Free Printable MCA semester review

1.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

2.

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

3.

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

4.

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

5.

f(x)=x³-3x
g(x)=-4x+1
Find f(x)*g(x)

a)

-4x³-5x²-3

b)

-4x³+2x²-3x

c)

-4x⁴+x³+12x²-3x

d)

-4x^4-x³+12x²⁺3x

6.

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

7.

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

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

8.

f(n)=n²+4n
g(n)=-n-5
Find f(n)+g(n)

a)

n²+3n-5

b)

-n³+2n-7

c)

n³+3n-3n

d)

n²-3n-5

9.

f(n)=x²+1
g(n)=2x-5
Find f(n)-g(n)

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

10.

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

a)

19

b)

23

c)

-10

d)

None of these.

11.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

a)

16

b)

4

c)

-4

d)

None of these.

12.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

13.

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

a)

8

b)

-8

c)

28

d)

None of these.

14.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

15.

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

16.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

17.

The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.

a)

y=20x

b)

y=84x

c)

y=7/3x

d)

y=3/7x

18.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

19.

If x and y vary directly, what is the missing value in the points (x, 4) and (-14, -8)?

a)

x = -7

b)

x = -2.3

c)

x = 2.3

d)

x = 7

20.

In a direct variation, y=39 when x=3. Find the value of y when x=2.

a)

26

b)

3

c)

58.5

d)

2

21.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

22.

Is this a direct variation?

a)

yes

b)

no

23.

Is this a direct variation?

a)

yes

b)

no

24.

When dealing with direct and inverse variation, the K represents what?

a)

Kangaroo

b)

K-Mart's Blue Light Special

c)

Constant

d)

King Cobra Snake

25.

What does the Direct Variation Equation look like?

a)

y= kx

b)

y = mx + b

c)

y = b

d)

y = x

26.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

27.

What is the form and vertex of quadratic equation y= 2x²+8x-2?

a)

Vertex form, Vertex (2,-10)

b)

Standard form, Vertex (-8,10)

c)

Vertex form, Vertex (-2, 10)

d)

Standard form, (-2,-10)

28.

What is the form and vertex of quadratic equation y=(x-2)²+4

a)

Vertex Form, (-2,4)

b)

Standard Form, (2, 4)

c)

Vertex Form, (2, 4)

d)

Standard Form, (-2,-4)

29.

What is the form and vertex of quadratic equation y= x²+6x+3?

a)

Vertex Form, Vertex (6,3)

b)

Standard Form, Vertex (-3, -6)

c)

Vertex Form, Vertex (-3, -6)

d)

Standard Form, Vertex (-3, 0)

30.

Identify the Form and Vertex of quadratic equation 2x²+16x-7.

a)

Vertex Form, Vertex (-4, -39)

b)

Standard Form, Vertex (4, -23)

c)

Vertex Form, Vertex (-8, -16)

d)

Standard Form, Vertex (-4,-39)

31.

Identify the Form and the Vertex for the quadratic equation y=6(x-6)²+5.

a)

Vertex Form, Vertex (6, 5)

b)

Standard Form, Vertex (6, -6)

c)

Vertex Form, Vertex (-6, 5)

d)

Standard Form, Vertex (-6,-5)

32.

Identify the Form and Vertex for quadratic equation y=3(x+5)²+5.

a)

Standard Format, Vertex (-5,5)

b)

Vertex Form, Vertex (-5,5)

c)

Standard Form, Vertex (3, 5)

d)

Vertex Form, Vertex (5, -5)

33.

Identify the Format and Vertex of quadratic equation y=4x²-16x+4.

a)

Vertex Form, Vertex (-2, 12)

b)

Standard Form, (2, -12)

c)

Vertex Form, Vertex (4, 16)

d)

Standard Form, Vertex (2, -20)

34.

What is the form and vertex of quadratic equation y=2(x+4)²-2?

a)

Vertex Form, Vertex (4, -2)

b)

Standard Form, Vertex (-4, 2)

c)

Vertex Form, Vertex (-4, -2)

d)

Standard Form, Vertex (4, 2)

35.

Identify the vertex.

a)

(5, 2)

b)

(5, -2)

c)

(-5, 2)

d)

(-5, -2)

36.

