Free Printable Math 2 Honors SM1 Final Review

1.

Match each radical expression to its equivalent exponential form.

a)

√18

1.

$18^{1/2}$

b)

∛27

2.

$27^{1/3}$

c)

$∛(27^2)$

3.

$27^{2/3}$

d)

$∛(27^3)$

4.

$27^{3/3}$

e)

$\sqrt{27^2}$

5.

$27^{2/2}$

2.

Which of these shows √(500x⁴y⁶) in simplest terms?

a)

2x²y²√25x

b)

5x²y³√20x

c)

10x²y³√5

d)

4x²y²√5

e)

8x²y³√10x

3.

Rationalize the denominator of (4 - √5) / (2 + √2).

a)

(4 - 4√2 - 2√5 + √10) / 2

b)

(8 - 4√2 - 2√5 + 2√10) / 8

c)

(8 - 4√2 - 2√5 + 2√10) / 6

d)

(8 - 4√2 - 2√5 + 2√10) / 4

e)

(8 - 4√2 - 2√5 + √10) / 2

4.

Match each polynomial expression with its equivalent simplified form.

a)

$3x^2 - 52x + 5$

1.

$-2x(6 - x) + 5(x^2 - 8x + 1)$

b)

$3x^2 - 28x + 5$

2.

$-2x(6 - x) + 5(x^2 + 6x + 1)$

c)

$7x^2 + 28x + 5$

3.

$2x(6 + x) + 5(x^2 + 6x + 1)$

d)

$7x^2 - 52x + 5$

4.

$-2x(6 - x) + 5(x^2 - 16x + 1)$

e)

$7x^2 + 52x + 5$

5.

$2x(6 + x) + 5(x^2 - 16x + 1)$

5.

Which of these expressions is equivalent to 4x(x - 2) - 5(x - 2)? Select ALL that apply.

a)

x - 2(4x - 5)

b)

$4x^2 - 3x - 10$

c)

(x - 2)(4x - 5)

d)

(x - 2)(4x + 5)

e)

$4x^2 - 13x + 10$

6.

Which are the solutions to the equation $(x + 3)^2 = 49$ ? Select all that apply.

a)

x = 4

b)

x = -10

c)

x = -7

d)

x = 3

e)

x = -2

7.

The total area of the playground, the larger rectangle, is
16x² − 5x + 2. The area of the play area, the smaller rectangle, is 10x² + 3x − 1. Write an expression to represent the area of the sidewalk.

a)

6x² − 8x + 3

b)

16x² − 8x + 3

c)

16x² − 2x + 1

8.

Find the AREA of the shaded region.

a)

2x²-x

b)

6x²+3x

c)

4x²-4x

d)

2x²+7x

9.

A rectangular piece of paper has area 4x² + 3x + 2. A square is cut from the rectangle and the remainder of the rectangle is discarded. The area of the discarded paper is 3x² + x + 1. What is the area of the square?

a)

7x² + 4x + 3

b)

x² + 2x + 1

c)

x² + 4x + 1

d)

x² -2x - 1

10.

The sum of

(4a³ - 8a - 4a²) and (7a³ - 7 - 6a) is...

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

11.

Put into standard form: (x + 6)²

a)

x² + 6x + 12

b)

x² + 6x + 36

c)

x² + 12

d)

x² + 12x + 36

e)

x² + 36

12.

Which of the following is NOT a perfect square trinomial?

a)

x² – 16x + 64

b)

x² – 10x + 20

c)

x² – 28x + 196

d)

x² – 24x + 144

13.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

14.

Factor completely. 16p²- 8p + 1

a)

(4p-1)²

b)

(4p+1)²

c)

(p-4)²

d)

(4p-1)(4p+1)

e)

(p-4)(p+4)

15.

FACTOR COMPLETELY

3x² + 8x + 5

16.

FACTOR COMPLETELY

6x² - 11x - 10

17.

Factor Completely:
x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

e)

Not Factorable

18.

Factor Completely:
2k²-14k-60

a)

2(k-10)(k-3)

b)

Not Factorable

c)

(k-5)(k+9)

d)

2(k-10)(k+3)

19.

