Free Printable IM1 Chapter 5 Review

1.

Simplify.
$y^{-2}$

a)

$\frac{4}{y^2}$

b)

$\frac{y}{2}$

c)

$\frac{2}{y}$

d)

$\frac{1}{y^2}$

2.

Simplify.
$4y^{-4}$

a)

$\frac{4}{y^4}$

b)

$\frac{4}{y}$

c)

$\frac{y^4}{4}$

d)

$\frac{1}{4y^4}$

3.

Simplify.
$x^{-3}y^0$

a)

$\frac{y}{x^3}$

b)

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

c)

$\frac{x}{y}$

d)

$\frac{1}{3y}$

4.

Simplify.
$xy^{-1}$

a)

$\frac{1}{xy}$

b)

$\frac{x}{y}$

c)

$\frac{y}{x}$

d)

$\frac{1}{x}$

5.

Simplify.
$x^4y^{-2}$

a)

$\frac{y^2}{x^4}$

b)

$\frac{2}{xy}$

c)

$\frac{x^4}{y^2}$

d)

$\frac{2x^4}{y}$

6.

Simplify.
$3x^{-3}y^0$

a)

$\frac{3x^3}{y}$

b)

$\frac{y}{3x^3}$

c)

$\frac{3}{x^3}$

d)

$x^3$

7.

Simplify.
$4x^3y^{-4}$

a)

$\frac{4x^3}{y^4}$

b)

$\frac{x^3}{4y}$

c)

$\frac{1}{4x^3}$

d)

$\frac{4}{x^3}$

8.

Simplify.
$4x^{-1}y^0$

a)

$\frac{1}{x^4}$

b)

$4x$

c)

$\frac{4}{xy}$

d)

$\frac{4}{x}$

9.

Simplify.
$2x^{-4}y^3$

a)

$\frac{2y^3}{x^4}$

b)

$\frac{x^4}{2y^3}$

c)

$\frac{y^3}{2x^4}$

d)

$\frac{2x^4}{y^3}$

10.

Simplify.
$3x^{-4}y^4$

a)

$\frac{3y^4}{x^4}$

b)

$\frac{3y}{x}$

c)

$\frac{3y^4}{4x}$

d)

$\frac{4y}{x}$

11.

$\frac{x^5}{x^2}$

a)

$x^2$

b)

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

c)

$3x$

d)

$x^3$

12.

$\frac{12x^7}{-3x^2}$

a)

$-4x^9$

b)

$-4x^5$

c)

$\frac{4}{x^5}$

d)

$4x^5$

13.

$\frac{9a^3b^5}{-3ab^2}$

a)

$-3a^3b^3$

b)

$-3a^4b^7$

c)

$12a^2b^3$

d)

$-3a^2b^3$

14.

$\frac{24x^2y}{-4x^2}$

a)

$-6y$

b)

$-6xy$

c)

$28y$

d)

$28xy$

15.

$\frac{49r^8}{-7r^{13}}$

a)

$-7r^5$

b)

$\frac{56}{r^5}$

c)

$-\frac{7}{r^5}$

d)

$-\frac{1}{7r^5}$

16.

$\frac{56cd}{8c^2d^4}$

a)

$7cd^3$

b)

$\frac{7}{cd^3}$

c)

$48cd^3$

d)

$\frac{48}{cd^3}$

17.

$\frac{\left(110c^3\right)\left(c^9\right)}{11c^5}$

a)

$10c^7$

b)

$\frac{10}{c^7}$

c)

$99c^7$

d)

$10c^{22}$

18.

$\frac{\left(3x^3y\right)\left(4x^2y^2\right)}{6x^4y^6}$

a)

$2xy^3$

b)

$6xy^3$

c)

$\frac{2x}{y^3}$

d)

$\frac{6x}{y^3}$

19.

$7x^{-3}$

a)

$7x^3$

b)

$\frac{x^3}{7}$

c)

$\frac{1}{7x^3}$

d)

$\frac{7}{x^3}$

20.

$4c^8d^{-3}\cdot5c^{-5}d^{-1}$

a)

$9c^3d^4$

b)

$\frac{20c^3}{d^4}$

c)

$20c^3d^4$

d)

$\frac{20}{c^3d^4}$

21.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

22.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

23.

