Free Printable Question Bank for Grade 10 Mathematics

1.

Write the recursive formula for 6, 17, 28, 39, 50....

a)

a_n=a_n-1+11
a₁=6

b)

a_n=a_n-1-4
a₁=6

c)

a_n=a_n-1+9
a₁=6

d)

a_n=a_n-1+6
a₁=6

2.

A formula that requires the computation of all previous terms to find the value of a_n.

a)

Explicit Formula

b)

Recursive Formula

c)

Arithmetic Formula

d)

Geometric Formula

3.

What is the 15th term of the sequence an = -3n+50

a)

95

b)

-5

c)

5

d)

-95

4.

Identify the common difference.

-6, -3, 0, 3, 6....

a)

4

b)

3

c)

-4

d)

-3

5.

Write a recursive formula for the following sequence:

10, 5, 0, -5,...

a)

a₁= 10

a_n= a_n-1 - 5

b)

a₁= 10

a_n= a_n-1 + 5

c)

a₁= 10

a_n= a_n (5)

d)

a₁= 10

a_n= a_n-1 (5)

6.

Which of the following equations is recursive?

a)

f(n) = f(n-1) +4

b)

f(n) = 2n - 5

7.

Which is an arithmetic sequence?

a)

1, 3, 5, 7, 9, ...

b)

1, 2, 4, 8, 16, 32, ...

c)

1, 1, 2, 3, 5, 8, 13, ...

8.

What does a₁ represent?

a)

Any term

b)

First term

c)

Last term

9.

Find $a_4$ for the sequence 2, 9, 16, 23, 30,...

a)

16

b)

23

c)

4

d)

30

10.

$a_n=a_1+\left(n-1\right)d$ , where n is the position in the sequence and d is the difference between terms.

a)

Sequence

b)

Recursive Formula

c)

Explicit Formula for an Arithmetic Sequence

d)

Explicit Formula for a Geometric Sequence

11.

Write a sequence to represent the number of smiley faces in each group. Select all that apply.

a)

$a_n=4+\left(n-1\right)2$

b)

$f\left(n\right)=2+4\left(n-1\right)$

c)

$f\left(n\right)=4+2\left(n-1\right)$

d)

$a_n=a_{n-1}+2$

e)

$a_n=a_{n-1}-2$

12.

This is an arithmetic sequence. How many dots would be in the next figure?

a)

4

b)

13

c)

14

d)

15

13.

On a scale of 1-5, 1 meaning "I have no clue what is going on" to 5 meaning "I got it completely," how would you rate your understanding of recursive & explicit sequences

a)

1

b)

2

c)

3

d)

4

e)

5

14.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

15.

What is the recursive rule for the sequence:
11, 22, 44, 88...

a)

a_n = 2(11)^n-1

b)

a_n = 11x 2

c)

a_n = 11(2)^n-1

d)

a_n = 2a_n-1

16.

Given the notation $3\cdot\sqrt{45}$ is this a form of long division?

a)

yes

b)

no

17.

Given the notation $3\cdot\sqrt{45t^2}$ what is the variable?

a)

2

b)

3

c)

45

d)

t

18.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{75g^3}$

a)

$5g\sqrt{3g}$

b)

$3g\sqrt{5g}$

c)

$75\sqrt{g^3}$

d)

$15\sqrt{3g^3}$

19.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{20b^2}$

a)

$5\sqrt{b^2}$

b)

$10\sqrt{2b}$

c)

$2b\sqrt{5}$

d)

$20b$

20.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{50a^7}$

a)

$25\sqrt{3a^4}$

b)

$25\sqrt{2a}$

c)

$5a^3\sqrt{2a}$

d)

$25a^2\sqrt{3a}$

21.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{18w}$

a)

$6w\sqrt{2}$

b)

$18\sqrt{w}$

c)

$2\sqrt{3w}$

d)

$3\sqrt{2w}$

22.

Simplify. Assume the variable is greater or equal to zero. $4\cdot\sqrt{18c^3}$

a)

$12c\sqrt{2c}$

b)

$6c\sqrt{6c}$

c)

$81\sqrt{c^2}$

d)

$2c\sqrt{16c}$

23.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{45a^{10}}$

a)

$5a^2\cdot\sqrt{2a}$

b)

$3a^5\cdot\sqrt{5}$

c)

$5a^3\cdot\sqrt{4a}$

d)

$2a^2\cdot\sqrt{a}$

24.

Simplify. Assume the variable is greater or equal to zero. $4\cdot\sqrt{50y^7}$

a)

$20y\cdot\sqrt{3y}$

b)

$20y^2\cdot\sqrt{3y}$

c)

$20y\cdot\sqrt{2y}$

d)

$20y^3\cdot\sqrt{2y}$

25.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{12t^5}$

a)

$2t^2\cdot\sqrt{3t}$

b)

$3t\cdot\sqrt{2t}$

c)

$4t\cdot\sqrt{3t}$

d)

$3t^2\cdot\sqrt{2t}$

26.

Simplify. Assume the variable is greater or equal to zero. $10\sqrt{20y^9}$

a)

$200y\sqrt{5y}$

b)

$20y^4\cdot\sqrt{5y}$

c)

$30y^2\cdot\sqrt{y}$

d)

$20\cdot\sqrt{300y}$

27.

Simplify. Assume the variable is greater or equal to zero. $\sqrt{20b^9}$

a)

$2b^2\cdot\sqrt{5b}$

b)

$2b^4\cdot\sqrt{5b}$

c)

$b^9\cdot\sqrt{5b}$

d)

$2b\cdot\sqrt{b^5}$

28.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

29.

Simplify the expression: 3x²⋅x²=

a)

3x

b)

3x²⁺²

c)

3x⁴

30.

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

31.

Simplify $4^{-2}$

a)

$\frac{1}{16}$

b)

$16$

c)

$\frac{1}{4}$

d)

$-42$

32.

When dividing powers with the same base, you _______________ the exponents.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

33.

a)

b)

c)

d)

34.

Rewrite it using positive exponents $x^{-3}$

a)

$-x^3$

b)

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

c)

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

d)

$-x^{-3}$

35.

a)

b)

c)

d)

36.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

37.

-4x⁰

a)

-4x

b)

-4

c)

1

d)

-1

38.

(5³x²y⁴)⁰

a)

5xy

b)

1

c)

0

d)

5

39.

(3xy)²

a)

9x²y²

b)

6x²y²

c)

3xy²

d)

3x²y²

40.

(t^-6)^-5

a)

t^-11

b)

t^-30

c)

t³⁰

d)

t¹¹

41.

According to exponent rules, when we multiply the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

42.

Simplify the expression:

$5x^9\cdot-6x^2$

a)

$-30x^{11}$

b)

$-30x^{18}$

c)

$-x^{11}$

d)

$-x^{18}$

43.

Simplify the expression:

$\left(k^2\right)^5$

a)

$k^7$

b)

$k^3$

c)

$k^{32}$

d)

$k^{10}$

44.

Simplify the expression:

\left(a^4b\right)^2\left(a^3b^2\right)^4

a)

$4a^8b$

b)

$a^{13}b^8$

c)

$-2a^8y^7$

d)

$a^{20}b^{10}$

45.

Simplify the expression:

$\frac{x^8}{x^2}$

a)

$x^6$

b)

$x^2$

c)

$x^4$

d)

$4x$

46.

Simplify the expression: $\frac{12x^9y^4z^2}{24x^3y^4z^6}$

a)

$2x^3z^3$

b)

$\frac{x^6}{2z^4}$

c)

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

d)

$\frac{2x^6}{x^4}$

47.