Factor Completely:
3x⁵ - 27x³

a)

3(x³ - 3)(x²+ 3)

b)

Not Factorable

c)

3x³(x² - 9)

d)

3x³(x - 3)(x + 3)

20.

$Factor\ -6n^2-5n+6$
HINT: Factor out the negative first! $-ax^2-bx-c=-\left(ax^2+bx+c\right)$

Type in answer with no spaces

[e.g. ?(n+?)(n-?)]

(a)

21.

What are the factors of this polynomial?

a)

(x - 2)(x + 1)

b)

(x - 2)(x - 1)

c)

(x + 2)(x + 1)

d)

(x + 2)(x - 1)

22.

Match each polynomial with the correct label for factoring.

a)

GCF Only

1.

$9x^2-64x$

b)

Difference of

Two Squares

2.

$9x^2-64$

c)

Sum of Two Squares

3.

$9x^2+64$

d)

Difference of

Two Cubes

4.

$64x^3-1$

e)

Sum of

Two Cubes

5.

$x^3+64$

23.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Not Factorable

24.

Rationalize the denominator

a)

A

b)

B

c)

C

d)

D

25.

√3 ( 4√5 + √12)

a)

4√15 + √36

b)

4√15 + 6

c)

12√5 + √40

d)

4√8 + √15

e)

None of these

26.

a)

A

b)

B

c)

C

d)

D

27.

Distribute and Simplify

$\sqrt[]{6}\left(-5\sqrt[]{3}+\sqrt[]{5}\right)$

a)

$-15\sqrt[]{2}+\sqrt[]{30}$

b)

$-15\sqrt[]{2}+15$

c)

None of these

d)

$-5\sqrt[]{18}+\sqrt[]{30}$

28.

a)

$y^2z^{10}\sqrt{xy}$

b)

$20yz\sqrt{xy}$

c)

$xy^2z^{10}\sqrt{y}$

d)

$yz^{20}\sqrt{xy}$

29.

Multiply and simplify if possible:

$\sqrt[]{4x^7}\cdot\sqrt[]{6x^2}$

a)

$4x^{3\ \ }\sqrt[]{5x^2}$

b)

$2x^4\ \ \sqrt[]{6x}$

c)

$6\ \sqrt[]{4x^9}$

d)

$2x\ \ \sqrt[]{6}$

e)

None of these

30.

Multiply and simplify if possible:

$\sqrt[]{5x^{ }}\cdot\sqrt[]{10x^5}$

a)

$\sqrt[]{15x^6}$

b)

$\sqrt[]{5x^4}$

c)

$5x^6\sqrt[]{2}$

d)

$5x^3\sqrt[]{2}$

31.

a)

A

b)

B

c)

C

d)

D

32.

a)

A

b)

B

c)

C

d)

D

33.

a)

A

b)

B

c)

C

d)

D

34.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

35.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

36.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

37.

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

38.

A function has a discriminant of 25.
______________
How many solutions does it have?

a)

0 Real

(aka 2 imagainary)

b)

1 Real

c)

2 Rational

d)

2 Irrational

39.

Determine the value of the discriminant and name the nature of the roots for the following:

x² + 7x + 13

Remember: b² - 4ac

a)

400, 2 real roots

b)

0, 1 real repeated root

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

40.

1 What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

41.

2 A function has a discriminant of 4.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

4

42.

2 A function has a discriminant of 0.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

5

43.

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

3

44.

Solve the following equation using the quadratic formula:

$3x^2+16x+5=0$

a)

$x=\frac{1}{3},\ x=5$

b)

$x=-\frac{1}{3},\ x=-5$

c)

$x=-1,\ x=-15$

d)

$x=1,\ x=15$

45.

What is the discriminant and how many solutions would this quadratic have?

x² - 6x + 9 = 0

a)

0, No Real Solutions

b)

0, 1 Real Solution

c)

72, 2 Real Solutions

d)

-72, No Real Solutions

46.

What is the discriminant and how many solutions would this quadratic have?

-8x² + 6x - 4 = 0

a)

-92, No Solutions

b)

164, 2 Solutions

c)

-164, No Solutions

d)

92, 2 Solutions

47.