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)

37.

Identify the vertex.

a)

(5, 2)

b)

(5, -2)

c)

(-5, 2)

d)

(-5, -2)

38.

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)

39.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

40.

What is the y-intercept of the function.

y=3x^2-7x+1,000,000

a)

0

b)

3

c)

$c=-7$

d)

$c=1,000,000$

41.

Does this graph open up or down?

y=\ -3x^2\ +7x\ +\ 1,000,000

a)

up

b)

down

42.

What is c in the following equation?
y=ax²+bx+c

a)

Zeroes

b)

Axis of Symmetry

c)

Direction

d)

y-intercept

43.

What is the y-intercept? $x^2-3x+9$

a)

(9, 0)

b)

(0, 9)

c)

(1, 0)

d)

(-3, 0)

e)

(0, -3)

44.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

45.

If a is negative in the quadratic function, which way does the parabola open?

a)

up

b)

down

c)

left

d)

right

46.

What is the y-intercept?
f(x) = -2x² + 4x - 6

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

47.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

48.

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)

49.

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

a)

(-2, 0) and (6, 0)

b)

(2, 0) and (-6, 0)

c)

(-2, 6)

d)

(¼, 0) and (-2, 0) and (6, 0)

50.

State the direction of opening of the following: y = -(x+3)(x-2)

a)

Left

b)

Up

c)

Down

d)

Right

51.

Write in exponential form.

a)

$7^{1.9545...}$

b)

$e^7$

c)

$e^{1.945...}$

d)

$1.945...^7$

52.

Write in exponential form.

a)

$7^{1.9545...}$

b)

$e^7$

c)

$e^{1.945...}$

d)

$1.945...^7$

53.

Write in exponential form.

a)

$e^0$

b)

$e^1$

c)

$1^0$

d)

$0^1$

54.

Evaluate to the nearest thousandths.

a)

2.900

b)

2.910

c)

2.913

d)

2.914

55.

Evaluate to the nearest thousandths.

a)

-0.905

b)

-0.904

c)

-0.903

d)

-0.900

56.

Solve for x using the One-to-One property.

a)

3

b)

16

c)

10

d)

8

57.

Solve for x using the One-to-One property.

a)

0

b)

1

c)

14

d)

49

58.

Solve for x using the One-to-One property.

a)

5

b)

-5

c)

$\pm5$

d)

21

59.

Solve for x using the One-to-One property.

a)

2,3

b)

-2,-3

c)

-2,3

d)

2,-3

60.

Evaluate to the nearest thousandths.

a)

-23.900

b)

-23.960

c)

-23.965

d)

-23.966

61.

Evaluate to the nearest thousandths.

a)

0.600

b)

0.690

c)

0.693

d)

0.694

62.

What values of b make an exponential growth function?

a)

b > 0

b)

b <1

c)

b > 1

d)

0 < b < 1

63.

What values of b make an exponential decay function?

a)

b > 0

b)

b < 1

c)

b > 1

d)

0 < b < 1

64.

6^{-2 =}

a)

12

b)

-36

c)

1/36

d)

1/6

65.

Write in exponential form: ∛4⁵

a)

4^3/5

b)

4^5/3

c)

4^1/5

d)

4^1/3

66.

Solve:
3^x-2= 27^4x

a)

-2/11

b)

-2/3

c)

2/11

d)

2/3

67.

Multiply:
2x(3xy²+ 4x³y)=

a)

6xy² + 8x⁴y

b)

6x²y + 8x³y

c)

6x²y² + 4x⁴y

d)

6x²y² + 8x⁴y

68.

Does this graph represent exponential growth or decay?

a)

Growth

b)

Decay

c)

cannot be determined

69.

Solve:
5^{1/2x + 4}= 125

a)

1

b)

2

c)

-2

d)

14

70.

Solve:
16^x-3 = 8^x-3

a)

9

b)

-3

c)

0

d)

3

71.

Solve:
2^4x+1 = √2

a)

-1/8

b)

1/8

c)

0

d)

-1/4

72.

Logarithmic form of $3^{x-4}=7$

a)

$Log_7\ 3\ =x-4$

b)

$Log_3\ \left(x-4\right)\ =3$

c)

$Log_3\ 7\ =x-4$

d)

$Log\ 3^7=x-4$

73.