Simplify the expression:

$\frac{a^3}{a^{12}}$

a)

$a^9$

b)

$\frac{1}{a^9}$

c)

$a^4$

d)

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

48.

Determine the symmetrical relationship

a)

Origin

b)

x-axis

c)

y-axis

d)

None

49.

a)

origin

b)

x-axis

c)

y-axis

d)

none

50.

a)

origin

b)

x-axis

c)

y-axis

d)

none

51.

Test for symmetry

a)

origin

b)

x-axis

c)

y-axis

d)

none

52.

Test for symmetry

a)

origin

b)

x-axis

c)

y-axis

d)

none

53.

Which one of the following functions is even?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

54.

Which one of the following functions is odd?

a)

f(x) = 3x⁴ - 4x³

b)

g(x) = 5x⁴ + 3x²

c)

h(x) = 6x⁵ - x³

d)

k(x) = x⁶ + 8x²

55.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

56.

$y=x^2+3x+9$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

57.

$y=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

58.

$y=12x^7+6x^5-8x^3+4x$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

59.

What is/are the increasing interval(s) for the function shown?

a)

$\left(4,\ 8\right)$

b)

$\left(-3,\ 1\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

d)

$\left(-\infty,\ 1\right)\ and\ \left(4,\ 8\right)$

60.

What is the decreasing interval on the function shown?

a)

$\left(-\infty,\ 1\right)$

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

61.

What is the decreasing interval(s) on the function shown?

a)

$\left(-\infty,\ -15\right)\ and\ \left(9,\ -15\right)$

b)

$\left(-2,\ 9\right)\ and\ \left(2,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)\ and\ \left(0,\ 2\right)$

d)

$\left(-2,\ 0\right)\ and\ \left(2,\ \infty\right)$

62.

Which best describes point P?

a)

Relative Minimum

b)

Relative Maximum

c)

Absolute Minimum

d)

Absolute Maximum

63.

Which best describes point R?

a)

Relative Minimum

b)

Relative Maximum

c)

Absolute Minimum

d)

Absolute Maximum

64.

Which is an interval of increase in the function?

a)

$\left(-\infty,\ -3\right)$

b)

$\left(-3,\ 4\right)$

c)

$\left(-11,\ -6\right)$

d)

$\left(-6,\ -3\right)$

65.

what is the amplitude of y=-3sin(7x)-2

a)

7

b)

-2

c)

3

d)

-3

66.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

67.

Write the equation for a sine function with an amplitude of 6 and a period of π/4. (Find the period of all of them to see which one has a period of π/4)

a)

y=-6sin(8x)

b)

y=-6sin(4x-1)

c)

y=6sin(1/4x)

d)

y=6sin(x)

68.

What is the period of this graph?

a)

2π

b)

π/2

c)

π/4

d)

π

69.

What is the amplitude and period of y = 2sin(πx)

a)

2 and 2

b)

π and 2

c)

2 and π

d)

2π and 2

70.

What is the amplitude and period of y = 2sin(3x)

a)

2 and 3

b)

3 and 2

c)

2,2π/3,

d)

2π/3, 2

71.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

72.

The period of a function is

a)

how long one cycle is before the function repeats

b)

how high and low the function goes from the center line

c)

the range of the function

73.

Amplitude refers to....

a)

how high and low the function varies from the center line.

b)

the length of the function

c)

how often the function repeats

74.

Is the following periodic?

a)

Yes

b)

No

75.

What is the maximum height on the Ferris wheel?

a)

1

b)

4

c)

7

d)

24

76.

What is the minimum height on the Ferris wheel?

a)

1

b)

4

c)

7

d)

24

77.

How high is the centre on the Ferris wheel?

a)

1

b)

4

c)

7

d)

0

78.

What is the period of this graph?

a)

4

b)

8

c)

3

d)

6

79.

What is the amplitude of this graph?

a)

7

b)

8

c)

3

d)

6

80.

Which of the following is a vertical asymptote for the graph of y = tan x?

a)

x = π/2

b)

x = π

c)

x = 3π

d)

x=0

81.

Does the graph of sine have asymptotes?

a)

no

b)

yes, at multiples of π

c)

sometimes

d)

yes at multiples of 2π

82.

What is the reciprocal of 2/3?

a)

2/3

b)

1/4

c)

3/2

d)

4/6

83.

What is the value of a if the function above is f(x) = a tan x

a)

1/2

b)

1

c)

2

d)

4

84.

What is the period of the function?

a)

π/2

b)

π

c)

2π

d)

4π

85.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

86.

Which function below matches this graph?

a)

tan(x-π/4)

b)

tan(x+π/4)

c)

cot(x)

d)

π/4cot(x)

87.

Name the graph

a)

y = cot x

b)

y = sinx

c)

y = tan x

d)

y = secx

88.

Which function below matches this graph?

a)

cot(x)

b)

cot4(x)

c)

cot8(x)

d)

π/4cot(x)

89.

What is the amplitude and period of the function: y= 2/5sin9x

a)

Amplitude: 2/5 Period: 2π/9

b)

Amplitude: 2/5 Period: π/6

c)

Amplitude: 5/2 Period: 2π/9

d)

Amplitude: 5/2 Period: π/6

90.

The __________ measure the distance from the midline to the max or min of the function.

a)

Amplitude

b)

Phase Shift

c)

Vertical Translation

d)

Horizantal Translation

91.

If no dilations exist, what is the normal period of a sine or cosine function?

a)

1/2π

b)

2π

c)

π

d)

π/2

92.

Assuming no transformations, what type of function is this?

a)

sin

b)

cos

c)

tan

d)

cot

93.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

94.

What is the equation of this graph?

a)

y=cos2x

b)

y=2sin2x

c)

y=2cos2x

d)

y=2sinx

95.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

96.

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

a)

y=6sin(8x)

b)

y=6sin8(x-1)

c)

y=6sin1/4x

d)

y=6sinx

97.

What is the period of y = 4Cos(2x)?

a)

4π

b)

π

c)

2π

d)

π/2

98.

What is the period of the function y=7cos6x?

a)

2π

b)

6π

c)

6

d)

π/3

99.

What shift is happening in the function y=2sinx+4

a)

Right 4

b)

Left 4

c)

Down 4

d)

Up 4

100.

What is the vertical shift?

a)

up 2

b)

right π/2

c)

left π/2

d)

down 2

101.

What is the period?

a)

1

b)

2π/3

c)

3π

d)

2π

102.

What is the maximum value of the wave y = 10sin(2x - 20) + 25?

a)

10

b)

20

c)

35

d)

30

103.

What is another name for a phase shift?

a)

Horizontal Dilation

b)

Horizontal Shift/Translation

c)

Vertical Dilation

d)

Vertical Shift/Translation

104.

Cos $0\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

105.

Cos $30\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

106.

Cos $45\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

107.

Cos $60\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

108.

Cos $90\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

109.

Sin $0\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

110.

Sin $30\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

111.

Sin $60\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

112.

Sin $90\degree$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

113.

Positive angles are measured in which direction from standard position on the unit circle?

a)

Clockwise

b)

Counterclockwise

114.

What is the radius length of a unit circle?

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

1

e)

0

115.

The coordinates of the points on the unit circle are written in which order?

a)

$\left(\cos\theta,\ \sin\theta\right)$

b)

$\left(\sin\theta,\ \cos\theta\right)$

116.

The x-coordinate on the unit circle is equivalent to which value

a)

$\cos\theta$

b)

$\sin\theta$

117.

The y-coordinate on the unit circle is equivalent to which value

a)

$\cos\theta$

b)

$\sin\theta$

118.

Which quadrant is 150^o in?

a)

I

b)

II

c)

III

d)

IV

119.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

120.