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

a)

-28, No Solutions

b)

28, 2 Solutions

c)

100, 2 Solutions

d)

-100, No Solutions

48.

Which is FALSE about the graph pictured?

a)

The discriminant is negative.

b)

The y-intercept is (0, -1).

c)

The discriminant is 0.

d)

The A value is negative.

49.

What is the discriminant for 5x² + x − 2 = 0

a)

-39

b)

42

c)

-41

d)

none of these

50.

Use the quadratic formula and completing the square to solve.

$x^2+2x-4=0$

a)

1.23, -3.23

b)

0.41, -2.41

c)

3.23, -1.23

d)

no solution

51.

Use the quadratic formula and completing the square to solve.

$2x^2+4x+1=0$

a)

3.73, 0.26

b)

-0.06, -1.93

c)

1.70, 0.29

d)

-0.29, -1.70

52.

Solve

x² - 2x = 8?

a)

x = 2 or x = -4

b)

x = 1 or x = -8

c)

x = 4 or x = -2

d)

x = 8 or x = -1

53.

3x²-48=0

a)

x= 4

b)

x= - 4

c)

x= - 4, 4

d)

x= - 16,16

54.

Solve using the quadratic formula...
9x² = 4 + 7x

a)

x = 2 and x = 3

b)

x = -1 and x = .25

c)

x = 1 and x = -.45

d)

x = 1.16, and x = -.38

55.

To solve a quadratic by graphing is to find where the parabola crosses the x-axis. We call these the ___. Select all that apply.

a)

zeros

b)

x-intercepts

c)

solutions

d)

roots

e)

y-intercept

56.

Which of the following graphs would have a NEGATIVE discriminant?

a)

b)

c)

d)

57.

Is the graph of the following quadratic equation concave up or concave down?

y=-x²+2x-3

a)

Concave up, because the a value is positive

b)

Concave up, because the b value is positive

c)

Concave down, because the a value is negative

d)

Concave down, because the b value is negative

58.

Solve by Factoring & ZPP and the Quadratic Formula:

x² + 44 = -15x

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

59.

Solve the following Quadratic my the method of your choice. $3\left(x+1\right)^2+9=15$

a)

$x=1\pm\sqrt{2}$

b)

$x=3\pm\sqrt{2}$

c)

$x=-1\pm\sqrt{2}$

d)

$x=-3\pm\sqrt{2}$

60.

$Simplify\ \ \ \frac{-18\pm12\sqrt{2}}{6}$

a)

$-3\pm2\sqrt{2}$

b)

$-3\pm12\sqrt{2}$

c)

$-18\pm2\sqrt{2}$

d)

$\frac{-6\pm4\sqrt{2}}{2}$

61.

$Simplify\ \ \ \frac{12\pm\sqrt{216}}{6}$

a)

$2\pm6\sqrt{6}$

b)

$2\pm36\sqrt{6}$

c)

$2\pm\sqrt{6}$

d)

$\frac{4}{3},-\frac{2}{3}$

62.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

None of these

b)

c)

d)

63.

What is the simplified form of (-6i)(3i)

a)

-18

b)

-18i

c)

18

d)

-18i²

e)

None of these

64.

What is the simplified form of (-3 + 2i)(1- 4i)

a)

-2 - 2i

b)

5 + 14i

c)

-11 -10i

d)

-3 -8i

e)

None of these

65.

What is the simplified form of (8 -3i)²?

a)

73

b)

16 - 6i

c)

55 + 48i

d)

55 - 48i

e)

None of these

66.

3i(4 - i)

a)

9i

b)

-3 +12i

c)

12 - 3i

d)

3 + 12i

e)

None of these

67.

What is the simplified form of the above?

a)

7/10 + 11/10 i

b)

13/10 +1/10 i

c)

5/4 - 3/2i

d)

7/10 - 11/10 i

e)

None of these

68.

Simplify i³⁷

a)

1

b)

i

c)

-i

d)

-1

69.

Simplify i²⁴

a)

i

b)

1

c)

-1

d)

-i

70.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

71.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

e)

None of these

72.

Multiply
3i(-2 + 4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

e)

None of these

73.