Logarithmic form of $10^{x+1}=8$

a)

$Log_{\left(x+1\right)}8=10$

b)

$Ln\ 10=8\left(x+1\right)$

c)

$Log_{10}\left(x+1\right)=8$

d)

$Log\ 8\ =\ x+1$

74.

Logarithmic form of $e^{x+3}=7$

a)

$Ln\ 7^x=3$

b)

$Ln\ 7\ =\ x+3$

c)

$Ln\ \left(x+3\right)=7$

d)

$Log_e\ 7\ =x+3$

75.

Logarithmic form of $3^5=x-1$

a)

$Log\ 3^{x-1}=5$

b)

$Ln\ 3^5=x-1$

c)

$Log_3\left(x-1\right)=5$

d)

$Log_5\ 3\ =x-1$

76.

Exponential form of $Log_3\left(5x\right)=\frac{4}{7}$

a)

$\left(5x\right)^e=\frac{4}{7}$

b)

$3^{\frac{4}{7}}=5x$

c)

$\left(\frac{4}{7}\right)^{5x}=3$

d)

$3^{5x}=\frac{4}{7}$

77.

Exponential form of $Ln\ \left(4x+1\right)=8$

a)

$e^{4x-1}=8$

b)

$e^8=4x-1$

c)

$10^{4x-1}=8$

d)

$\left(4x+1\right)^8=10$

78.

Exponential form of $Log\ \left(2x\right)=9$

a)

$10^{9x}=2$

b)

$e^9=2x$

c)

$9^x=2$

d)

$10^9=2x$

79.

Exponential form of $Log_{\frac{2}{5}}\left(\frac{5}{3}\right)=5x$

a)

$\left(\frac{2}{5}\right)^{\frac{5}{3}}=5x$

b)

$\left(5x\right)^{\frac{2}{5}}=\frac{5}{3}$

c)

$\left(\frac{5}{3}\right)^{\frac{2}{5}}=5x$

d)

$\left(\frac{2}{5}\right)^{5x}=\frac{5}{3}$

80.

Logarithmic form of $e^{3e}=ex$

a)

$Ln\ ex=3e$

b)

$Ln\ \left(ex\right)^3=e$

c)

$Log\ \left(e\right)^{3e}=ex$

d)

$Ln_e\left(ex\right)=3e$

81.

The logarithmic form of $e^{\frac{3}{4}}=7x$

a)

$Log\ \left(7x\right)=\frac{3}{4}$

b)

$Log_{7x}e=\frac{3}{4}$

c)

$Ln\ \left(\frac{3}{4}\right)^7=x$

d)

$Ln\ \left(7x\right)=\frac{3}{4}$

82.

Evaluate $Log_{\frac{2}{5}}\left(3\pi\right)$ .

Round your answer to the nearest hundredth

a)

-2.448

b)

-2.49

c)

-2.45

d)

-2.44

83.

Evaluate $1.5e^{2\pi}$

Round your answer to the nearest hundredth

(a)

84.

Evaluate $5Log_{3.4}\left(\frac{4}{9}\right)$

Round your answer to the nearest hundredth

(a)

85.

Evaluate $7Log\ \left(8.7\right)$

Round your answer to the nearest hundredth

(a)

86.

Evaluate $\frac{12+Ln\ 7.8}{4.5e^3}\$

Round your answer to the nearest hundredth

(a)

87.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

88.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

89.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

90.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

91.

Solve for x and y
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

92.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

93.

Solve the system given:
3x - y = 7
2x + y = 3

a)

(-1,2)

b)

(5,4)

c)

(4,5)

d)

(2,-1)

94.

Give the solution to the system.

a)

(3,1)

b)

(1,3)

c)

(-1,3)

d)

(1, -3)

95.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

96.

Parallel Lines never intersect because...

a)

they have the same slopes.

b)

they have the same y-intercept.

c)

they have different slopes.

d)

they have different y-intercepts.

97.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

a)

1.5x+0.5y=78.5
x+y=87

b)

1.5x+0.5y=78.5
1.5x+0.5y=87

c)

x+y=78.5
1.5x+0.5y=87

d)

x+y=78.5
x+y=87

98.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

99.