What is 11π/6 radians in degrees?

a)

30

b)

330

c)

360

d)

300

121.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

122.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

123.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

124.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

125.

a)

-√3/2

b)

-½

c)

-√2/2

d)

-1

126.

a)

-1

b)

0

c)

undefined

d)

√3

127.

a)

√3/3

b)

√3

c)

1

d)

undefined

128.

cot 3π/4

a)

-√2/2

b)

-1

c)

1

d)

√2/2

129.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

130.

Divide (m²-7m-11) by (m-8).

a)

m+2 + 3/(m-8)

b)

m+1 -3/(m-8)

c)

m-4

d)

m-8 +1/(m-8)

131.

Factor
81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

132.

Solve the equation.

a)

36

b)

18

c)

-18

d)

27

133.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

134.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

135.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

136.

Function notation
If f(x) = 3x² - 4 + 2x,find f(6)

a)

332

b)

116

c)

84

d)

-16

137.

Function - Domain
Give the domain of this relation:
{(2, 5), (3, 6), (5, 2), (0, 5), (8, 1), (9, 3)}

a)

{2, 3, 5, 0, 8, 9}

b)

{5, 6, 2, 1, 3}

c)

{(2, 5), (3, 6), (5, 2), (0, 5), (8, 1), (9, 3)}

138.

Function - Vertical Line Test
Is this a function?

a)

Yes

b)

No

c)

Not enough information to decide

139.

Find the difference quotient when f(x) = 3 - 7x

a)

7

b)

21

c)

-7

d)

-21

140.

Where is the function increasing?

a)

x≤1

b)

x≥1

c)

y≤-4

d)

y≥-4

141.

What is the relative max of this function?

a)

x = 5

b)

infinity

c)

there is no relative maximum

d)

2.5 and it occurs at x = 5

142.

Choose the correct translated function.

a)

f(x)= |x|+2

b)

f(x)= |x|-2

c)

f(x)= -|x|

d)

f(x)= -|x|+2

143.

What equation represents the quadratic function?

a)

y = (x - 4)²

b)

y = (x + 4)²

c)

y = x² - 4

d)

y = x² + 4

144.

What equation represents the quadratic function?

a)

y = -(x - 6)² - 3

b)

y = -(x - 6)² + 3

c)

y = -(x + 6)² - 3

d)

y = -(x + 6)² + 3

145.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

146.

g(n)=4n-4
f(n)=n³+4
Find (g+f)(n)

a)

-2n²-n+9

b)

-n³-4n

c)

-3n³-3n-5

d)

n³+4n

147.

p(x) = 3x + 4
q(x) = 2x²
Find (p∘q)(x)

a)

10x²

b)

18x² + 4

c)

6x² + 4

148.

What is the inverse of this function?

a)

A

b)

B

c)

C

d)

D

149.

Identify the vertex and whether the graph opens up or down.

a)

(-1, 4); opens up

b)

(-1, 4); opens down

c)

(1, 4); opens up

d)

(1, 4); opens down

150.

Convert to vertex form.

a)

y=3(x+1)² - 8

b)

y=3(x-1)² - 8

c)

y=3(x+2)² - 8

d)

y=3(x-2)² - 8

151.

List all possible rational zeros
f(x) = 3x⁵-5x²+x+6

a)

1, 2, 3, 6, -1, -2, -3, -6

b)

1/3,2/3,1,2,3,6,-1/3,-2/3,-1,-2,-3,-6

c)

1/3,2/3,1,2,3,6

152.

Tisha deposited $200 in a savings account earning 12% interest, compounded annually.
To the nearest cent, how much will she have in 3 years?

a)

$280.99

b)

$224

c)

$80.99

d)

$136.29

153.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x.. What translation happens to the parent function?

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

154.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much will she owe if she makes no payments for 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

155.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

156.

Evaluate.

a)

A

b)

B

c)

C

d)

D

157.

Expand

a)

A

b)

B

c)

C

d)

D

158.

Condense

a)

A

b)

B

c)

C

d)

D

159.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

160.

5^x= 15,625

a)

3

b)

4

c)

5

d)

6

161.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

162.

Solve log₅(4x-7)=log₅(x+5).

a)

x=4

b)

x=-4

c)

x=3

d)

x=-2

163.

Convert from radians to degrees: 7π ∕ 4

a)

330°

b)

45°

c)

315°

d)

75°

164.

Convert from degrees to radians: 135°

a)

2π ∕ 3

b)

3π ∕ 4

c)

5π ∕ 4

d)

3π ∕ 5

165.

Find an angle coterminal with an angle which measures 11π ∕ 3.

a)

17 π / 3

b)

4π ∕ 3

c)

-π ∕ 3

d)

8π ∕ 3

166.

Find all rational zeros, one zero has been given.
f(x) = x³-5x²-2x+24; -2

a)

-2,1,0

b)

-2,-3,-4

c)

4,3,-2

d)

0,0,0

167.

Use the Quadratic Formula:
x=[-b +/- sq rt(b^2-4ac)]/2a

a)

x=3, x=-2

b)

x=-3, x= 1/2

c)

x=-3, x=2

d)

x=3, x=-1/2

168.

Solve for x: 9^2x = 27

a)

x = 3/4

b)

x = 81

c)

x = 3

d)

x = 3/2

169.

log₇(x - 48) + log₇x = 2

a)

7

b)

49

c)

-1

d)

undefined

170.

Solve for x.
e^2x - 6e^x + 8 = 0

a)

x = ln 2

b)

x = ln 4 and x = ln 2

c)

x = ln 4

d)

No solution

171.

What is the domain of:

a)

All real numbers

b)

x ≠ -5/9

c)

x < -5/9

d)

x > -5/9

172.

Given g(x) = (2 - 3x)/(5x), write an equation for g^-1(x).

a)

g^-1(x) = 2/(5x - 3)

b)

g^-1(x) = (2 - 3x)/(5x)

c)

g-1(x) = (2 + 3x)/(5x)

d)

g^-1(x) = 2/(5x + 3)

173.

What is the domain of :

a)

x > -2

b)

x ≠ -2

c)

x ≠ 2

d)

x > 2

174.

Is f(x) = 3x⁴ - 6x² even, odd or neither?

a)

Even

b)

Odd

c)

Neither

175.

x⁵ - 3x³ - x even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

176.

Write the equation in slope-intercept form of the line that is perpendicular y = -5x + 1 and goes through the point (2, -1).

a)

y = -5x + 11

b)

y = -5x + 9

c)

y = (1/5)x - (2/5)

d)

y = (1/5)x - (7/5)

177.

Simplify completely.

a)

(12√15)/15

b)

(4√15)/5

c)

4/5

d)

Can't Simplify

178.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

179.

What is the remainder of the following problem?
x⁴-3x³+6x²-2x+8 Divide by x-3

a)

-224

b)

56

c)

224

d)

-83

180.

What is f(2)?

a)

0

b)

1

c)

2

d)

-1

181.

The King Arthur Carousel at Disneyland has a 50 foot diameter and makes 4 revolutions per minute. Find the angular speed.

a)

8 feet per minute

b)

8pi radians per minute

c)

8

d)

25 feet per minute

182.

The King Arthur Carousel at Disneyland has a 50 foot diameter and makes 4 revolutions per minute. Find the linear speed.

a)

1256.6 feet per min

b)

100 feet per min

c)

2500 feet per min

d)

628.3 feet per min

183.

What is $\frac{2\pi}{3}$ radians in degrees?

a)

$150\degree$

b)

$120\degree$

c)

$180\degree$

d)

$30\degree$

184.

What is $225\degree$ in radians?

a)

$\frac{7\pi}{4}$

b)

$\frac{5\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

$\frac{5\pi}{3}$

185.