(10-6i) - (2+3i)

a)

12 + 3i

b)

8 - 3i

c)

8 - 9i

d)

-9i + 8

e)

None of these

74.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

e)

None of these

75.

a)

A

b)

B

c)

C

d)

D

76.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

e)

None of these

77.

Was the inverse function found correctly?

a)

no

b)

yes

78.

Which is the inverse of the table?

a)

b)

c)

d)

79.

When using composition to verify 2 functions are inverses, g(f(x)) and f(g(x)) must equal

a)

x

b)

1

c)

f(x)

d)

g(x)

e)

0

80.

Find the correct order to find the inverse of f(x)= 2x-5

a)

y=2x-5

b)

2y-5=x

c)

2y= x+5

d)

$y=\frac{x+5}{2}$

e)

$f^{-1}\left(x\right)=\frac{1}{2}x+\frac{5}{2}$

1)

2)

3)

4)

5)

81.

Use function composition to determine if f(x) and g(x) are functions or not

a)

Inverse Functions

b)

Not Inverse Functions

82.

Use function composition to determine if f(x) and g(x) are functions or not

a)

Inverse Functions

b)

Not Inverse Functions

83.

Are these functions inverses?

a)

No

b)

Yes

c)

No way to tell

84.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

85.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

86.

Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the ordered pairs.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

87.

Are these equations inverses?

a)

Yes

b)

No

88.

Find the graph of $f\left(x\right)=x^2$

a)

b)

c)

d)

89.

Find the graph of $f\left(x\right)=x^3$

a)

b)

c)

d)

90.

Find the graph of $f\left(x\right)=\sqrt[3]{x}$

a)

b)

c)

d)

91.

This graph shown is increasing on the interval

a)

$\left(-\infty,\ 0\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

92.

This graph shown is increasing on the interval

a)

$\left(-\infty,\ 0\right)$

b)

$\left(0,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

93.

What is the end behavior of f(x) = 3x⁶ as x goes to negative infinity?

a)

positive infinity

b)

negative infinity

c)

zero

94.

Which statement is true about the end behavior of the function

y = -3x²?

a)

As x approaches negative infinity, y approaches 0.

b)

As x approaches positive infinity, y approaches negative infinity.

c)

As x approaches positive infinity, y approaches 0.

d)

As x approaches negative infinity, y approaches positive infinity.

95.

What is the domain of f(x) = 4x²?

a)

(-∞, +∞)

b)

(0, ∞)

c)

(-∞, 0)

d)

(1, ∞)

96.

a)

b)

c)

d)

97.

What is the end behavior of $f(x)=5x^3$ as x goes to positive infinity?

a)

$\infty$

b)

$-\infty$

c)

$0$

d)

5

e)

3

98.

What is the range of f(x) = 4x⁵?

a)

(-infinity, +infinty)

b)

y>0

c)

y<0

d)

(-infinity, 0) U (0, +infinity)

99.

What is the end behavior of f(x) = 5x³ as x goes to positive infinity?

a)

positive infinity

b)

negative infinity

c)

zero

100.

What is the end behavior of f(x) = 3x⁶ as x goes to negative infinity?

a)

positive infinity

b)

negative infinity

c)

zero

101.

Match the following parent functions graphs to their equations

a)

1.

$f\left(x\right)=x$

b)

2.

$f\left(x\right)=x^2$

c)

3.

$f\left(x\right)=x^3$

d)

4.

$f\left(x\right)=\frac{1}{x}$

e)

5.

$f\left(x\right)=\sqrt[]{x}$

102.

Select ALL symmetries displayed in the graph.

a)

symmetry with respect to the x-axis

b)

symmetry with respect to the y-axis

c)

symmetry with respect to the origin

d)

all of the above

e)

none of the above

103.

The function with the graph depicted is an even function.

a)

True

b)

False

104.

If a function has symmetry with respect to the origin and the point (-3, 5) is on the graph, which other point must be on the graph?

a)

(-5, 3)

b)

(5, -3)

c)

(3, -5)

d)

(-3, 5)

105.

