Free Printable BQ 2024 CALCULUS 2-5

1.

In the equation, y = mx + b, the letter b is the ___________.

a)

y-intercept

b)

x-intercept

c)

slope

d)

rate of change

2.

What is the slope of the equation?
y = -3x + 4

a)

-3

b)

3

c)

4

d)

-4

3.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

4.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

5.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

6.

a)

Function

b)

Not a Function

7.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

8.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

9.

Bob has $150 in his savings account and saves $40 per month. Which function models his savings?

a)

y = 150 + 40

b)

y = 40x + 150

c)

y = 150x + 40

10.

A golf course charges $15 to rent golf clubs and charges $25 per round to play. Write an equation to represent the total cost, T, for one player.

a)

T = 15 + 25r

b)

T = 15g + 25r

c)

T = 40 r

d)

T = 15r + 25

11.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{-4, 0, 1, 2}
R:{-4, -3, 1}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

12.

Evaluate f(-4) for the function f(x)=3x²-5

a)

f(-4) = 43

b)

f(-4) = 139

c)

f(-4) = -52

d)

f(-4) = -149

13.

What is the domain of the graph shown?

a)

{-2, -1, 0, 1, 2, 3, 4}

b)

{2, 3, 4}

c)

2 ≤ y ≤ 4

d)

-2 ≤ x ≤ 4

14.

What is the range of the following graph?

a)

all real numbers

b)

all integers

c)

any real number greater than zero

d)

it can not be determined

15.

a)

6

b)

-6

c)

14

d)

-14

16.

Find f(2)

a)

5

b)

4

c)

3

d)

0

17.

_{What is the y-intercept of the line?}

a)

(0,¹/₂)

b)

(0,1)

c)

(0, ^-1/2)

d)

(0, -1)

18.

^{What is the x- intercept of the line?}

a)

(1, 0)

b)

(2, 0)

c)

( -1, 0)

d)

(-2, 0)

19.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

20.

What is the y-intercept in the equation x + 2y = 4

a)

(0, 0)

b)

(0, 2)

c)

(4, 0)

d)

(2, 0)

21.

Identify the slope and y-intercept of:
y = 1/5x + 5

a)

slope: 1/6 y-intercept: 4

b)

slope: 1/5 y-intercept: 5

c)

slope: 5/1 y-intercept: 5

d)

slope: 1 y-intercept: 5

22.

Identify the slope and y-intercept of:
y = 3 -x

a)

slope:-1 y-intercept: 3

b)

slope: 1/5 y-intercept: 5

c)

slope: 1 y-intercept: -3

d)

slope: -1 y-intercept: -3

23.

Write a rule: A plumber charges $50 for a house call plus $12 per hour for labor.

a)

y = 50 x + 12

b)

y = 50 + 12 x

c)

y = 62 x

d)

x = 50 + 12y

24.

Write a rule : Miles has joined a weight loss program. His weight is 225 lbs and he is losing weight at a rate of 3 lbs per week.

a)

y = 222 x

b)

y = 225 + 3 x

c)

y = 225 - 3x

d)

y=225x - 3

25.

What slope is parallel to:
m = 3/4

a)

4/3

b)

3/4

c)

-3/4

d)

-4/3

26.

What slope is perpendicular to:
m = 5/8

a)

-5/8

b)

5/8

c)

-8/5

d)

8/5

27.

What is the definition of a function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

28.

Which statement is true?

a)

A vertical line has a slope of zero.

b)

A line that contains points in Quadrant I and Quadrant III must have a negative slope.

c)

A line that rises as you move to the right along the line has a positive slope.

d)

A horizontal line has no slope.

29.

Which of the following is NOT a function?

a)

y = 4

b)

x = 3

c)

y=2x

d)

y=x

30.

Which of the following has a y-intercept of 3?

a)

y = 3x +2

b)

x=3

c)

y=2x+3

d)

y=x

31.

Slope is another word for:

a)

Initial Value

b)

Rate of Change

c)

Change in Y's

d)

Y-intercept

32.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

33.