What is $\frac{11\pi}{6}$ radians in degrees?

a)

30

b)

330

c)

360

d)

300

186.

What is $270\degree$ in radians?

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{2}$

c)

$\frac{3\pi}{4}$

d)

$\frac{\pi}{2}$

187.

What is $\frac{7\pi}{4}$ in degrees?

a)

$300\degree$

b)

$135\degree$

c)

$315\degree$

d)

$45\degree$

188.

Convert 150⁰ to radians

a)

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

b)

$\frac{3\pi}{4}$

c)

$\frac{7\pi}{6}$

d)

$\frac{2\pi}{3}$

189.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

190.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

191.

Which is the correct conversion factor to use when converting from DEGREES TO RADIANS?

a)

180^o/π rad

b)

π rad / 180^o

c)

π rad / 360^o

d)

^360o/π rad

192.

How many DEGREES are in a circle?

a)

180^o

b)

360^o

c)

π rad

d)

2π rad

193.

How many RADIANS are in a circle?

a)

180^o

b)

360^o

c)

π rad

d)

2π rad

194.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

195.

Which quadrant is 2π/3 in?

a)

I

b)

II

c)

III

d)

IV

196.

In what quadrant is 285°

a)

I

b)

II

c)

III

d)

IV

197.

What is the co-terminal angle of 210⁰ ?

a)

-30⁰

b)

-150⁰

c)

-40⁰

d)

150⁰

198.

What is the co-terminal angle of -80⁰ ?

a)

-10⁰

b)

-280⁰

c)

10⁰

d)

280⁰

199.

What is 60 degrees in radians?

a)

2π/3

b)

π/3

c)

4π/3

d)

π/6

200.

Given the point (-12,5) on the triangle shown,

what is sin $\theta?$

a)

$\frac{-12}{13}$

b)

$\frac{5}{13}$

c)

$\frac{5}{-12}$

d)

$\frac{-12}{5}$

201.

Given the point (-4, -3) on the terminal side of the angle $\theta.$

What is sin $\theta?$

a)

3/5

b)

-5/4

c)

-3/5

d)

-4/5

202.

Given the point (6, 3) on the terminal side of the angle $\theta.$

What is sec $\theta?$

a)

$\sqrt{5}$

b)

$\frac{\sqrt{5}}{2}$

c)

1/2

d)

2

203.

Given the point (-7, $\sqrt{15}$ ) on the terminal side of the angle $\theta.$

What is cos $\theta?$

a)

-8/7

b)

$-\frac{\sqrt{15}}{7}$

c)

-7/8

d)

$-\frac{7\sqrt{15}}{15}$

204.

Given the point (3, $\sqrt{7}$ ) on the terminal side of the angle $\theta.$

What is sec $\theta?$

a)

3/4

b)

$\frac{\sqrt{7}}{3}$

c)

$\frac{3\sqrt{7}}{7}$

d)

4/3

205.

sin (π/2)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

206.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

207.

cos(π)

a)

√3/2

b)

-√2/2

c)

-1

d)

1

208.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

209.

tan(3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

210.

tan(300^o)

a)

-√3 /3

b)

½

c)

2√3 /3

d)

-√3

211.

cos(30^o)

a)

- ½

b)

√3/2

c)

2√3 /3

d)

½

212.

Based on the unit circle, what is the value of tan?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

213.

sin(11π/6)

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

214.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

215.

Find sin(-240°)

a)

(√3)/2)

b)

(-1/2)

c)

(√2/2)

d)

(1/2)

216.

Find cos(600°)

a)

(-1/2)

b)

(-√3/2)

c)

(√3/2)

d)

(√2/2)

217.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

218.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

219.

At θ = 30°, what is the equivalent angle measure in radians?

a)

π/2

b)

π/3

c)

π/4

d)

π/6

220.

What radian measure corresponds to the point on the unit circle?

a)

π/4

b)

3π/2

c)

5π/4

d)

7π/3

221.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$6\sin\theta=3$

a)

$60\degree$

b)

$300\degree$

c)

$30\degree$

d)

$150\degree$

222.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$4\cos\theta=-2$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

223.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-1+\sin\theta=-1$

a)

$0\degree$

b)

$90\degree$

c)

$180\degree$

d)

$270\degree$

e)

$360\degree$

224.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$5+\tan\theta=4$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

225.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-15+4\cos\theta=-15-2\sqrt{2}$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

226.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$1-2\sin\theta=-1$

a)

$0\degree$

b)

$90\degree$

c)

$180\degree$

d)

$270\degree$

e)

$360\degree$

227.

Solve on the Interval [0,2π)
tan(x)+1=2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

228.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

229.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

230.

Solve on the domain [0,2π)
1/4sin x + 1= 0

a)

0

b)

7π/4

c)

5π/4

d)

No solution

231.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

232.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

233.

4π/3 is equal to how many degrees?

a)

60°

b)

240°

c)

300°

d)

120°

234.

What is tan 45°?

a)

1

b)

^√2/₂

c)

^√3/₂

d)

½

235.

What is tan 90°?

a)

1

b)

undefined

c)

0

d)

½

236.

How many radians in a full circle?

a)

π/2

b)

π

c)

3π/2

d)

2π

237.

Find the exact value of each trigonometric function:

\tan270\degree

a)

$0$

b)

Undefined

c)

$-1$

d)

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

238.

Find the exact value of each trigonometric function:

\tan\frac{5\pi}{3}

a)

$\frac{\sqrt{3}}{3}$

b)

$\frac{1}{2}$

c)

$-\sqrt{3}$

d)

$-\frac{\sqrt{3}}{3}$

239.

Find the exact value of each trigonometric function:

\sin\frac{3\pi}{2}

a)

$Undefined$

b)

$-\frac{\sqrt{3}}{2}$

c)

$-1$

d)

$\frac{1}{2}$

240.

Find the exact value of each trigonometric function:

\tan0

a)

$1$

b)

$0$

c)

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

d)

$Undefined$

241.

Find the exact value of each trigonometric function:

\tan180\degree

a)

$-1$

b)

$0$

c)

$-\sqrt{3}$

d)

$-\frac{\sqrt{3}}{3}$

242.

a)

dandelion

b)

crocus

c)

rose

d)

lily

243.

a)

lily

b)

snowdrop

c)

lily of the valley

d)

sunflower

244.

a)

rose

b)

lily

c)

tulip

d)

carnation

245.

a)

sunflower

b)

rose

c)

daffodil

d)

lily

246.

a)

rose

b)

lily

c)

orchid

d)

sunflower

247.

a)

rose

b)

poppy

c)

tulip

d)

lily

248.

The study of birds is known as

a)

Herpetology

b)

Ornithology

c)

Entomology

d)

Archaeoptry

249.

Green, Orange, & Violet are created after mixing two Primary colors together. What are these colors also referred to as?

a)

Secondary Colors

b)

Primary Colors

c)

Tertiary Colors

d)

Analogous Colors

250.

These colors are opposite from each other on the color wheel:

a)

Tertiary Colors

b)

Primary Colors

c)

Analogous Colors

d)

Complementary Colors

251.

Blues, Greens, and Violets depict feelings of coolness, relaxation, and zen. These colors are also known as:

a)

Warm Colors

b)

Cool Colors

c)

Tertiary Colors

d)

Analogous Colors

252.

Which among the image is the CLAW HAMMER

a)

b)

c)

d)

253.

Solve for x: 9^2x = 27

a)

x = 3/4

b)

x = 81

c)

x = 3

d)

x = 3/2

254.

What is the domain of:

a)

All real numbers

b)

x ≠ -5/9

c)

x < -5/9

d)

x > -5/9

255.

