.

Inflexion points occur when the graph changes from concave down to concave up or vice versa.

a)

false

b)

true

40.

Let g(x) = -xcosx and find g'(x).

a)

-cosx-xsinx

b)

cosx-sinx

c)

-cosx+xsinx

d)

-cosx+sinx

41.

Consider the curves $y=\sqrt[]{3x+1}$ and $y=\sqrt[]{5x-x^2}$ . Find the point of intersection.

a)

(1,3)

b)

(1,2)

c)

(3,5)

d)

(3,1)

42.

Consider the curve $y=\frac{a}{x}-x^2+1$ . The gradient of the tangent to the curve is -5 when x = 2. Find the value of a.

a)

1

b)

4

c)

3

d)

5

43.

Find the gradient of the tangent to $f\left(x\right)=\cos^4x$ at the point where $x=\frac{3\pi}{4}$ .

a)

4

b)

3

c)

0.5

d)

1

44.

Find $f'\left(t\right)$ if $f\left(t\right)=\frac{t+9}{e^t}$ .

a)

$\frac{-t-8}{e^t}$

b)

$\frac{-t+8}{e^t}$

c)

$\frac{t+8}{e^t-8t}$

d)

$\frac{-t-8}{8t-e^t}$

45.

Given $f\left(x\right)=e^{ax+2}+x^2$ and $f\left(2\right)=f'\left(2\right)$ . Find a

a)

1.5

b)

3

c)

2

d)

1

Baldi's Math Quiz: 39. Calculus Summary

Total questions: 45

Worksheet time: 4hrs 45mins

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