Is function represented by the table linear or nonlinear?

a)

linear

b)

nonlinear

34.

Is this function linear or nonlinear?

a)

Linear

b)

Nonlinear

35.

Is this function linear or nonlinear?

a)

Linear

b)

Nonlinear

36.

Is the table linear or nonlinear?

a)

Linear

b)

Nonlinear

37.

Which graph is linear?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

38.

What is the y-intercept in the following equation: y=-4x-5

a)

-4

b)

-4x

c)

5

d)

-5

39.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

40.

Find the slope from the table.

a)

-4

b)

1

c)

4

d)

-2

41.

What is the slope of the equation?
y = -3x + 4

a)

-3

b)

4

c)

-4

d)

3

42.

What are the coordinates of the y-intercept of

y=2x^{2\ }-8x+3

a)

(0,3)

b)

(3,0)

c)

(0,2)

d)

(0,-8)

43.

What are the coordinates of the vertex of

y=-2\left(x+1\right)^2-5

a)

(-2,-5)

b)

(1,-5)

c)

(-1,-5)

d)

(0,-5)

44.

What are the x-intercepts of

y=-\left(x+4\right)\left(x-3\right)

a)

-4 and 3

b)

4 and -3

c)

-1 only

d)

x + 4

45.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

46.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

47.

Convert to vertex form:
f(x) = x² + 10x + 24

a)

f(x) = ( x - 5 )² + 1

b)

f(x) = ( x + 5 )² - 1

c)

f(x) = ( x - 5 )² - 1

d)

f(x) = ( x + 5 )² + 1

48.

Does the following function have a maximum or a minimum:

y=250-3x-x^2

a)

Maximum

b)

Minimum

c)

Cannot be determined

d)

Both

49.

(Part 1 of 3)

A ball is launched into the air. Its height in meters, t seconds after launching is given by

h\left(t\right)=16t-t^2

At what time does the ball reach its maximum height?

a)

t = 0

b)

t = 4

c)

t = 8

d)

t = 16

50.

(Part 2 of 3)

A ball is launched into the air. Given that the ball reaches its maximum height (in meters) at t = 8 seconds, find the maximum height

h\left(t\right)=16t-t^2

a)

1 m

b)

8 m

c)

16 m

d)

64 m

51.

(Part 3 of 3)

At what time does the ball hit the ground again?

h\left(t\right)=16t-t^2

a)

t = 2

b)

t = 8

c)

t = 16

d)

t = 50

52.

A quadratic function has x-intercepts of (-2,0) and (3,0) and has a y-intercept of (0,-12). Which is the correct equation for the function?

a)

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

b)

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

c)

$y=-12\left(x+2\right)\left(x-3\right)$

d)

$y=-2\left(x-3\right)$

53.

A quadratic function has a vertex of (3,-1) and passes through the point (4,2). Which the correct function?

a)

$y=\left(x-3\right)^2-1$

b)

$y=\left(x+3\right)^2-1$

c)

$y\ =\ 3\left(x-3\right)^2-1$

d)

$y\ =\ \left(x-3\right)\left(x+1\right)$

54.

(Part 1 of 2)

The cost per day of making x chairs given by $C\left(x\right)=x^2-40x+2500$ dollars.

How many chairs must be made so cost is minimized?

a)

1 chair

b)

20 chairs

c)

25 chairs

d)

35 chairs

55.

(Part 2 of 2)

Given that 20 chairs must be made to minimize cost, what then is the minimum cost?

$C\left(x\right)=x^2-40x+2500\$ dollars

a)

$0

b)

$2100

c)

$2500

d)

$3000

56.

The profit for preparing and selling x sandwiches at a fast food is given by

P\left(x\right)=-x^2\ +200x-1500

in euros.
What is the maximum profit?

a)

100 euros

b)

1500 euros

c)

4500 euros

d)

8500 euros

57.

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

a)

maximum

b)

minimum

c)

neither

d)

both

58.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-1

d)

x=2

59.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

(0, -8)

b)

(0, 3)

c)

(0, 7)

d)

(0, -7)

60.

