Free Printable Spotlight- Precalc Spiral Review

1.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

2.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

3.

Simplify: x⁸/x²

a)

x¹⁶

b)

x⁴

c)

x⁵

d)

x⁶

4.

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

a)

add

b)

subtract

c)

multiply

d)

divide

5.

Identify where the function is positive.

a)

$-7<x<3,\ \ x\ >\ 5$

b)

$x<-7,\ -3<x<5$

c)

$x\ <-7,\ x\ >5$

d)

$-7<x<5$

6.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

7.

Write the following in interval notation
x < 3 or x ≥ 5

a)

(3, -∞) or (∞, 5]

b)

[-∞, 3) or [5, ∞]

c)

(-∞, 3) or [5, ∞)

d)

(3, -∞] or [∞, 5]

8.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

9.

Simplify using your exponent rule(s) x⁵⁄x³

a)

x²

b)

x

c)

1

d)

x⁸

10.

Simplify: x¹⁰⋅x⁴

a)

x⁴⁰

b)

x¹⁴

c)

x⁶

d)

2x¹⁴

11.

Simplify using your exponent rule(s) x⁻⁶

a)

1 ⁄ x⁶

b)

x⁶

c)

-x⁶

d)

-1 ⁄ x⁶

12.

Simplify using your exponent rule(s) -14x⁷/7x

a)

-2x⁶

b)

-2x

c)

-2x⁵

d)

-2x⁸

13.

Simplify using your exponent rule(s) (5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

14.

Rewrite using positive exponents

a)

2⁴

b)

1/2⁴

c)

4²

d)

1/4²

15.

Simplify using your exponent rule(s) (2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

16.

True or False?

a)

True

b)

False

17.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

18.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

19.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

20.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

21.

Factor x²-2x-15

a)

(x+5)(x-3)

b)

(x-5)(x-3)

c)

(x-5)(x+3)

d)

(x+5)(x+3)

22.

Factor x² + 7x + 12

a)

(x + 2)(x + 10)

b)

(x + 3)(x + 4)

c)

(x + 4)(x + 5)

d)

(x + 4)(x + 6)

23.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

24.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

25.

Factor
n² + 5n - 6

a)

(n - 2)(n - 3)

b)

(n - 1)(n + 6)

c)

(n + 1)(n - 6)

d)

(n + 2)(n - 3)

26.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

27.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

28.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

29.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

30.

Factor:
x²-15x + 36

a)

(x - 18)(x + 2)

b)

(x - 12)(x - 3)

c)

(x - 12)(x + 3)

d)

(x + 18)(x - 2)

31.

Factor:
x² - 8x - 128

a)

(x - 16)²

b)

(x - 16)(x + 8)

c)

(x + 16)(x - 8)

d)

(x - 16)(x - 8)

32.

x² + 5x + 6

a)

(x+2)(x+3)

b)

(x+1)(x+6)

c)

(x-1)(x+6)

d)

(x-2)(x-3)

33.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

34.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

35.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

36.

x²- 16

a)

Prime

b)

( x - 4) ( x + 4)

c)

( x - 8) ( x + 8)

d)

( x - 4) ( x - 4)

37.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

38.

Factor the following: $x^2-1$

a)

(x+1)(x +1)

b)

(x - 1)(x - 1)

c)

prime

d)

(x + 1)(x - 1)

39.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

40.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

41.

4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

42.

25x² - 36y²

a)

5x + 6y(5x - 6y)

b)

(5x + 6y) (5x - 6y)

c)

(5x + 6y)²

d)

(5x - 6y)²

43.

x⁴ - 100y²

a)

(x² + 10y) (x² - 10y)

b)

(x + 10y) (x - 10y)

c)

(x + 10y) (x³ - 10y)

d)

(x³ + 10y) (x - 10y)

44.

We can't factor using difference of two square this

49x² + 4y². Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

45.

Factor:

4x + 6

a)

4(x + 2)

b)

2(2x + 3)

c)

2(2x + 4)

d)

4(x + 2/3)

46.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

47.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

48.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

49.

Look at the graph. Write the inequality in interval notation.

a)

(-2,5)

b)

(-∞,-2)⋃(5,∞)

c)

[-2,5]

d)

(-∞,-2]∪[5,∞)

50.

Write the following in interval notation
x < 8

a)

(8, ∞)

b)

(8, -∞)

c)

(-∞, 8)

d)

[-∞, 8]

51.

Simplify: (6m⁷)/(4m³)²

a)

(6m)/16

b)

(3/8)m

c)

3/(8m)

d)

(3m)/4

52.

Write the following in interval notation
x ≥ 100

a)

(0, 100] (Real quick)

b)

(∞, 100]

c)

[100, ∞)

d)

(∞, 100)

53.

Look at the Graph. Write the inequality in interval notation.

a)

[-4, -1)

b)

(-4, -1)

c)

(-4, -1]

d)

[-4, -1]

54.

Look at the picture. Which graph best represents the solution set (-∞, -2) U (5, ∞)?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

55.

On what interval is the graph decreasing?

a)

(∞, 3)

b)

(3, -∞)

c)

(3, ∞)

d)

(-∞, 3)

56.

On which interval is the graph increasing?

a)

[-5,-3]

b)

[-3,-1]

c)

[1,4]

d)

[5,∞)

57.

What is the maximum?

a)

None

b)

(0,4)

c)

(3,1)

d)

y = -1

58.

What is the minimum?

a)

None

b)

(0,4)

c)

(3,1)

d)

y = -1

59.

What is the domain of the function?

a)

(-∞,5]

b)

(-∞,5)

c)

(-∞,2]

d)

(-∞,2)

60.