Solve the system.

a)

(2, -2, 3)

b)

(2, 1, 4)

c)

(-2, 2, -3)

d)

No Solution

100.

Solve the system.

a)

(1, 2, -2)

b)

(1, -3, -2)

c)

(-1, 3, 2)

d)

No Solution

101.

Solve the system.

a)

(1, 3, -4)

b)

(-2, -1, 3)

c)

(-8, -2, 1)

d)

Infinitely many solutions

102.

Solve the system.

a)

(3, -9, 2)

b)

(3, -2, 9)

c)

(2, 3, -1)

d)

No Solution

103.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

104.

Solve the system.

a)

(1/2, 4, -2)

b)

(3, 3/2, -1/2)

c)

(-1, 6, -4)

d)

Infinitely many solutions

105.

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

x = 1/2, -6

b)

x = -1/2, 6

c)

x = 4, -1/2, 6

d)

x = -4, 1/2, -6

106.

Factor:
x³-12x²+47x-60=0 when 5 is a root.

a)

(x-3)(x-4)(x-5)=0

b)

(x+1)(x-4)(x-5)=0

c)

(x-3)(x-4)(2x-5)=0

d)

(x-5)(x-4)(x-5)=0

107.

Find all rational zeros, one zero has been given.
f(x) = x³-3x²-x+3; 3

a)

2,4,3

b)

-1,1,3

c)

3,2,1

d)

4,5,6

108.

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

109.

Factor
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

110.

How could you determine if x-2 is a factor of 2x³-5x²+x-2?

a)

Use synthetic division and see if the quotient is even

b)

Ask the person sitting next to me

c)

Use synthetic division and see if the remainder is zero

d)

Flip a coin

111.

Factor f(x)= x³ - 2x²-13x - 10 given that
(x - 5) is one factor.

a)

(x- 5)(x - 1)(x - 2)

b)

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

c)

(x - 5)(x + 2) (x + 1)

d)

(x - 5)(2x - 13)

112.

Find all zeroes given a factor of (x+3).

f(x) = 2x³+ 5x²- 6x - 9

a)

-1,-3,-3

b)

-1,-3,3/2

c)

3,3,3

d)

-3,2/3,-1

113.

Find all solutions, one factor has been given.

f(x) =x³-3x²-25x+75; (x-5)

a)

5,-3,5

b)

5,5,5

c)

3,-5,5

d)

1,1,1

114.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

115.

Find the zero(s) of the function.

a)

x = 1

b)

x = -3

c)

x = {-1, 3}

d)

x = 2

116.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

117.

What are the zeroes of this graph?

a)

x = -2, x = 1, x = 4

b)

x = -4, x = 0, x = 1, x = 2,

c)

x = -2, x = -1, x = 0, x = 4

d)

x = -4, x = -1, x = 2

118.

What are the zeroes of this graph?

a)

x = -3, x = 5

b)

x = -3, x = 0, x = 5

c)

x = -3, x = 2, x = 5

d)

x = 0

119.

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)

120.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

121.

Identify the zeros

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

122.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

123.

What is the equation of this graph in factored form?

a)

(x - 1)(x + 3)²

b)

(x - 1)²(x + 3)

c)

(x + 1)²(x - 3)

d)

(x + 1)(x - 3)²

124.

What does the h term tell you?

a)

left or right

b)

left or right, opposite sign, axis of symmetry, x-value of the vertex.

c)

axis of symmetry, x-value of the vertex

d)

nothing.

125.

What does the k term tell you?

a)

up.

b)

down.

c)

up/down, y-value in the vertex

d)

nothing

126.

Describe the transformations below: $\left(x+1\right)^2-4$

a)

left: 1, up: 4

b)

left: 1, down: 4

c)

right: 1, up: 4

d)

right: 4, up: 1

127.

Describe the transformation below: $-\left(x+3\right)^2+6$

a)

reflect over the x-axis

b)

reflect over the x-axis, left: 3, up: 6

c)

stretch, left: 3, down: 6

d)

left: 3, down: 6

128.