If given the equation
y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

61.

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

62.

What is the range of this function?

a)

(- ∞,+∞)

b)

[0, +∞)

c)

[-2, +∞)

d)

[2, +∞)

63.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

64.

Solve:
2x² - 9x = 35

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

65.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

66.

Solve:
4x²= -4x -1

a)

x = -½

b)

x = -2

c)

x = 0

67.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

68.

Solve the equation
(x + 3)² = 49.

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

69.

a)

A

b)

B

c)

C

d)

D

70.

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

71.

Convert to vertex form:
f(x) = x² + 10x + 24

a)

f(x) = ( x - 5 )² + 1

b)

f(x) = ( x + 5 )² - 1

c)

f(x) = ( x - 5 )² - 1

d)

f(x) = ( x + 5 )² + 1

72.

What is the degree of the polynomial function
P(x)=3x⁴- 7x²- 2x⁷- x + 4?

a)

4

b)

7

c)

2

d)

1

73.

Identify the end behavior:

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→-∞

d)

The end behavior of the graph is The end behavior of the graph is x →∞,y→⁻∞ and x→∞, y→⁻∞

74.

Identify the end behavior:

a)

The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞

b)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞

c)

The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0

d)

The end behavior of the graph is x →∞,y→∞and x→⁻∞, y→⁻∞

75.

Identify the x-intercepts:

a)

No x-intercpts

b)

x = -2, x = 3, x = -8

c)

x = -2, x = 3

d)

x = -2, x = 3, x = 8

76.

How many relative maximums does this function have?

a)

1

b)

2

c)

3

d)

4

77.

How many relative minimums does this function have?

a)

1

b)

2

c)

3

d)

4

78.

What are all the y-intercepts?

a)

(0, -6.25)

b)

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

c)

(0, 36)

d)

(-∞, ∞)

79.

Identify the decreasing interval:

a)

(0, 4)

b)

(-1, 1)

c)

(∞, -1) U (1, -∞)

d)

(-∞, -1) U (1, ∞)

80.

Is this an odd or even function?

a)

even function

b)

odd function

81.

A rational function can be written in the form

a)

n(x)/d(x)

b)

3x+4

c)

4x²+3x+4

d)

3^x-7

82.

A vertical asymptote is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

83.

Find the domain of the rational function

f(x) = x/(x²-25)

a)

( -∞ , -5) U (5, ∞)

b)

(-∞, -5) U (-5, 5) U (5, ∞)

c)

(-∞, 5) U (5, ∞)

d)

(-∞, 25) U (25, ∞)

84.

Find the x-intercept of the function f(x) = (x - 7) / x

a)

(0, 0)

b)

(0, -7)

c)

(7, 0)

d)

there is no x- intercept

85.

State the end behavior asymptote:
(2x²-5x +1)/(x²-x)

a)

y = 2

b)

y = 1

c)

y = 0

d)

There is no EBA

86.

Determine the x-coordinate of the hole on the graph of
f(x)= (x²-2x + 1)/(x²+2x - 3)

a)

-1

b)

3

c)

1

d)

-3

87.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

88.

What is the limit of the function as x approaches negative infinity?

a)

-2

b)

-3

c)

negative infinity

d)

positive infinity

89.

a)

Function

b)

Not a Function

90.

a)

Function

b)

Not a Function

91.

Factor by grouping:
5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

92.

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)

93.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

94.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

95.

Factor Completely: 6x² + 5x - 6

a)

6(x + 1)(x - 6)

b)

(6x + 6)(x - 1)

c)

(2x - 3)(3x + 2)

d)

(3x - 2)(2x + 3)

96.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

97.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

98.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

99.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

100.

What value(s) make the expression undefined?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

101.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

102.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

103.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

104.

What is the RANGE?

a)

{-3, 3]

b)

all real numbers

c)

[-4, 5]

d)

[-4, ∞)

105.

What is the DOMAIN?

a)

[0, ∞)

b)

(-∞, 0)

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

106.