If a function has symmetry with respect to the origin and the point (-3, 5) is on the graph, which other point must be on the graph?

a)

(-5, 3)

b)

(5, -3)

c)

(3, -5)

d)

(-3, 5)

106.

If a function has symmetry with respect to the x-axis and the point (1, 4) is on the graph, which other point must be on the graph?

a)

(-1, -4)

b)

(-1, 4)

c)

(1, -4)

d)

(4, 1)

107.

If a function is an even function and the point (-2, 7) is on the graph, which other point must be on the graph?

a)

(-2, -7)

b)

(2, 7)

c)

(2, -7)

d)

(-7, 2)

108.

Select ALL symmetries displayed in the graph.

a)

symmetry with respect to the x-axis

b)

symmetry with respect to the y-axis

c)

symmetry with respect to the origin

d)

all of the above

e)

none of the above

109.

Identify the type of symmetry based on the graph:

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

110.

Describe the transformations of Function

from Parent Function

$g\left(x\right)=\sqrt[]{x+4}-6$

a)

Shift Left 4

and

Shift Down 6

b)

Shift Left 4

and

Shift Up 6

c)

Shift Right 4

and

Shift Down 6

d)

Shift Up 4

and

Shift Left 6

111.

The Domain of

$g\left(x\right)=\sqrt[8]{x+4}-6$

is All Real Numbers except ___?

a)

No Restrictions.

X can be anything

b)

x can't be less than -4

c)

x can't be greater than -4

d)

x can't be less than -6

e)

x can't be greater than -4

112.

The Domain of

$g\left(x\right)=\ \sqrt[3]{x+4}-6$

is All Real Numbers except ___?

a)

No Restrictions.

X can be anything

b)

x can't be less than -4

c)

x can't be greater than -4

d)

x can't be less than -6

e)

x can't be greater than -4

113.

The Domain of

$g\left(x\right)=\ \sqrt[5]{x+4}-6$

is All Real Numbers except ___?

a)

No Restrictions.

X can be anything

b)

x can't be less than -4

c)

x can't be greater than -4

d)

x can't be less than -6

e)

x can't be greater than -4

114.

State the transformations of the function from the Parent Function

$g\left(x\right)=\left(x-2\right)^2+3$

a)

Shift Left 2

and

Shift Down 3

b)

Shift Right 2

and

Shift Up 3

c)

Shift Right 2

and

Shift Down 3

d)

Shift Left 2

and

Shift Up 3

115.

The Range is

$g\left(x\right)=-\left(x-2\right)^2+3$

a)

(-infinity , 2]

b)

(-infinity , 3]

c)

[2 , infinity )

d)

[-2 , infinity )

e)

[3 , infinity )

116.

a)

Left 2; Down 1

b)

Reflection over x-axis; Left 2; Up 1

c)

Reflection over x-axis; Left 2; Down 1

d)

Reflection over y-axis; Right 2; Down 1

117.

Identify the parent function of the graph.

a)

Square Root

b)

Linear

c)

Quadratic

d)

Cubic

e)

Cube Root

118.

Identify the transformation.

a)

Reflection across y axis

b)

Reflection across x-axis

c)

180 Rotation

d)

Translation 2 units down

119.

When a coordinate reflects over the y-axis the x-coordinate...

a)

changes to its opposite sign

b)

stays the same

120.

When a coordinate reflects over the y-axis the y-coordinate...

a)

changes to its opposite sign

b)

stays the same

121.

The blue triangle is reflected over the x-axis. True or False?

a)

True

b)

False

122.

The blue figure is reflected over the x-axis. True or False?

a)

True

b)

False

123.

What is the rule for a reflection over the y-axis?

a)

(x,y)→(-x,y)

b)

(x,y)→(x,-y)

c)

(x,y)→(-x,-y)

d)

(x,y)→(y,x)

124.

What is the rule for a reflection over the x-axis?

a)

(x,y)→(-x,y)

b)

(x,y)→(x,-y)

c)

(x,y)→(-x,-y)

d)

(x,y)→(y,x)

125.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

126.

The complex ( a+bi ) conjugate can be found by...

a)

Changing the sign of both a and b

b)

Changing the sign of a

c)

Changing the sign of b

d)

Switching the a and b values

127.