Describe the transformation below: $-3\left(x+4\right)^2-1$

a)

stretch by 3, right: 4, down: 1

b)

reflect over the x-axis, right: 4, down: 1

c)

reflect over the x-axis, stretch by 3, left: 4, down: 1

d)

stretch by 4, down: 3, left: 1

129.

Identify the a, h, and k term from the following equation: $\left(x+3\right)^2+2$

a)

a=-1, h=3, k=2

b)

a=3, h=3, k=3

c)

a=1, h=-3, k=2

d)

a=1, h=-3, k=-2

130.

Identify the a, h, and k terms in the following equation: $2\left(x+4\right)^2-1$

a)

a=2, h=-4, k=-1

b)

a=-2, h=4, k=1

c)

a=2, h=4, k=1

d)

a=-2, h=-4, k=1

131.

Identify the a, h, and k terms in the following equation: $\left(x+4\right)^2-3$

a)

a=-1, h=4, k=3

b)

a=-1, h=-4, k=3

c)

a=1, h=4, k=3

d)

a=1, h=-4, k=-3

132.

Determine the vertex from the following equation: $-3\left(x-4\right)^2+1$

a)

Vertex: (4,1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, -1)

d)

Vertex: (-4, 1)

133.

Determine the vertex from the following equation: $-\left(x+1\right)^2-1$

a)

Vertex: (1,-1)

b)

Vertex: (-1, 1)

c)

Vertex: (-1, -1)

d)

Vertex: (1, 1)

134.

Determine the vertex from the following equation: $\frac{1}{2}\left(x+4\right)^2+1$

a)

Vertex: (-4, 1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, 1)

d)

Vertex: (4, -1)

135.

Determine the axis of symmetry from the following equation: $-\left(x-2\right)^2+4$

a)

A. O. S: 2

b)

A. O. S: 4

c)

A. O. S: -2

d)

A. O. S: -1

136.

Determine the axis of symmetry of the following equation: $-2\left(x+2\right)^2+3$

a)

A. O. S: 3

b)

A. O. S: -2

c)

A. O. S: 2

d)

A. O. S: 1

137.

Determine the axis of symmetry of the following equation: $\left(x-3\right)^2+5$

a)

A. O. S: 1

b)

A. O. S: -3

c)

A. O. S: 3

d)

A. O. S: 5

138.

Determine if the parabola has a maximum or minimum, if it opens up (+) then it will have a minimum, if it opens down (-) then it will have a maximum. $3\left(x+3\right)^2-2$

a)

Maximum

b)

Minimum

139.

Determine if the following equation has a maximum or minimum: $-\left(x-2\right)^2+7$

a)

Maximum

b)

Minimum

140.

Determine if the following function will be narrow (stretch) or wider (shrink): $4\left(x-3\right)^2+4$

a)

Narrow

b)

Wider

141.

Determine if the following is narrow or wider: $\frac{2}{3}\left(x+3\right)^2+6$

a)

Narrow

b)

Wider

142.

What is a quadratic funtion in the form of $f\left(x\right)=a\left(x-h\right)^2+k$ called?

a)

Factored Form

b)

Standard Form

c)

Vertex Form

143.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

144.

In the equation f(x)=1/2(x+9)²-1, what happens to the parabola?

a)

Reflect, horizontal compress by 1/2, left 9, down 1

b)

Vertical compress by 1/2, left 9, down 1

c)

Horizontal Compress by 1/2, right 9, down 1

d)

Vertical Stretch by 1/2, left 9, down 1

145.

What are the transformations of the following polynomial from the parent function $f\left(x\right)=x^3$ ?

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

a)

Vertical compression by a factor of 2, and shifted right by 1 unit

b)

Reflected over the x-axis, vertical stretch by a factor of 2, and shift left by 1 unit

c)

Reflected over the y-axis by a factor of 2, and shifted up by 1 unit

d)

Reflected over the x-axis, horizontal compression by a factor of 2, and shifted down by 1 unit

146.

Describe the transformations of the graph y = (x - 3)³ -2

a)

Right 3, Down 2

b)

Left 3, Up 2

c)

Right 3, Up 2

d)

Left 3, Down 2

147.

Describe the transformation of the graph y = -2(x + 5)³

a)

Shrink by 2, Reflected over y-axis, Right 5

b)

Stretch by 2, Reflected over x-axis, Left 5

c)

Stretch by 2, Reflected over x-axis, Right 5

d)

Shrink by 2, reflected over y-axis, Left 5

148.