What is the domain of :

a)

x > -2

b)

x ≠ -2

c)

x ≠ 2

d)

x > 2

256.

Find the zeros of the polynomial function: x³ - x² - 10x - 8

a)

-1, -2, 4

b)

1, -2, -4

c)

1, 2, -4

d)

-1, 2, 4

257.

Is f(x) = 3x⁴ - 6x² even, odd or neither?

a)

Even

b)

Odd

c)

Neither

258.

Given g(x) = (2 - 3x)/(5x), write an equation for g^-1(x).

a)

g^-1(x) = 2/(5x - 3)

b)

g^-1(x) = (2 - 3x)/(5x)

c)

g-1(x) = (2 + 3x)/(5x)

d)

g^-1(x) = 2/(5x + 3)

259.

Convert 210 degrees to radians.

a)

7pi/6

b)

2pi/3

c)

5pi/3

d)

5pi/6

260.

(3+8i)(-2-i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

261.

What type of function is this?

a)

Quadratic

b)

Linear

c)

Rational

d)

square root

262.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

263.

Which of these is NOT an asymptote on this graph?

a)

x=-3

b)

x=3

c)

y=2

d)

y=-3

264.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

265.

Factor Completely: 4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

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

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

266.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

267.

What is the domain of this function?

a)

All real x except -4

b)

All real x except -3

c)

All real x except 3

d)

All real x except 0

268.

What is the domain of the graph?

a)

All real numbers

b)

To Infinity and beyond

c)

y ≥ 0

d)

x ≥ 0

269.

Find the domain.

f(x) = x³ + 9x - 8

a)

[-8, ∞)

b)

all real numbers

c)

all real numbers except 8

d)

(∞, -8]

270.

Find the domain of h(x):

a)

(-∞, +∞)

b)

(-∞, -2) U (-2, ∞)

c)

(2, ∞)

d)

[-2, ∞)

271.

Given g(x)= -3x and f(x)=x²+2, find g(f(x)).

a)

g(f(x))= -3x²-6

b)

g(f(x))= -3x²+2

c)

g(f(x))=9x²+2

d)

g(f(x))= -9x²+2

272.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

273.

If g(x) = 6x + 4 and
f(x) = 2x - 7
Find f(x) * g(x)

a)

8x - 3

b)

4x + 11

c)

12x² - 28

d)

12x² - 34x - 28

274.

g(n)=4n-4
f(n)=n³+4
Find (g+f)(n)

a)

-2n²-n+9

b)

-n³-4n

c)

-3n³-3n-5

d)

n³+4n

275.

g(x)=2x+2
f(x)=x-1
Find (gf)(x)

a)

-3x³-7x²-2x

b)

2x³-2

c)

2x²-2

d)

2x²+4x+2

276.

What is the inverse of the function
f(x) = 2x + 4 ?

a)

f^-1(x) = 4(x -2)

b)

f^-1(x) = (x-4)/2

c)

f^-1(x) = x/2 - 4

d)

f^-1(x) = x/4 + 2

277.

Find the inverse of y = x² + 1

a)

x = y² - 1

b)

x = y² + 1

c)

y = √(x+1)

d)

y = √(x-1)

278.

Where is the function decreasing?

a)

(4, ∞)

b)

(-∞,4)

c)

(-4, ∞)

d)

4 < x < 6

279.

Where is the function increasing?

a)

(4, ∞)

b)

(−4, ∞)

c)

(6, ∞)

d)

4 < x < 6

280.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and
x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and
x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and
x→∞, y→⁻∞

281.

Has magnitude and direction

a)

Scalar

b)

Vector

c)

Initial Point

d)

Terminal Point

282.

Two vectors that have the same magnitude and direction

a)

Parallel vectors

b)

Equivalent vectors

c)

Opposite vectors

283.

Find the component form of a vector whose initial point is (5, 7) and terminal point is (1, 10)

a)

<-4, 3>

b)

<4, -3>

c)

5

d)

<6, 17>

284.

The solution of the dot product is always a vector

a)

True

b)

False

285.

u + v

a)

4i - j

b)

6i + j

c)

3j + 4j

d)

i + 6j

286.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

287.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

288.

Find the angle between the two vectors <3, 4> and <4, -3>

a)

90°

b)

45°

c)

53.13°

d)

106.26°

289.

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

a)

<21, 2>

b)

<-11, 26>

c)

<8, 3>

d)

23

290.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

291.

Find the magnitude of the vector <-5, 12>

a)

13

b)

10.91

c)

7

d)

17

292.

Find the unit vector in the direction of <4, -3>

a)

<⅘, -⅗>

b)

<0.57, -0.43>

c)

<1, -1>

d)

-¾

293.

Find the angle between the two vectors <3, 4> and <4, -3>

a)

90°

b)

45°

c)

53.13°

d)

106.26°

294.

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).

a)

6

b)

8.2

c)

10

d)

10.4

295.

Determine the magnitude of the vector <8, -2>

a)

2√3

b)

2√17

c)

2√15

d)

2√5

296.

What is the sum of 1/2 + 1/3 + 1/6?

a)

3/14

b)

3/11

c)

1

d)

6/8

297.

1/8 + 1/12

a)

5/24

b)

2/96 = 1/48

c)

2/20 = 1/10

d)

1/20

298.

11/12 - 3/4

a)

14/12 = 1 2/12 = 1 1/6

b)

8/8 = 1

c)

2/12 = 1/6

d)

8/12 = 2/3

299.

9 - 4 1/3

a)

4 2/3

b)

5 1/3

c)

5 2/3

d)

4 1/3

300.

1/4 ÷ 2

a)

1/8

b)

2

c)

8

d)

1/2

301.

6 ÷3/5

a)

18/5 = 3 3/5

b)

3/30 = 1/10

c)

5/18

d)

30/3 = 10

302.

a)

13/3

b)

13/27

c)

9/39

d)

3/13

303.

a)

5/6

b)

3/15

c)

3/8

d)

2/15

304.

a)

9/12

b)

9/14

c)

7/8

d)

6/24

305.

a)

5/7

b)

4/33

c)

8/66

d)

11/48

306.

a)

4/10

b)

2/5

c)

4/7

d)

5/8

307.

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

a)

^.08

b)

^1.08

c)

.92

d)

8

308.

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

309.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

310.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

311.

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

312.

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

a)

$5n+1$

b)

$-5n+1$

c)

$-2n+1$

d)

$-6n-1$

313.

$f(x)=x^2+1$ $g(x)=2x-5$

Find $f(x)-g(x)$

a)

$x^2-2x+6$

b)

$-x^2+2x+4$

c)

$-x^2-2x-6$

d)

$x^2-2x-4$

314.

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

315.

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

a)

x² + 8x + 1

b)

x² + 6x - 1

c)

5x² + 8x - 1

d)

x² + 8x -1

316.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

317.

a)

b)

c)

d)

318.

a)

b)

c)

d)

319.

$f(x)=3x^2-2x+1$ and g(x) = x - 4. What restrictions, if any, are there for $\frac{f(x)}{g(x)}$ ?

a)

no restrictions

b)

x ≠ -4

c)

x ≠ 4

d)

x ≠ 0

320.

f(x)=x²-1
g(x)=x-1
Find (f/g)(x)

a)

x+1

b)

x²+1

c)

x

d)

x²-1

321.

f(x) = 4x+8
g(x) = x+3,
Find f(x)*g(x)

a)

4x²+24

b)

4x²+20x+24

c)

4x²+12x+24

d)

4x²+4x+24

322.

What is the domain of the graph of the radical function?

a)

(-∞, ∞)

b)

[-7, ∞)

c)

[0, ∞)

d)

[4, ∞)

323.