64x² - 81y²

a)

(8x + 7y) (8x - 7y)

b)

(8x + 9y) (8x - 9y)

c)

(6x + 7y) (6x - 7y)

d)

(6x + 9y) (6x - 9y)

107.

49x² - 144y²

a)

(7x + 16y) (7x - 16y)

b)

(7x + 12y)²

c)

(12x + 7y) (12x - 7y)

d)

(7x + 12y) (7x - 12y)

108.

x² - 9

a)

(x + 3)²

b)

(x + 3) (x - 3)

c)

(x - 3)²

d)

x + 3(x - 3)

109.

√75x²

a)

5x²√3

b)

5x

c)

5x√3x

d)

5x√3

110.

√36n⁴

a)

6n

b)

6n⁴

c)

6n²√2

d)

6n²

111.

Solve for n:
2³ⁿ = 4

a)

2

b)

3

c)

2/3

d)

4

112.

Solve for x:
2^x+6=2⁵

a)

-1

b)

11

c)

1

d)

-11

113.

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

a)

5

b)

-5

c)

1/5

d)

-1/5

114.

Solve for b:
36^3b = 216^b+4

a)

6

b)

1

c)

4

d)

-4

115.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

116.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

117.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

118.

Use multiple log properties to write as a sum or difference of two logs: log(4x³)

a)

log 4 + 3log x

b)

3log 4 + 3log x

c)

3log 4 + log x

d)

log 12 + log x

119.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

120.

Solve for x: log₆x + log₆(x-5) = 2

a)

√7

b)

9

c)

4

d)

none of these

121.

To solve e^{4 – 3x}= x + 9 by graphing, which equations should be graphed?

a)

y = 0

b)

y = x + 9

c)

y = 4 - 3x

d)

y = e⁴

122.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

123.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

124.

e^ln(f)

a)

f

b)

e

c)

e^f

d)

undefined

125.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

126.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

127.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

128.

a)

A

b)

B

c)

C

d)

D

129.

Solve for x.
e^x+6 + 5 = 1

a)

-4.614

b)

-4.236

c)

No Solution

d)

-0.334

130.

log (-1) =

a)

0.1

b)

.01

c)

all real numbers

d)

does not exist

131.

What is the asymptote of y = 2^x ?

a)

y = 0

b)

x = 0

132.

What is the asymptote of y = log₂x ?

a)

y = 0

b)

x = 0

133.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

134.

What is the asymptote of y = log₂x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

135.

What is the asymptote of y = 2^x-3 ?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

136.

What is the asymptote of y = log₂(x - 3) ?

a)

y = 0

b)

y = 3

c)

x = 0

d)

x = 3

137.

The asymptote of y = 2^x + 4 will shift...

a)

up four to y = 4

b)

down four to y = -4

c)

not shift at all and remain y = 0

138.

The asymptote of y = 2^x+5 will shift...

a)

up five to y = 5

b)

down five to y = -5

c)

will not shift and remain y = 0

139.

The asymptote of y = log₂x + 1 will shift...

a)

right one to x = 1

b)

left one to x = -1

c)

not shift at all and remain x = 0

140.

The asymptote of y = log₂(x + 2) will shift...

a)

right two to x = 2

b)

left two to x = -2

c)

not shift and remain x = 0

141.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

142.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

143.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

144.

What type of function is $f\left(x\right)=2\left(\frac{1}{7}\right)^x$ ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

145.

How are exponential and logarithmic functions related?

a)

Opposites

b)

Inverses

c)

Cousins

d)

Reciprocals

146.

Tommy starts an ant farm will 100 ants. The ants increase at a rate of 4% each day. How many ants will Tommy have after 12 days?

a)

160

b)

61

c)

144

d)

105

147.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

148.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

149.

What is the relationship between
f(x) = log₅(x)
and
g(x) = 5^x?

a)

No Relationship

b)

Inverses

c)

Same Function

150.

Is your General Mathematics teacher handsome?

a)

YES

b)

NO

BQ 2024 CALCULUS 2-5

Total questions: 150

Worksheet time: 7hrs 57mins

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