Describe the transformation of the graph y = - ½(x + 4)⁴- 1

a)

Left 4 and Down 1

b)

Reflected x-axis, Down 1, Left 4, Shrink by 1/2

c)

Reflected x-axis, Down 1, Left 4, Stretch by 1/2

d)

Reflected x-axis, Up 1, Right 4, Shrink by 1/2

149.

Describe the transformation of the graph y = (x)³ + 6

a)

Right 6

b)

Left 6

c)

Up 6

d)

Down 6

150.

List the transformations to the parent function in y = -(x + 4)⁸- 3

a)

reflect over y, right 4, down 3

b)

reflect over y, left 4 down 3

c)

reflect over x, right 4, down 3

d)

reflect over x, left 4, down 3

151.

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

a)

3 units right, 2 units up, reflected across the y-axis

b)

3 units right, 2 units up, reflected across the x-axis

c)

3 units left, 2 units up, reflected across the y-axis

d)

3 units left, 2 units up, reflected across the x-axis

152.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

153.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

154.

Describe the transformations from $f\left(x\right)=x^2$ to $g\left(x\right)=-\frac{1}{2}\left(x-8\right)$ .

a)

Reflection across the x-axis, Vertical compress by 1/2, left 8

b)

Reflection across the x-axis, Vertical compress by 1/2, right 8

c)

Vertical compress by 1/2, left 8

d)

Vertical Stretch by 1/2, right 8

155.

What are the transformations of the following polynomial from the parent function $f\left(x\right)=x^3$ ?

$g\left(x\right)=-2x^3+4$

a)

Vertical compression by a factor of 2, and shifted left by 4 units

b)

Reflected over the x-axis, vertical stretch by a factor of 2, and shifted up 4 units.

c)

Reflected over the y-axis by a factor of 2, and shifted up by 4 units.

d)

None

156.

Is the power even or odd?

a)

Odd

b)

Even

157.

List the transformations to the parent function in y = -(x + 4)²- 3

a)

right 4, down 3

b)

left 4 down 3

c)

reflect over x-axis, right 4, down 3

d)

reflect over x axis, left 4, down 3

158.

In the equation f(x)=5(x+3)²-10 what does the 5 do?

a)

Vertical stretch by 5

b)

Vertical compression by 5

c)

Reflect

d)

Move up 5

159.

If the blue graph is
f(x) = x²the red must be...

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x²+ 3

d)

g(x) = x²- 2

160.

Which could be the resulting function?

a)

$g\left(x\right)=1.5\left(x-3\right)^3+4$

b)

$g\left(x\right)=0.5\left(x+2\right)^3+8$

c)

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

d)

$g\left(x\right)=2\left(x+3\right)^3+4$

161.

Match the equation to its description.

a)

Stretched by 4 and up 4

b)

Compressed by 4 and up 4

c)

Stretched by 4 and left 4

d)

Compressed by 4 and left 4

162.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

163.

Which equation describes the transformation of shifting f(x)=x³ three units left?

a)

x³ + 3

b)

x³ - 3

c)

(x + 3)³

d)

(x - 3)³

164.

Which equation describes the transformation of shifting f(x)=x³ two units right?

a)

x³ + 2

b)

x³ - 2

c)

(x + 2)³

d)

(x - 2)³

165.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

166.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

167.

Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)

f is directly proportional to b and inversely proportional to e

(a)

168.

Write the mathematical equation of the given statement: (no spacing, use / for fraction bar)

The time (t) needed to answer a set of problems is directly proportional to the number (N) of problems, and inversely proportional to the number of students (P) working on the solutions.

(a)

169.

Solve for the constant of variation, k.

A varies directly as D and inversely as F. A=10.5, when D=2 and F=4

(a)

170.

Solve for the constant of variation, k.

D is directly proportional to e² and inversely proportional to f. D=12, when e=2 and f=7.

(a)

171.

Given that z varies directly with y and inversely with x when x = 12, y=36 and z=15, find the value of z when x= -8 and y=24.

(a)

172.

