Free Printable December 2022 Alg 2H Final Exam

1.

Given the pattern, which of the following could represent the number of squares in the pattern in step n?

a)

3n - 1

b)

n² - n

c)

(n - 1)² + 2n

d)

n² - 1

2.

Which of the following identifies the total number of dots in step n?

a)

2n

b)

n + 2

c)

2ⁿ

d)

n² + 2

3.

What function type models this graph?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear Growth

d)

Quadratic

4.

Is this graph linear, quadratic, or exponential?

a)

Linear

b)

Quadratic

c)

Exponential

5.

Which function is represented by the following equation.

y = x²+4

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of these

6.

Is the equation linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

7.

Is the equation linear, exponential, or quadratic?

a)

Linear

b)

Exponential

c)

Quadratic

8.

What type of function is f(x)=2(1/7)^x ?

a)

Quadratic

b)

Linear

c)

Exponential

9.

This table represents what kind of function?

a)

Linear

b)

Exponential Growth

c)

Exponential Decay

d)

Quadratic

10.

Is the table linear, exponential, Quadratic, or not a function at all?

a)

Linear

b)

Exponential

c)

Quadratic

d)

Not a function

11.

Is the Equation Linear, Exponential, Quadratic, or not a function at all?

a)

Linear

b)

Exponential

c)

Quadratic

d)

Not a function

12.

Is the table linear or exponential?

a)

Linear

b)

Exponential

13.

What is the vertex for
f(x)=4(x-2)² + 3

a)

(-2, 3)

b)

(2,-3)

c)

(4,3)

d)

(2,3)

14.

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)

15.

Which way does the following equation open? $f\left(x\right)=-\frac{1}{2}\left(x-5\right)^2+6$

a)

upward

b)

downward

16.

Which of the following is the correct equation of this graph?

a)

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

b)

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

c)

$y=4\left(x+3\right)^2+1$

d)

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

17.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

18.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

19.

Which equation matches the graphed above?

a)

$p\left(x\right)=\left(x-1\right)^2+4$

b)

$p\left(x\right)=\left(x-4\right)+1$

c)

$p\left(x\right)=-\left(x+1\right)^2-4$

d)

$p\left(x\right)=-\left(x+4\right)\ ^2-1$

20.

Which quadratic equation models the parabola shown?

a)

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

b)

y = (x+2)(x+5)

c)

y = -(x+2)(x+5)

d)

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

21.

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3,-7) and passes through the point (1,-10)?

a)

b)

c)

d)

22.

Write the equation of the quadratic function that has a vertex of (-5, 9) and passes through the point (-7, -15).

a)

y = 6(x + 5)² + 9

b)

y = -6(x - 5)² + 9

c)

y = 6(x - 5)² + 9

d)

y = -6(x + 5)² + 9

23.

Which equation matches the x-intercepts x=5,-7 ?

a)

(x+5)(x-7)=0

b)

(x-5)(x+7)=0

c)

$3x^2+6x-105$

d)

$3x^2-6x-105$

24.

What are the x-intercepts for g(x) = (x + 8)(x + 2)

a)

8 and 2

b)

(8, 2)

c)

-8 and - 2

d)

(-8, -2)

25.

Change the quadratic equation from factored form to standard form:

(3m + 5) (2m - 3)

a)

$5m^2+19\ -\ 15$

b)

$6m^2+10m\ +15$

c)

$6m^2+1m-15$

d)

$5m^2+19m\ -\ 15$

26.

What is the greatest number of solutions that a Quadratic Equation can have?

a)

0

b)

1

c)

2

d)

3

27.

Factor: 3x²- 6x - 24

a)

(3x - 8)(x + 3)

b)

(3x + 4)(x - 6)

c)

3(x - 2)(x + 4)

d)

3(x + 2)(x - 4)

28.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

29.

$\sqrt{-36}$ can be classified as which of the following? Select all that apply.

a)

A real number

b)

An imaginary number

c)

A complex number

d)

An integer

30.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

31.

a)

10

b)

-10

c)

10i

d)

-10i

32.

Simplify:
√-108

a)

3i√6

b)

3i√20

c)

6i√3

d)

20i√3

33.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

34.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

35.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

36.

Simplify
(-6 - 2i)²

a)

32

b)

36-4i

c)

36+24i

d)

32+24i

37.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

38.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

39.

What are the solutions to the graphed system?

a)

(0,-2) and (-3,1)

b)

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

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

40.

Solve the system of linear and quadratic equations:

y = 5

y = 2x² - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

41.

Find the solution:
y = x² - 4x + 6
y = x + 2

a)

(3, 1) and (6, 4)

b)

(-1, 1) and (4, 2)

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

42.

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t, and is graphed below. How high will the ball be after 3 seconds?

a)

20 ft

b)

15 ft

c)

5 ft

d)

10 ft

43.