What is the conjugate of 2 + √3

a)

2 + √3

b)

2 - √3

c)

-2 + √3

d)

-2 - √3

128.

Determine the complex conjugate of (-3-12i)

a)

-3-12i

b)

3-12i

c)

3+12i

d)

-3+12i

129.

Solve for x:

a)

x = {-4, -1}

b)

x = {-1, -4}

c)

x = {2+i, 2-i}

d)

x = {-2+i, -2-i}

130.

Solve -2x² + 4x = 9

a)

(2 - i√14)/2 , (2 + i√14)/2

b)

(2 - i√-56)/2 , (2 + i√-56)/2

c)

(2 - i√-14)/2 , (2 + i√-14)/2

d)

(2 - √14)/2 , (2 + √14)/2

131.

Graph the function below one using 1 transformation at a time and in the proper order

4 lines

132.

Graph the function below one using 1 transformation at a time and in the proper order

4 lines

133.

Graph the function below one using 1 transformation at a time and in the proper order

4 lines

134.

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula h t = −16 t² + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?

a)

.25 ft

b)

24 ft

c)

25 ft

d)

8 ft

135.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t² + 64t + 80. What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

136.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

6 seconds

137.

The height of an object thrown into the air can be modeled by the formula $y=-16x^2+70x+95$ , where y is in feet after x seconds.
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

138.

The height of an object thrown into the air can be modeled by the formula $y=-16x^2+70x+95$
, where y is in feet after x seconds.
What is the initial height of the object?

a)

70 feet

b)

95 feet

c)

149 feet

d)

-16 feet

139.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
How many seconds did it take for the ball to reach its maximum height?

a)

10 seconds

b)

64 seconds

c)

960 seconds

d)

2 seconds

140.

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = –16t²+ 16t + 480, where t is the time in seconds and h is the height in feet. How long does it take Jason to hit the water?

a)

-16 seconds

b)

-6 seconds

c)

0 seconds

d)

6 seconds

141.

Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t² + 96t. When does the rocket hit the ground?

a)

7 seconds

b)

6 seconds

c)

3 seconds

d)

8 seconds

142.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

a)

8 seconds

b)

1 second

c)

1/2 second

d)

1/4 second

143.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

What is the Domain?

a)

All Real Numbers

b)

[ 0 , 25 ]

c)

[ 0 , 1.5 ]

d)

[ 0 , 24 ]

e)

[ -1 , 1.5 ]

144.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

What is the Range?

a)

All Real Numbers

b)

[ 0 , 25 ]

c)

[ 0 , 1.5 ]

d)

[ 0 , 24 ]

e)

[ -1 , 1.5 ]

145.

If each mark on the x-axis represents one second, when did the object reach the ground?

a)

2.5 seconds

b)

6 seconds

c)

5.5 seconds

d)

5 seconds

146.

The domain of

$y=\frac{\left(x-1\right)\left(x+4\right)}{\left(x+2\right)\left(x-3\right)}$ ?

is All Real Numbers except ___?

(Check all that applies.)

a)

$x\ne-2$

b)

$x\ne-1$

c)

$x\ne3$

d)

$x\ne4$

147.

Find the range of

$y=\frac{2}{x+1}$

*Hint: Find the inverse's domain

a)

$y\ne-1$

b)

$y\ne0$

c)

$y\ne1$

d)

$y\ne2$

148.

Find the domain of

$y=\frac{2}{x+1}$

is All Real Numbers except ___?

a)

$x\ne-1$

b)

$x\ne0$

c)

$x\ne1$

d)

$x\ne2$

149.

Find the domain for the function. f(x)= 2x -1 / 3x + 6

a)

x cannot equal to 2

b)

x cannot equal to -2

c)

x cannot equal to 3

d)

All real numbers

150.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

151.

What is the domain and range?

a)

D : $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$
R: $\left(-\infty,1\right)\cup\left(1,\infty\right)$

b)

D : $\left(-\infty,1\right)\cup\left(1,\infty\right)$
R: $\left(-\infty,-3\right)\cup\left(-3,\infty\right)$

c)

D : $\left(-\infty,3\right)\cup\left(3,\infty\right)$
R: undefined

d)

D: $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$
R: $\left(-\infty,3\right)\cup\left(3,\infty\right)$

152.