Where is the function increasing?

a)

(-∞,5]

b)

(-∞,0]

c)

(-∞,2]

d)

[0,2]

61.

Identify where the function is positive.

a)

$x<-5\ \ ,\ \ \ x>0$

b)

$-5<x<0\ \ ,\ \ \ x>6$

c)

$x<-5\ \ ,\ 0<x<6$

d)

$x>-5\ \ ,\ \ \ x<6$

62.

Identify where the function is negative.

a)

$x\ >-3$

b)

All Real Numbers

c)

$-3<x<3$

d)

$x<-3,\ x>3$

63.

Identify where the function is positive.

a)

$-3<x<3$

b)

All Real Numbers

c)

$x<-3,\ \ x>3$

64.

Identify where the function is negative.

a)

$x<-7,\ \ \ x\ >5$

b)

$-7<x<-3,\ \ \ x\ >5$

c)

$x<-7,\ \ \ -3<x<5$

d)

$-7<x<5$

65.

Identify where the function is increasing.

a)

$x\ <-4\ \ \ \ \ ,\ \ \ \ x\ >1$

b)

$-\ 4<x<1$

c)

$-6<x<-2$

d)

$x<-6\ \ \ \ ,\ \ \ x\ >-2$

66.

Identify where the function is decreasing.

a)

x < -5 , x > -1

b)

-5 < x < 1 , x > 8

c)

x < -5 , -1 < x < 8

d)

All Real Numbers

67.

Identify where the function is increasing.

a)

x < 0

b)

x > 0

c)

x < -3 , x > 3

d)

-3 < x < 3

68.

On which interval is the graph decreasing?

a)

[-5,-3]

b)

[-3,-1]

c)

[1,4]

d)

[5,∞)

69.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

70.

What is m(-3) if:

a)

-3

b)

0.5

c)

3

d)

-3.5

71.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

72.

What is f(-1)?

a)

6

b)

-2

c)

sqrt(2)

d)

DNE

73.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

74.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

75.

What is f(6)?

a)

20

b)

33

c)

3

d)

3, -3

76.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

77.

What is f when x equals 8?

a)

0

b)

5

c)

11

d)

16

78.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

79.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

80.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

81.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

Left 1 Unit

b)

Right 1 unit

c)

vertical stretch

d)

up 1 unit

82.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

Down 9 units

c)

Left 9 units

d)

Right 9 Units

83.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

84.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

85.

Describe the transformation that occurred

t(x) = f(x) - 1

a)

Right 1 Unit

b)

Down 1 Unit

c)

vertical compression

d)

vertical stretch

86.

Describe the transformation that occurred

s(x) = 7f(x)

a)

vertical compression

b)

Up 7 Units

c)

Over 7 Units

d)

vertical stretch

87.

Describe the transformation that occurred
d(x) = f(x) - 1

a)

Left 1 Unit

b)

Right 1 Unit

c)

Up 1 Unit

d)

Down 1 Unit

88.

0.5f(x)

a)

vertical compression

b)

vertical stretch

c)

vertical shift up 3

d)

vertical shift down 3

89.

3f(-x)

a)

reflection over x-axis, vertical compression

b)

reflection over y-axis, vertical stretch

c)

reflection over x-axis, horizontal compression

d)

reflection over y-axis, horizontal stretch

90.

¼f(x) + 1

a)

vertical stretch, shift up 1

b)

vertical compression, shift up 1

c)

vertical stretch, shift up ¼

d)

vertical compression, shift down ¼

91.

-f(x) + 2

a)

horizontal reflection, translation up 2

b)

vertical reflection, translation up 2

c)

vertical reflection, translation right 2

d)

vertical reflection, translation down 2

92.

¾f(x − 7)

a)

vertical compression, translation right 7

b)

vertical stretch, translation down 7

c)

vertical compression, translation left 7

d)

vertical stretch, translation right 7

93.

Write in function form: translation 3 units right

a)

g(x) = f(x − 3)

b)

g(x) = f(x) − 3

c)

g(x) = -3f(x)

d)

g(x) = f(-3x)

94.

vertical compression

a)

2f(x)

b)

f(½x)

c)

½f(x)

d)

f(2x)

95.

reflection over y-axis, shift right 1

a)

f(-x - 1)

b)

-f(x + 1)

c)

-f(x) - 1

d)

-f(x - 1)

96.

translation up 1

a)

f(x) + 1

b)

f(x - 1)

c)

f(x) - 1

d)

f(x + 1)

97.

vertical stretch, translation left 3

a)

½f(x + 3)

b)

4f(x - 3)

c)

4f(x) + 3

d)

4f(x + 3)

98.

vertical reflection, horizontal stretch

a)

g(x) = ½f(-x)

b)

g(x) = -f(¼x)

c)

g(x) = -3f(x)

d)

g(x) = -f(4x)

99.

horizontal compression

a)

g(x) = 3f(x)

b)

g(x) = ½f(x)

c)

g(x) = f(¼x)

d)

g(x) = f(5x)

100.

horizontal compression, translation up 3

a)

f(4x) + 3

b)

4f(x) - 3

c)

4f(x) + 3

d)

f(4x) - 3

101.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

102.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

103.

Which parent function matches the graph?

a)

y = |x|

b)

y = x

c)

y = x²

d)

y = 2^x

104.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

105.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

106.

a)

g(x)=2x²

b)

g(x)=0.5x²

c)

g(x)=x²+2

d)

g(x)=(x+2)²

107.

Vertical stretch is af(x) when...

a)

a is greater than 0

b)

a is less than 0

c)

a is greater than 1

d)

a is a fraction/decimal

Spotlight- Precalc Spiral Review

Total questions: 107

Worksheet time: 4hrs 12mins

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