Free Printable BC Unit 6 Test Review

1.

a)

A

b)

B

c)

C

d)

E

2.

a)

A

b)

B

c)

C

d)

D

3.

a)

B

b)

C

c)

D

d)

E

4.

a)

A

b)

B

c)

D

d)

E

5.

a)

A

b)

C

c)

D

d)

E

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

B

b)

C

c)

D

d)

E

8.

a)

A

b)

B

c)

C

d)

E

9.

Find the antiderivative of
x²

a)

(1/3)x³+C

b)

x³

c)

(1/3)x³

d)

2x

10.

Find the antiderivative of
4x-7

a)

4 +C

b)

2x²-7x+C

c)

x²-7x + C

d)

8x²+ C

11.

What is an antiderivative?

a)

The opposite of a derivative

b)

The same as a derivative

c)

A second derivative

d)

It always represents velocity.

12.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

13.

Find the antiderivative of
(1/3)x³-5x

a)

(1/12)x⁴-(5/2)x²+C

b)

(1/4)x⁴-(1/2)x²+C

c)

(1/12)x³-(5)x²+C

d)

(12)x⁴-(5)x²+C

14.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

15.

INTEGRATE

a)

A

b)

B

c)

C

d)

D

16.

∫ 6 x (x² +1 )² dx

a)

( x² + 1)³ + C

b)

3 ( x² + 1)³ + C

c)

( x² + 1)¹ + C

d)

6 ( x² + 1)³ + C

17.

∫ 2x cos(x²) dx

a)

sin(x²) + C

b)

2 sin ( 2x ) + C

c)

(1/2) sin(x²) + C

d)

4 cos(2x ) + C

18.

a)

ln(2x²+6) + C

b)

ln(2x²+6)(4x) + C

c)

1/(2x²+6) + C

d)

1/(2x²+6)²+ C

19.

What should be used for u in the integral?

a)

no u needed

b)

4t²

c)

t³

d)

1/4t²

20.

What should be assigned to u in the integral?

a)

2x²

b)

sin (2x²)

c)

5x

d)

no u needed

21.

∫ 2 x (x²- 3)^(1/2) dx

a)

(x²- 3)^(3/2⁾+C

b)

(3/2)(x²- 3)^(3/2)+C

c)

(2/3)(x²- 3)^(3/2)+C

d)

(2/3)(x²- 3)^(-1/2)+C

22.

∫ x (x² + 7 )^(1/3) dx

a)

(3/4) ( x²+ 7 )^(4/3) + C

b)

(3/8) ( x²+ 7 )^(4/3) + C

c)

( x²+ 7 )^(4/3) + C

d)

(3/2) ( x²+ 7 )^(4/3) + C

23.

∫ g ' ( x ) f (u) dx, u = g ( x )

a)

∫ f ( u ) du

b)

g ( x ) + C

c)

( 1/ g ( x ) ) g ( x)⁴ + C

d)

cannot be determined

24.

Solve for u-substitution: ∫x(x²-2)¹⁵ dx

a)

((x²-2)¹⁶)/32 + C

b)

(x²-2)¹⁶ + C

c)

(x³-3)¹⁵ + C

25.

What is the choice of u for ∫ e^x(1+e^x)^(1/2) dx?

a)

e^x

b)

1+e^x

c)

(1+e^x)^(1/2)

d)

(e^x)^(1/2)

26.

What should "du" equal in this integral?

a)

tanxsecx dx

b)

secx dx

c)

sec²x dx

d)

tanx dx

27.

What should "u" equal in this integral?

a)

x

b)

(lnx)/x

c)

lnx

d)

sin(lnx)

28.

What is the Integration by Parts Formula?

a)

b)

c)

d)

29.

What would you choose for your u here if you used integration by parts?

a)

t

b)

3t

c)

e^2t

d)

e^t

e)

don't use IBP, let u = 2t

30.

Evaluate the indefinite integral using integration by parts.
$\int3x\ e^{2x}\ dx\$

a)

$-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$

b)

$\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$

c)

$xe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C$

d)

$-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$

31.

Evaluate the indefinite integral using integration by parts.
$\int t^2\ln t\ dt\$

a)

$\frac{2t^2\ln2t-t^2}{4}+C$

b)

$\frac{t^3\ \ln3}{3}-\frac{t^3}{9}+C$

c)

$\frac{e^t}{2t+2}+C$

d)

$\frac{-2t-1}{4e^{2t}}+C$

32.