If a varies jointly as b and c, and inversely as d when a=140, b=5, c=4, and d=3, find a when b=10, c=8, and d=12.

(a)

173.

The volume of gas varies directly as the temperature and inversely as the pressure. If the volume is 180 cu cm when the temperature is 270 K and the pressure is 15 lbs/sq cm, what is the volume when the temperature is 220 K and the pressure is 25 lbs/sq cm? (Write your final answer in this form: _ cu cm )

(a)

174.

The resistance of a wire varies directly as its length and inversely as the square of the diameter. If a 15-ft long wire and a diameter of 1/2 inch has a resistance of 3 ohms, what is the resistance of a wire with a length of 25 ft and a diameter of 2 inches? (Write your final answer in fraction and of the form: _ ohms )

(a)

175.

What type of variation is pictured?

a)

Direct

b)

Inverse

c)

Joint

d)

None

176.

What type of variation is pictured?

a)

Direct

b)

Inverse

c)

Joint

d)

None

177.

What type of variation is represented by this equation?

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

a)

Direct

b)

Inverse

c)

Joint

d)

None

178.

What type of variation is represented by this equation?

$k=\frac{y}{x}$

a)

Direct

b)

Inverse

c)

Joint

d)

None

179.

What type of variation is represented by this equation?

$y=7xz$

a)

Direct

b)

Inverse

c)

Joint

d)

None

180.

What type of variation is represented by this scenario?

The amount of time that has passed versus how much water is left in a bath as it drains.

a)

Direct

b)

Inverse

c)

Joint

d)

None

181.

What type of variation is represented by this scenario?

The more hours you work versus the money in your bank account.

a)

Direct

b)

Inverse

c)

Joint

d)

None

182.

What type of variation is represented by this scenario?

The number of lottery tickets you buy versus your chances of winning the lottery.

a)

Direct

b)

Inverse

c)

Joint

d)

None

183.

If Y varies directly with X, and Y = 24 when X = 6, find Y when X = 8.

a)

144

b)

32

c)

18

d)

10

184.

If Y varies inversely with X, and Y = 60 when X = 3, find Y when X = 18.

a)

180

b)

20

c)

57

d)

10

185.

If Y varies directly with the product of X and Z, and Y = 320 when X = 8 and Z = 20, what is the value of K?

a)

2

b)

80

c)

40

d)

16

186.

The gallons of water in a pool varies directly with how many minutes the drain has been open. If there are 300 gallons in the pool after the drain has been open for 2 min, how long will it take for there to be 50 gallons remaining?

a)

0.33333 minutes

b)

6 minutes

c)

20 minutes

d)

12 minutes

187.

When 40 people decide to ride the bus to the basketball game it costs $6.50 per person. When 20 people ride the bus to the game it costs $13.00 per person. Find K based on the scenario?

a)

130

b)

260

c)

60

d)

520

188.

The special number, natural base "e", is a ________________ number.

a)

rational

b)

irrational

c)

real

189.

The approximate value of e is (a) . Use two decimal places.

190.

What is the y-intercept for the graph of $y=3e^x$ ?

a)

(1,0)

b)

(0, 1)

c)

(0, 3)

d)

(3, 0)

191.

Does the function $y=4e^{-0.75x}$ represent exponential growth or decay?

a)

exponential growth because r>0

b)

exponential growth because r<0

c)

exponential decay because r>0

d)

exponential decay because r<0

192.

Which of the following graphs matches the function $y=4e^{-0.5x}$ ?

a)

b)

c)

d)

193.

Which of the following graphs matches the function $y=0.75e^x$ ?

a)

b)

c)

d)

194.

Evaluate the expressions using a calculator/desmos. Rounds to 2 decimal places.

$e^3\cdot e^5$

(a)

195.

Without graphing, tell if the function below is growth or decay.

$y=4e^{3x}-2$

a)

Growth

b)

Decay

196.

You deposit $5,000 in an account that earns 3% interest compounded continuously. Which equation could be used to determine how much money would be in the account after 8 years?

a)

$A=5000e^{3\cdot8}$

b)

$A=5000e\cdot3\cdot8$

c)

$A=5000e\cdot0.03\cdot8$

d)

$A=5000e^{.03\cdot8}$

197.