Determine the domain of $f\left(x\right)=\frac{6}{\sqrt{x+2}}$

a)

$x>2$

b)

$x\ge0$

c)

$\left(-\infty,-2\right)$

d)

$\left(-2,\infty\right)$

324.

Given h(x) = 2x- 1
and g(x) = 3x + 4, find (4h - 3g)(x).

a)

-x - 5

b)

-x -16

c)

-x + 5

d)

-x + 16

325.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

326.

What is the domain of the graph of the radical function?

a)

(-∞, ∞)

b)

[-7, ∞)

c)

[0, ∞)

d)

[4, ∞)

327.

Find the domain for the function: $f(x)=\frac{2x-1}{3x+6}$

a)

All real numbers x ≠ 2

b)

All real numbers x ≠ -2

c)

All real numbers x ≠ 3

d)

All real numbers

328.

Find the Difference Quotient

a)

2x

b)

2x - h

c)

2x + h

d)

2h

329.

Find the Difference Quotient

a)

2x - 2

b)

2x - h - 2

c)

2x + h - 2

d)

2h - 2

330.

Does this graph in the back have maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

331.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

332.

Is the leading coefficient for the polynomial shown positive or negative?

a)

Negative

b)

Positive

c)

Cannot be determined

333.

The function is decreasing when...

a)

(-1.5, 1.5)

b)

(-∞, -1.5)

c)

(1.5, ∞)

d)

(-1.5, 2)

334.

The polynomial is...

a)

Odd degree, positive leading coefficient.

b)

Odd degree, negative leading coefficient.

c)

Even degree, positive leading coefficient.

d)

Even degree, negative leading coefficient.

335.

How many extrema (maxes and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

336.

Factor.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

337.

Factor by grouping:

x³-5x²+5x-25

a)

(x²-5)(x-5)

b)

(x²+5)(x-5)

c)

(x²+5)(x+5)

d)

(x²-1)(x-25)

338.

(2x - 1)(x + 2)

a)

2x² + 3x - 2

b)

2x² - 5x - 2

c)

2x² + 3x + 2

d)

2x² - 5x + 2

339.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

340.

What is the leading coefficient for the polynomial given by:

y = 3x² + 9x⁵ − 4 + 10x⁸ + 2x⁹ ?

a)

2

b)

10

c)

9

d)

3

341.

Which one of the following could be the polynomial seen in the image?

a)

y = (x + 3)(x + 1)(x − 2)

b)

y = -(x + 3)(x + 1)(x − 2)

c)

y = -(x − 3)(x + 1)(x + 2)

d)

y = (x + 3)(x + 1)(x + 2)

342.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

343.

What is the domain of the following graph?

a)

(-∞,∞)

b)

(-∞,4]

c)

(-∞,3]

d)

[-2.5,4]

344.

What is the domain of the graph?

a)

{x| -∞ ≤ x ≤ ∞}

b)

(-∞,∞)

c)

$\left[-3,3\right]$

d)

[-15. 9]

345.

What is the range of this functions?

a)

[-6, 3]

b)

(-6, 3)

c)

All real numbers

d)

[-2, 4]

346.

What are all the x-intercepts?

a)

(-2.55, 0), (2.55, 0)

b)

(-3,0), (-2,0), (2,0), (3,0)

c)

(0, 36)

d)

(-∞,∞)

347.

What is the relative min?

a)

(0, 36)

b)

(-2.55, -6.55), (2.55, -6.55)

c)

(-∞, ∞)

d)

None

348.

(4a + 2)(6a² − a + 2)

a)

24a³ + 16a² + 6a + 4

b)

24a³ + 8a² + 10a + 4

c)

24a³ + 8a² + 6a + 4

d)

24a³ - 8a² - 6a + 4

349.

Find the area of the rectangle.

a)

8x² + 14x + 6

b)

12x + 10

c)

8x² + 6

d)

6x² + 14x + 6

350.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

351.

Using the degree and leading coefficient, match the graph to an equation.

a)

y=(2x-1)(x+2)²

b)

y=(2x-1)(x+2)³

c)

y=(2x+1)(x+2)²

d)

y=(2x+1)(x+2)

352.

Write the equation of the polynomial function with

zeros: 0, -2, 4 and the root of zero having an order of 3

a)

f(x) = x³(x-2)(x+4)

b)

f(x) = x³(x+2)(x-4)

c)

f(x) = x²(x-2)(x+4)

d)

f(x) = x²(x+2)(x-4)

353.

Select all the even degree functions.

a)

A

b)

B

c)

C

d)

D

354.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

355.

What is row 5 of Pascal's Triangle?

a)

1, 2, 1

b)

1, 3, 3, 1

c)

1, 4, 9, 4, 1

d)

1, 5, 10, 10, 5, 1

356.

a)

A

b)

B

c)

C

d)

D

357.

FInd the domain and range.

a)

A

b)

B

c)

C

d)

D

358.

Select the correct expansion of

(1 + 4x)³

a)

1 + 12x + 12x² + 4x³

b)

1 + 12x + 48x² + 64x³

c)

1 + 3x + 3x² + x³

d)

1 + 4x + 16x² + 64x³

359.

Use Pascal's Triangle to expand the expression.

(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

360.

What is the degree of the polynomial 3x⁴ + 2x² + 5x ?

a)

1

b)

2

c)

3

d)

4

361.

How many terms are in

$3x^2\ +4x\ -\ 5$

a)

1

b)

2

c)

3

d)

None

362.

Classify the polynomial by degree

$5x-1$

a)

quadratic

b)

linear

c)

binomial

d)

constant

363.

Put the polynomial in standard form

$6x\ -\ 4x^2+2\ -\ 5x^3$

a)

$-5x^3-4x^2+6x+2$

b)

$-4x^2+6x-5x^3+2$

c)

$-5x^3-6x+4x^2+2$

d)

it is in standard form

364.

What is the constant in

$7y^4-5x^3+9y^2-8x+4$

a)

7

b)

-5

c)

-8

d)

4

365.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

366.

Identify the degree of the monomial:
8a³

a)

8

b)

1

c)

3

d)

11

367.

Identify the constant term:
4x³ + 2x - 9

a)

4

b)

-2

c)

-9

d)

9

368.

What is the degree of the polynomial? 3x² + 5xy - 4x⁷y

a)

7

b)

8

c)

2

d)

3

369.

Given the polynomial:
9x⁷ + 3x⁶ - 5 + x²What is the constant?

a)

9

b)

3

c)

5

d)

-5

370.

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

a)

1

b)

2

c)

3

d)

4

371.

What is the degree of the polynomial 17x + 4

a)

0

b)

1

c)

2

d)

3

372.

What is the degree of this term?
-7xyz²

a)

3

b)

4

c)

-7

d)

7

373.

The number in front of the variable is called the....

a)

exponent

b)

base

c)

coefficient

d)

fronter

374.

A letter that represents an unknown number

a)

coefficient

b)

base

c)

variable

d)

constant

375.

f(x) = 3x² + 5x - 9

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

376.

f(x) = -3x² - 5x + 12

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

377.

f(x) = 4 + 3x - 6x⁷ + 3x⁴

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

378.

Describe the end behavior of the graph.

a)

down, down

b)

down, up

c)

up, down

d)

up, up

379.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

380.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

381.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

382.

Determine the end behavior of the graph of
f(x) = 3x⁴ + 2x - 5

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

383.

What is the name of the term that affects the end behavior

a)

Last Term

b)

First Term

c)

Leading Term

d)

Middle Term

384.

Determine the end behavior of the graph of
f(x) = -7x³ + 2x - 1

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

385.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

386.