Evaluate the indefinite integral using integration by parts. u and v' are provided.
$\int x^{4\ }\ln x\ dx\ ;\ \ u=\ln x,\ v\ '=x^4$

a)

$\frac{e^x}{4x+4}+C$

b)

$\frac{2x^{\frac{3}{2}}\ln4x}{3}-\frac{4x^{\frac{3}{2}}}{9}+C$

c)

$\frac{\left(4x^2-1\right)\cdot e^{4x^2}}{32}+C$

d)

$\frac{x^5\ln x}{5}-\frac{x^5}{25}+C$

33.

Evaluate the indefinite integral using integration by parts. u and v ' are provided.
$\int t\sin t\ dt\ ;\ \ \ u=t,\ v\ '=\sin t\$

a)

$t\cos^{-1}t-\left(1-t^2\right)^{\frac{1}{2}}+C$

b)

$-t\cos t+\sin t+C$

c)

$t\sin^{-1}t+\left(1-t^2\right)^{\frac{1}{2}}+C$

d)

$t\sin t+\cos t+C$

34.

What would you choose for your u here if you used integration by parts?

a)

x

b)

sin(x)

c)

cos(x)

d)

e^x

35.

What method would you use here?

a)

antiderivative rules.

b)

u-substitution

c)

integration by parts

d)

Stare at the question... forever.

36.

What would you choose for your u here if you used integration by parts?

a)

x

b)

x⁴

c)

e^-x

d)

e^x

37.

Use substitution to evaluate the integral $\int4\sec^24x\ \sqrt{\tan4x}\ dx$

a)

$2\left(\tan4x\right)^{\frac{3}{2}}+c$

b)

$\frac{15}{4}\left(\tan4x\right)^{\frac{4}{3}}+c$

c)

$\frac{4}{3}\left(\tan4x\right)^{\frac{3}{2}}+c$

d)

$\frac{2}{3}\left(\tan4x\right)^{\frac{3}{2}}+c$

38.

Break this into partial fractions.

a)

b)

c)

d)

39.

$\int_{ }^{ }\frac{3x+2}{x^2-1}dx$

a)

$\ln\left|x^2-1\right|+c$

b)

$\frac{1}{2}\ln\left|x+1\right|+\frac{5}{2}\ln\left|x-1\right|+c$

c)

$\frac{3}{2}\ln\left|x+1\right|+\frac{1}{2}\ln\left|x-1\right|+c$

d)

$\frac{5}{2}\ln\left|x+1\right|+\frac{1}{2}\ln\left|\left(x-1\right)^2\right|+c$

40.

$\int_{ }^{ }\frac{1}{x^2+2x-15}dx$

a)

$\frac{1}{8}\ln\left|\frac{x-3}{x+5}\right|+C$

b)

$\frac{1}{4}\ln\left|\frac{x-3}{x+5}\right|+C$

c)

$\frac{1}{8}\ln\left|\frac{x+3}{x-5}\right|+C$

d)

$\frac{1}{4}\ln\left|\frac{x+3}{x-5}\right|+C$

41.

We're interested in calculating the area under the curve for x between -6 and 6. Order the areas from LEAST to GREATEST.

a)

left-hand, right-hand, midpoint

b)

right-hand, left-hand, midpoint

c)

right-hand, midpoint, left-hand

d)

left-hand, midpoint, right-hand

42.

What kind of Riemann sum is described by the diagram?

a)

Left-hand

b)

Right-hand

c)

Midpoint

43.

What is the correct description of the subdivisions in the Riemann sum?

a)

five uniform subdivisions

b)

five nonuniform subdivisions

c)

six uniform subdivisions

d)

six nonuniform subdivisions

44.

Approximate the area under y=h(x) from x=-2 to x=4 using a Right-hand sum and three equal subdivision

a)

20 units²

b)

26.5 units²

c)

28 units²

45.

What method would you use here?

a)

inverse trig

b)

u-substitution

c)

integration by parts

d)

partial fractions

46.

What method would you use here?

a)

antiderivatives

b)

u-substitution

c)

integration by parts

d)

slope fields

47.

$\int5x^4\left(x^5-7\right)^3dx$ can be solved by

a)

integration by parts

b)

u-substitution

c)

partial fractions

d)

natural log pattern

48.

Which technique should be used to integrate this:

a)

natural log pattern

b)

u-substitution

c)

integration by parts

d)

partial fractions

49.

Find the partial fraction decomposition...

a)

b)

c)

d)

50.

$\int\ \frac{dx}{4+9x^{2\ }\ }$ can be solved by

a)

natural log pattern

b)

inverse trig integration

c)

partial fractions

d)

u-substitution

51.