What is the domain and range?

a)

D:\ \left(-\infty,2\right)\cup\left(2,\infty\right)

R:\ \left(-\infty,1\right)\cup\left(1,\infty\right)

b)

$D:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$
$R:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$

c)

$null$
$R:\ \left(-\infty,\frac{1}{2}\right)\cup\left(\frac{1}{2},\infty\right)$

d)

$D:\ \left(-\infty,-2\right)\cup\left(-2,\infty\right)$
$R:\ \left(-\infty,-1\right)\cup\left(-1,\infty\right)$

153.

What is the domain and range of this rational function?

a)

D: $\left(-\infty,\infty\right),\ x\ne4$

R: $\left(-\infty,\infty\right),\ y\ne0$

b)

D: $\left(-\infty,\infty\right)$

R: $\left(-\infty,\infty\right)$

c)

D: $\left(-\infty,4\right)$

R: $\left(-\infty,\infty\right)$

d)

D: $\left(-\infty,\infty\right)$

R: $\left(-\infty,0\right)$

154.

The daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. The plumber works a maximum of 8 hours per day.

For one day of work, what is the range of the function for this situation?

a)

$0\le x\le8$

b)

$80\le y\le440$

c)

$0\le x\le10$

d)

$45\le y\le685$

155.

The height in inches of concrete being poured for a foundation can be found using the function y=15+2.5x, where x is the number of minutes. If the concrete is poured between 5 and 10 minutes, find the domain and range of this situation.

a)

Domain: $5\le x\le10$ Range: $27.5\le y\le40$

b)

Domain: $27.5\le x\le40$ Range: $5\le y\le10$

c)

Domain: {5, 6, 7, 8, 9, 10} Range: {28, 29, 30, ..., 40}

d)

Domain: {28, 29, 30, ..., 40} Range: {5, 6, 7, 8, 9, 10}

156.

Leslie's car travels about 25 miles per gallon of gas.

This situation can be represented by function f(x) = 25x

Her car needs 14 gallons of gas to be full. What is a reasonable RANGE?

a)

$y\ge25$

b)

$0\le y\le14$

c)

$y\le14$

d)

$0\le y\le350$

157.

What is the Range of the situation?

a)

All real numbers greater than or equal to 0 and less than or equal to 28

b)

All real numbers greater than or equal to 0 and less than or equal to 9

c)

All real numbers less than or equal to 28

d)

All real numbers less than or equal to 9

158.

Simplify:

a)

2

b)

8

c)

16

d)

32

159.

Write the expression in radical form: $x^{\frac{3}{4}}$

a)

$\sqrt[4]{x^3}$

b)

$\sqrt[3]{x^4}$

c)

$x^{.75}$

d)

$\sqrt[]{x^2}$

160.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

161.

a)

$\frac{a^6}{b^{12}}$

b)

$\frac{b^{12}}{a^4}$

c)

$\frac{a^{12}}{b^6}$

d)

$\frac{1}{a^6b^{10}}$

162.

What is the inverse to $g\left(x\right)=\sqrt[3]{x+5}-2$ ?

$g^{-1}\left(x\right)=$

163.

Write the inverse of each function: 9. y = $\sqrt{x}$ - 2

a)

$y = (x + 2)^2$

b)

$y = x^2 + 2$

c)

y = $\sqrt{x + 2}$

d)

$y = x^2 - 2$

164.

What is the inverse of the function y = $\sqrt{x + 8}$ ?

a)

$y = x^2 - 8$

b)

y = $x^2 + 8$

c)

y = $\sqrt{x - 8}$

d)

y = $\sqrt{x + 8}$

165.

Find the inverse of f(x) = x² - 5

a)

b)

c)

d)

166.

a)

A

b)

B

c)

C

d)

D

167.

a)

A

b)

B

c)

C

d)

D

168.

a)

A

b)

B

c)

C

d)

D

Math 2 Honors SM1 Final Review

Total questions: 168

Worksheet time: 13hrs 3mins

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