What is the degree?

a)

Odd

b)

Even

387.

Identify the sign of the leading coefficient and the degree of the polynomial.

a)

Leading Coefficient Positive

Degree - Even

b)

Leading Coefficient Positive

Degree - Odd

c)

Leading Coefficient Negative

Degree - Even

d)

Leading Coefficient Negative

Degree - Odd

388.

What is the degree classification of this polynomial?
x²+4x-8

a)

binomial

b)

trinomial

c)

quadratic

d)

cubic

389.

The degree of a polynomial can be determined by the largest powered monomial of the polynomial.
What is the degree of the polynomial:
f(x) = 3x² + 4x - 5

a)

Degree 2 (quadratic)

b)

Degree 3 (cubic)

c)

Degree 4 (quartic)

d)

Degree 5 (quintic)

390.

g\left(n\right)=n^2+4+2n

and

h\left(n\right)=-3n+2

Find\ \left(g\cdot h\right)\left(1\right)

a)

-7

b)

-5

c)

0

d)

35

391.

$h\left(x\right)=3x+3$ and $g\left(x\right)=-4x+1$

$Find\ \left(h+g\right)\left(0\right)$

a)

2

b)

1

c)

4

d)

3

392.

$g\left(x\right)=3x+3$ $h\left(x\right)=4x+5$

$Find\ g\left(3\right)-h\left(3\right)$

a)

9

b)

-5

c)

-9

d)

5

393.

$g\left(a\right)=3a+2$ and $f\left(a\right)=9a-4$

$Find\ \left(\frac{g}{h}\right)\left(1\right)$

a)

0

b)

2

c)

3

d)

1

394.

If\ f\left(x\right)=x+2\ and\ g\left(x\right)=2x^2

Find\ \left(f+g\right)\left(x\right)

a)

$3x^3+2$

b)

$3x^2+2$

c)

$2x^3+x^2+2x$

d)

$2x^2+x+2$

395.

$If\ f\left(x\right)=2x+3\ and\ g\left(x\right)=3x-1$

Find\ \left(f\cdot g\right)\left(x\right)

a)

$5x+2$

b)

$6x^2+7x-3$

c)

$6x^2-3$

d)

$6x^2+11x-3$

396.

$If\ f\left(x\right)=1-x\ and\ g\left(x\right)=1+x$
$Find\ g\left(f\left(1\right)\right)$

a)

1

b)

4

c)

3

d)

2

397.

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

a)

7

b)

-2

c)

-9

d)

-10

398.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

399.

If\ f\left(x\right)=x+2\ and\ g\left(x\right)=2x^2

Find\ \left(f+g\right)\left(x\right)

a)

$3x^3+2$

b)

$3x^2+2$

c)

$2x^3+x^2+2x$

d)

$2x^2+x+2$

400.

$If\ f\left(x\right)=2x+3\ and\ g\left(x\right)=3x-1$

Find\ \left(f\cdot g\right)\left(x\right)

a)

$5x+2$

b)

$6x^2+7x-3$

c)

$6x^2-3$

d)

$6x^2+11x-3$

401.

Solve: 3(x-4) = -3

a)

3

b)

-3

c)

5

d)

-5

402.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

403.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

404.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

405.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

406.

2x + 3(5x - 7) = 47

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

407.

Solve and graph the inequality.
77 ≤ 5 + 8n

a)

A

b)

B

c)

C

d)

D

408.

5z - 2 - 2z < 13

a)

z > 5

b)

z < 5

c)

z > 1

d)

z < 1

409.

solve 5( 6 + 3r) + 7 ≥ 127

a)

r ≤ 6

b)

r ≥ 6

c)

r ≤ -6

d)

r ≥ -6

410.

Which graph corresponds to the solution set of $5\left(x-4\right)<3x+8$ ?

a)

b)

c)

d)

411.

Solve: 3(x-4) = -3

a)

3

b)

-3

c)

5

d)

-5

412.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

413.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

414.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

415.

For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?

a)

4x=472

b)

9x=472

c)

4+9x=472

d)

4+x=472

416.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

417.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

418.

2x + 3(5x - 7) = 47

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

419.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

420.

2x + 3(5x - 7) = 47

a)

1

b)

2

c)

3

d)

4

421.

Solve by completing the square.
$x^2-8x-20=0$

a)

$x=\left\{-2,\ 10\right\}$

b)

$x=\left\{-10,\ 2\right\}$

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

422.

Solve by completing the square.
$x^2-12x+20=0$

a)

$x=\left\{2,\ 10\right\}$

b)

$x=\left\{-10,\ -2\right\}$

c)

$x=\left\{-12,\ 20\right\}$

d)

$x=\left\{12,\ 20\right\}$

423.

Solve by completing the square.
$x^2-4x-20=0$

a)

$x=\left\{\pm6\sqrt{2}-2\right\}$

b)

$x=\left\{\pm6\sqrt{2}+2\right\}$

c)

$x=\left\{\pm2\sqrt{6}+2\right\}$

d)

$x=\left\{\pm2\sqrt{6}-2\right\}$

424.

Solve by completing the square.
$x^2-6x-27=0$

a)

$x=\left\{-9,\ -3\right\}$

b)

$x=\left\{-3,\ 9\right\}$

c)

$x=\left\{-9,\ 3\right\}$

d)

$x=\left\{3,\ 9\right\}$

425.

Solve by completing the square.
$x^2-14x-15=0$

a)

$x=\left\{1,\ 15\right\}$

b)

$x=\left\{-15,\ -1\right\}$

c)

$x=\left\{-15,\ 1\right\}$

d)

$x=\left\{-1,\ 15\right\}$

426.

Solve by completing the square.
$x^2-6x-59=0$

a)

$x=\left\{\pm2\sqrt{17}+3\right\}$

b)

$x=\left\{\pm17\sqrt{2}+3\right\}$

c)

$x=\left\{\pm2\sqrt{17}-3\right\}$

d)

$x=\left\{\pm17\sqrt{2}-3\right\}$

427.

Solve by completing the square.
$x^2-4x-5=0$

a)

$x=\left\{-5,\ 1\right\}$

b)

$x=\left\{-1,\ 5\right\}$

c)

$x=\left\{-5,\ -1\right\}$

d)

$x=\left\{1,\ 5\right\}$

428.

Solve by completing the square.
$x^2-4x-21=0$

a)

$x=\left\{-7,\ 3\right\}$

b)

$x=\left\{3,\ 7\right\}$

c)

$x=\left\{-3,\ 7\right\}$

d)

$x=\left\{-7,\ -3\right\}$

429.

Solve by completing the square.
$x^2-16x+48=0$

a)

$x=\left\{-12,\ 4\right\}$

b)

$x=\left\{-12,\ -4\right\}$

c)

$x=\left\{-4,\ 12\right\}$

d)

$x=\left\{4,\ 12\right\}$

430.

Solve by completing the square.
$x^2-8x-14=0$

a)

$x=\left\{\pm\sqrt{30}+4\right\}$

b)

$x=\left\{\pm\sqrt{4}+30\right\}$

c)

$x=\left\{\sqrt{30}+4\right\}$

d)

$x=\left\{\sqrt{30}-4\right\}$

431.

What is the value of cosine at 0

a)

0

b)

1/2

c)

1

d)

√3 / 2

432.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

433.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

434.

What is the value of cosine at 135

a)

0

b)

1/2

c)

√2 /2

d)

-√2 /2

435.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

436.

What is the value of cosine at 270

a)

0

b)

1

c)

-1

437.

At what point are sine and cosine the same value?

a)

0

b)

90

c)

45

d)

60

438.

What is the value of sine at 330

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

439.