$\int\ \frac{x^2}{x^2-x+1}dx$ must be solved by first

a)

completing the square

b)

finding the partial fractions

c)

using u-substitution

d)

performing long division

52.

$\int\ \frac{3x-1}{x^2+1}dx$ can be solved by first

a)

using inverse trig

b)

separating the integral into two fractions

c)

completing the square in the denominator

d)

using the natural log pattern

53.

What does this picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

54.

What does picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

55.

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

a)

Overestimate

b)

Underestimate

c)

Exact Solution

d)

Unable to Determine

56.

For a function that is strictly increasing, a right hand Riemann Sum is which of the following:

a)

Overestimate

b)

Underestimate

c)

Unable to Determine

d)

Exact Solution

57.

For a function that is strictly decreasing, a trapezoidal approximation will be which of the following:

a)

Underestimate

b)

Overestimate

c)

Exact Solution

d)

Unable to Determine

58.

Based on the table, use a left Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

59.

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

a)

14

b)

7

c)

26

d)

11

60.

Find the Left-hand Riemann Sum, with three sub-intervals indicated by the table.

a)

28

b)

16

c)

34

d)

23

61.

Find the area under the curve y =3x²-2x from x= 1 to x =5.

a)

100

b)

99

c)

150

d)

152

62.

a)

Distance

b)

Displacement

c)

Velocity

d)

Acceleration

63.

Use 3 trapezoids to determine the approximate area of the shaded area.

a)

12

b)

9

c)

10

d)

5

64.

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve.

a)

32.5

b)

40.5

c)

78

d)

160

65.

Determine $\int_0^8x^2dx$ using an estimate of 4 equivalent based trapezoids

a)

176

b)

352

c)

420

d)

488

66.

If $\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^5\ f\left(x\right)dx.$

a)

$-\pi$

b)

$0$

c)

$-0$

d)

$\pi$

67.

$If\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^4\ f\left(x\right)dx.$

a)

$0$

b)

$-1$

c)

$-\pi$

d)

$\pi$

68.

$\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_2^4\ f\left(x\right)dx.$ If

a)

$\pi-5$

b)

$2$

c)

$5-\pi$

d)

$-\left(5-\pi\right)$

69.

∫₀²⁰C(n)dn =

a)

1000

b)

250

c)

750

d)

1125

70.

∫₄¹⁰f(x)dx =

a)

2π + 3

b)

4π + 3

c)

2π - 3

d)

π - 3

71.

$\int_2^5\left(x^3+3\right)dx$ as limit of a sum is equivalent to

a)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\cdot\frac{1}{n}$

b)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{3i}{n}\right)^3+3\right]\cdot\frac{3}{n}$

c)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\cdot\frac{3i}{n}$

d)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(2+\frac{3i}{n}\right)^3+3\right]\cdot\frac{3}{n}$

72.

$\int_0^{\pi}\cos xdx$ as limit of a sum is equivalent to

a)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\cdot\frac{i}{n}$

b)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\cdot\frac{i}{n}$

c)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{\pi i}{n}\right)\right]\cdot\frac{\pi}{n}$

d)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\cos\left(\frac{i}{n}\right)\right]\cdot\frac{\pi}{n}$

73.

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\left[\left(\frac{5i}{n}\right)^2+\frac{5i}{n}+1\right]\cdot\frac{5}{n}$ in integral notation would be

a)

$\int_0^5\left(x^2+x+1\right)dx$

b)

$\int_5^6\left(x^2+x+1\right)dx$

c)

$\int_0^1\left(\left(5x\right)^2+5x+1\right)dx$

d)

$\int_0^{10}\left(\frac{x^2}{2}+\frac{x}{2}+1\right)dx$

74.

a)

1 ⁄ (1+x³)

b)

(3x²) ⁄ (1+x³)

c)

x³ ⁄ (1+x³)

d)

HELP

75.

a)

-cos(x⁶)

b)

sin(x⁶)

c)

2x sin(x³)

d)

2x sin(x⁶)

76.

a)

-8x cos(8x²)

b)

-8x sin(8x²)

c)

8x cos(8x²)

d)

8x sin(8x²)

77.

Find the antiderivative of

f'(x) = x² when f(3) = 11.

a)

(1/3)x³+ 2

b)

x³ + 29

c)

(1/3)x³ + 9

d)

x³ + 11

78.

a)

10

b)

20

c)

23

d)

35

BC Unit 6 Test Review

Total questions: 78

Worksheet time: 4hrs 32mins

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