Tritium is a chemical that decays over time. In a sample of tritium, the amount y(in millligrams) remaining after t years is given by the equation below. What is the initial amount of Tritium?

$y=10e^{-0.0562t}$

(a)

198.

Sodium-22 is a manmade radioactive isotope that decays over time. The graph shows the amount of Sodium-22 remaining over time. How much Sodium-22 was there initially?

(a)

199.

Based on the Soduim-22 decay table, approximately how much is remaining after 10 years?

a)

1

b)

5

c)

10

d)

20

200.

Solve ln e

a)

10

b)

1

c)

5

d)

3

201.

Solve ln 1

a)

10

b)

4

c)

0

d)

1

202.

Expand ln(4x)

a)

ln4 + lnx

b)

ln 4 - lnx

c)

ln4x

d)

ln 4 - x

203.

Expand $\ln\ x^5y^2$

a)

5lnx + ln2y

b)

lnx5y2

c)

5lnx + 2lny

d)

5lnx - 2lny

204.

Using a calculator approximate ln 2.3 to the nearest thousandth

a)

.8322

b)

.8329

c)

.8320

d)

.9238

205.

Using a calculator approximate ln 4.5 to the nearest thousandth

a)

1.5041

b)

1.5

c)

1.5040

d)

1.540

206.

condense 4ln7 + 2lnx

a)

ln7⁴x

b)

ln7x

c)

ln7x²

d)

ln7⁴x²

207.

Expand ln(uw²)

a)

ln u + ln w

b)

2ln uw

c)

ln u + 2ln w

d)

ln (uw) + 2

208.

Expand ln(xyz)

a)

ln x + ln y

b)

ln x + yz

c)

lnx + ln y + z

d)

lnx + lny + lnz

209.

Graph ln (x +1)

a)

b)

c)

d)

210.

Solve the following equation. Round to the nearest ten-thousandth.

$e^x=30$

a)

0.2871

b)

3.4012

c)

2.1842

d)

-9.3587

211.

Solve the following equation. Round to the nearest ten-thousandth.

$e^n=83$

a)

4.4188

b)

2.3687

c)

5.2387

d)

8.2356

212.

Solve the following equation. Round to the nearest ten-thousandth.

$e^n=80$

a)

6.8975

b)

0.2357

c)

5.2689

d)

4.3820

213.

Solve the following equation. Round to the nearest ten-thousandth.

$e^b=68$

a)

5.8796

b)

4.2195

c)

2.5874

d)

-0.2698

214.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(8\right)+\ln\left(x\right)=2$

a)

4.2598

b)

1.8542

c)

-3.2587

d)

0.9236

215.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(x\right)-\ln\left(6\right)=2$

a)

44.3345

b)

6.2587

c)

24.3987

d)

-67.2587

216.

Solve the following equation. Round to the nearest ten-thousandth. (Challenge Question!)

$\ln\left(x\right)-\ln\left(x-1\right)=5$

a)

4.2587

b)

1.0068

c)

2.6879

d)

0.2879

217.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(7\right)+\ln\left(x\right)=1$

a)

2.3461

b)

1.9687

c)

-1.9563

d)

0.3883

218.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(x^2+3\right)+\ln\left(6\right)=\ln\left(18\right)$

a)

$\sqrt{6}$

b)

1

c)

0

d)

2.3657

219.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(2x^2\right)+\ln\left(2\right)=4$

a)

$\pm0.2358$

b)

$\pm2.0147$

c)

$\pm3.6945$

d)

$\pm5.2398$

220.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(5\right)+\ln\left(x\right)=3$

a)

1.3969

b)

2.3587

c)

3.2587

d)

4.0171

221.

$\ln\left(4x^2\right)-\ln\left(9\right)=2$

a)

$\pm2.3687$

b)

$\pm1.0258$

c)

$\pm0.2669$

d)

$\pm4.0774$

222.

Solve the following equation. Round to the nearest ten-thousandth.

$\ln\left(x^2+7\right)+\ln\left(5\right)=\ln\left(40\right)$

a)

$\pm\sqrt{2}$

b)

$\pm1$

c)

0

d)

$\pm2.3587$

MCA semester review

Total questions: 222

Worksheet time: 9hrs 44mins

Similar Resources on Wayground