What is the value of cosine at 315

a)

0

b)

1

c)

√2 / 2

d)

-√2 /2

440.

What is the value of sine at 150

a)

0

b)

1/2

c)

1

d)

√3 / 2

441.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

442.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

443.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

444.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

445.

log(216)=(x-4)log(6)

a)

1

b)

3

c)

7

d)

0

446.

2log₅7 = 3x+1 log₅49

a)

1

b)

-1

c)

5

d)

0

447.

3^{2x – 6} = 81

a)

x = log 4

b)

x = 5

c)

x = 4

d)

x = -1

448.

Solve the equation for x.

a)

7.389

b)

0.693

c)

0.0183

d)

6.581

449.

Graph: f(x) = 2^-x+2 - 1

a)

A

b)

B

c)

C

d)

D

450.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

451.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

452.

Determine the equation of the asymptote?

a)

x=3

b)

x=4

c)

y=-4

d)

y=4

453.

2 * 4^{3x – 6}– 8 = 120

a)

x = 3

b)

x = 4

c)

x = 2.9

d)

x = 8

454.

log₂(2) + log₂(8x) = 6

a)

x = 3

b)

x = 2

c)

x = 6

d)

x = 4

455.

2log (2x)⁴ = 16

a)

x = 4

b)

x = 10

c)

x = 50

d)

x = 2

456.

To solve, 16^5x = 64^x+7, what would be the correct set-up?

There is more than one correct answer.

a)

4^4(5x)=4^16(x+7)

b)

8^2(5x)=8^8(x+7)

c)

4^2(5x)=4^3(x+7)

d)

2^4(5x)=2^6(x+7)

457.

Solve each equation. Select the closest answer.

a)

8

b)

-10

c)

75

d)

20

458.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

459.

Solve

a)

46/5

b)

5/46

c)

-46/5

d)

-5/46

460.

Solve the equation:

$625^{-3x}=125^{\left(2x+2\right)}$

a)

$0$

b)

$1$

c)

$-\frac{1}{3}$

d)

$-9$

461.

Solve:

log₂ x + log₂ (x + 5) = log₂ (3x + 8)

a)

x = 2

b)

x = -4

c)

x = 2 and x = -4

d)

no solution

462.

Solve log₉ (x - 4) + log₉ (x + 1) = log₉ (x + 5) + log₉ (x - 6)

a)

17/2

b)

-9/16

c)

13

d)

-8

463.

Simplify the following: $\log_5\left(3\right)+\log_5\left(r\right)-\log_5\left(w\right)$

a)

$\log_5\left(3rw\right)$

b)

$\log_5\left(3+r-w\right)$

c)

$\log_5\left(\frac{3r}{w}\right)$

d)

$\frac{\log_5\left(3r\right)}{\log_5\left(w\right)}$

464.

Expand the following: $\log_2\left(5a^{10}\right)$
hint: $5a^{10}=5\cdot a^{10}$

a)

$\log_25+10\log_2a$

b)

$10\log_25+\log_2a$

c)

$\log_2\left(50a\right)$

d)

$\log_250+\log_2a$

e)

$10\log_25-10\log_2a$

465.

a)

log₅(x²z²y¹⁰)

b)

log₅(z²y²x¹⁰)

c)

log(zy²x¹⁰)

d)

log₅(z² + y²+ x¹⁰)

466.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

467.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

468.

Choose the correct expanded natural logarithm:

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

$\ln2+2\ln x+\ln y+4\ln z$

b)

$\ln2+2\ln x+\ln y-4\ln z$

c)

$2\ln(2xy)-4\ln z$

d)

$2\ln2x+\ln y-4\ln z$

469.

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$

a)

$\log_6\left(\frac{6\sqrt{a}}{b}\right)\$

b)

$\log_6\left(\frac{\sqrt{a}}{b}+1\right)\ \$

c)

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +1$

d)

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +6$

470.

Use the properties of logarithms to find the exact value of each expression.

$e^{\ln8}=$

(a)

471.

Use the properties of logarithms to find the exact value of each expression.

$2^{\log_27}=$

(a)

472.

What is the domain of the function in this graph?

a)

(-∞, 3]

b)

[3, ∞)

c)

(-∞, 0]

d)

[0, ∞)

473.

What is the range of the function in this graph?

a)

(-∞, 3]

b)

[3, ∞)

c)

(-∞, 0]

d)

[0 ∞)

474.

Which of the following correctly describes the domain and range for the function graphed?

a)

Domain: [-5, ∞)

Range: (-∞, 4]

b)

Domain: [-5, ∞)

Range: [4, -∞)

c)

Domain: (-∞, ∞)

Range: (-∞, ∞)

d)

Domain: [4, ∞)

Range: (-∞, -5]

475.

Describe the end behavior for the function graphed.

a)

b)

c)

d)

476.

Was the inverse function found correctly?

a)

no,

b)

yes

477.

How can you determine if a graph is a function or not a function?

a)

it passes the vertical line test

b)

every input has exactly two output

c)

passes the horizontal line test

d)

it looks straight

478.

Range is:

a)

All x values, from left to right.

b)

All y values, from left to right.

c)

All y values, from bottom to top.

d)

All x values, from bottom to top.

479.

Domain is:

a)

All x values, from left to right.

b)

All y values, from bottom to top.

c)

All x values from bottom to top.

d)

All y values from left to right.

480.

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

a)

g(f(x))= -6x²+31

b)

g(f(x))= -6x²+24

c)

g(f(x))=18x²-84x+90

d)

g(f(x))=9x²-42x-41

481.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

482.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

483.

Which scenario describes the picture shown?

a)

A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?

b)

A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?

c)

An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?

d)

A 5 foot man is 8 feet away from a building. What is the angle of elevation?

484.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

485.

A ramp is being built next to a 4-inch high sidewalk. The ramps angle of inclination is 10 degrees. Estimate the horizontal length of the ramp to the nearest tenth of an inch.

a)

4.1 inches

b)

3.9 inches

c)

22.7 inches

d)

0.7 inches

486.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. How many degrees should the tourist tilt his camera down to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

487.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is closest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

488.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

489.

Which trigonometric ratio is correct?

a)

sinA= opp/adj

b)

cosA= opp/hyp

c)

tanA= opp/adj

d)

sinA= adj/opp

490.

What is the green side labelled as from the starred angle?

a)

adjacent

b)

opposite

c)

hypotenuse

491.

What is the green side labelled as using the starred angle as a starting point?

a)

adjacent

b)

opposite

c)

hypotenuse

492.

Divide $\frac{4}{\sqrt{3}}$

a)

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

b)

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

c)

$4\sqrt{3}$

493.

What is side c?

a)

hypotenuse

b)

leg

c)

long leg

d)

short leg

494.

What is the measure of side c?

a)

7

b)

$\frac{7}{\sqrt{2}}$

c)

$7\sqrt{2}$

d)

14

495.

What type of special right triangle is this?

a)

isosceles right

b)

30-60-90

c)

not a special right triangle

496.

Which expression is equivalent to $\log_2\left(\frac{m^4}{n^7}\right)$

a)

$4\log_2m+7\log_2n$

b)

$7\log_2m+4\log_2n$

c)

$4\log_2m-7\log_2n$

d)

$7\log_2m-4\log_2n$

497.

Solve for x.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

498.

How are exponential and logarithmic functions related?

a)

Opposites

b)

Inverses

c)

Cousins

d)

Reciprocals

499.

Solve for x: log₉(x-5) + log₉(x+3) = 1.

a)

x = 2

b)

x = 4

c)

x = 6

d)

x = 9

Question Bank for Grade 10 Mathematics

Total questions: 499

Worksheet time: 28hrs 51mins

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