You invest $400 for 5 years and the interest rate is 4.29% each year.

a)

y=400(1 - 0.0429)⁵

b)

y=400(1+.0429)⁵

c)

y=400(1+ 4.29)⁵

d)

y=400e^0.049*5

24.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1 + .08)^x

c)

y=15,000(1 - .08)^x

d)

y=15,000(0.08)^x

25.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

26.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

27.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

28.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

29.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

30.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

31.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

32.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

33.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

34.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

35.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

36.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

37.

What does r represent?

a)

Radical

b)

Common difference

c)

Common ratio

38.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

39.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

40.

Is the sequence -432, 72, -12, 2,...geometric?

a)

yes

b)

no

41.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

42.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

43.

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

a)

4

b)

3

c)

2

d)

6

44.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

45.

What is the 14th term of the geometric sequence?

a)

14,348,907

b)

4,782,969

c)

1,594,323

d)

45

46.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

47.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

48.

The rule for finding a_n of a geometric sequence is

a_n = 10(2)^n-1_{What is the common ratio(r) of the sequence?}

a)

²

b)

¹⁰

c)

²⁰

d)

2ⁿ

49.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

50.

What is the 9^th term in a geometric sequence with a common ratio of 2 and a first term of 3?

a)

384

b)

768

c)

1,536

d)

27

51.

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

a)

$10

b)

$300

c)

$162

d)

$416

52.

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

53.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

54.

When f(x) = 4x+8 and
g(x) = x+3, find
f(x) * g(x).

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

55.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

56.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

57.

f(x)=2x+4
g(x)=3x²-1
Find f(x)*g(x)

a)

6x⁴+12x³-4x²-8x

b)

-6x³+12x²+2x-4

c)

6x³+12x²-2x-4

d)

5x²-18x+20

58.

f(x)=x+3
g(x)=x-2
Find (g/f)(x)

a)

(x+3)/(x-2)

b)

(x-2)/(x+3)

c)

-2/3

d)

3/2

59.

h(x) = 3x + 3

g(x) = -4x + 1

Find (h + g)(10)

hint: add h(x) and g(x), then plug in 10

a)

-6

b)

6

c)

82

d)

-72

60.

g(x) = 2x - 5

h(x) = 4x + 5

Find (g - h)(3)

hint: subtract g(x) and h(x), then plug in 3

a)

18

b)

16

c)

-16

d)

28

61.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

62.

√96

a)

4√6

b)

3√6

c)

6√5

d)

6√8

63.

Simplify the following radical: 2√24

a)

4√6

b)

2√6

c)

24√2

d)

4√4

64.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

65.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

66.

Simplify

√45n³

a)

3n√5n

b)

4n√8

c)

4n√-8

d)

10√n

67.

Simplify.

√20a²b⁴

a)

2a²b²√5ab

b)

ab√5

c)

2√5

d)

2ab²√5

68.

a)

A

b)

B

c)

C

d)

D

69.

Rationalize the denominator:
$\frac{2\sqrt{8}}{\sqrt{12x^3}}$

a)

$\frac{\sqrt{96x}}{6x^2}$

b)

$\frac{2\sqrt{6x}}{3x^2}$

c)

$\frac{2x\sqrt{6x}}{3}$

d)

$\frac{4\sqrt{2x}}{2x\sqrt{3}}$

70.

Graph

a)

b)

c)

d)

71.

What is the domain restriction of the blue piece of this function?

a)

x > 0

b)

x ≥ 0

c)

x > 2

d)

x ≥ 2

72.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

73.

Graph

a)

b)

c)

d)

74.

Graph

a)

b)

c)

d)

75.

a)

A

b)

B

c)

C

d)

D

76.

Which of these equations shifts a radical equation left 3 times?

a)

y = √(x) + 3

b)

y = √(x) - 3

c)

y = √(x + 3)

d)

y = √(x - 3)

77.

Which of these equations shifts a radical equation right 5 times and down once?

a)

y = √(x - 5) - 1

b)

y = √(x + 5) - 1

c)

y = √(x - 5) + 1

d)

y = √(x + 5) + 1

78.

Match the correct equation with the given graph.

a)

y = √(x) + 2

b)

y = √(x) - 2

c)

y = √(x + 2)

d)

y = √(x - 2)

79.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

IM1 Chapter 5 Review

Total questions: 79

Worksheet time: 6hrs 47mins

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