You are trying to throw a ball over a wire that is 40 feet above the ground. The height of the ball is modeled by the equation h(t) = -16t² + 48t. How many seconds will it take to clear the wire?

a)

1 sec

b)

1.5 sec

c)

2 sec

d)

It won't clear the wire

44.

Superman kicks a ball into the air. The path can be found using the equation d(t) = -16t²+ 48x, how long is the ball above 30 feet?

a)

1 seconds

b)

5 seconds

c)

4 seconds

d)

6 seconds

45.

Teresa throws a baton in the air. The baton reaches a height which is modeled by the function f(x) = -16x² +48x, where x represents time, in seconds, and f(x) represents the height of the baton in feet. How many seconds will it take the baton to return to Teresa?

a)

0 seconds

b)

1 seconds

c)

2 seconds

d)

3 seconds

46.

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

a)

0 ≤ y ≤ 145

b)

y ≤ 145

c)

0 ≤ x ≤ 6

d)

All Reals

47.

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

a)

0 ≤ y ≤ 145

b)

x ≤ 145

c)

0 ≤ x ≤ 6

d)

All Reals

48.

Compare

a)

p(x)

b)

q(x)

49.

Compare

a)

b(x)

b)

c(x)

50.

Compare

a)

d(x)

b)

f(x)

51.

Compare

a)

g(x)

b)

h(x)

52.

Compare

a)

p(x)

b)

q(x)

53.

Choose the best equation for the graph.

a)

b)

c)

d)

54.

Choose the best equation for the graph.

a)

b)

c)

d)

55.

Choose the best equation for the graph.

a)

b)

c)

d)

56.

Choose the best equation for the graph.

a)

b)

c)

d)

57.

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

58.

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

59.

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

60.

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

61.

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

62.

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

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

63.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →-∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

64.

The graph shows the function f(x)=x³ in blue and another function g(x) in red. Which could be the equation for g(x)?

a)

A. g(x) = -x³

b)

B. g(x) = x³ - 1

c)

C. g(x) = (x + 1)³

d)

D. g(x) = (x - 1)³

65.

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

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

66.

The parent cubic function is vertically compressed by

\frac{1}{4}

, horizontally shifted 3 units to the left, and vertically shifted up 5 units. Which equation corresponds to the transformations.

a)

$y=\frac{1}{4}\left(x+3\right)^2+5$

b)

$y=-\frac{1}{4}\left(x+3\right)^3+5$

c)

$y=\frac{1}{4}\left(x+3\right)^3+5$

d)

$y=-\frac{1}{4}\left(x-3\right)^3-5$

67.

What is the average rate of change from x=0 to x=1

a)

-3

b)

3

c)

0

d)

2

68.

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) →-∞.

69.

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) →-∞.

70.

a)

4th degree polynomial with a positive leading coefficient

b)

4th degree polynomial with a negative leading coefficient

c)

3rd degree polynomial with a positive leading coefficient

d)

3rd degree polynomial with a negative leading coefficient

71.

Fill in the blank: The maximum number of turning points is ____ less than the degree of the polynomial.

a)

0

b)

1

c)

2

d)

3

72.

What is the maximum number of turning points for the function?
f(x) = -x⁵ - 4x +2

a)

1

b)

2

c)

3

d)

4

73.

Fill in the blank: The maximum number of real zeros is equal to the ____________ of the polynomial.

a)

degree

b)

number of terms

c)

turning points

74.

State the maximum number of real zeros for the function:
f(x) = 2x⁴ + 19x² + 24

a)

0

b)

1

c)

2

d)

4

75.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

76.

Which one of these are not a zero of $f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7$

a)

-2

b)

0

c)

$-\frac{1}{3}$

d)

-7

77.

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)

78.

The possible number of turning points for the graph of a 4th degree polynomial (a quartic) is:

Select all that apply!

a)

4

b)

3

c)

2

d)

1

e)

0

79.

Which statement is true based on the data in the table?

a)

f(x) is an exponential function

b)

g(x) is a linear function

c)

The y-intercept of g(x) is 10

d)

The slope of f(x) is 3

80.

Which statement is true based on the data in the table?

a)

$\ f\left(x\right)\cdot g\left(x\right)$ has no x-intercepts

b)

$f\left(x\right)\cdot g\left(x\right)$ has one x-intercept at x=0

c)

undefined has two x-intercepts at x=5 & x=9

d)

undefined has three x-intercepts at x=0, x=5 & x=9

81.

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

a)

-4, -1, 3

b)

3, -3, 4, 1

c)

4, 1, -3

d)

3, -4, -1, 3

82.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

83.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

84.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

85.

What are the zeros of the graph? SELECT THE BEST ANSWER

a)

-4, -1, 2, 1 multiplicity 2

b)

-4, -1, 1, 2

c)

4, 1, -2, -1 multiplicity 2

d)

4, 1, -1, -2

86.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

87.

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. What is the domain of the function?

a)

0 < x < 0.25

b)

0 < x < 0.75

c)

0 < x < 0.5

d)

x < 0.5

88.

$The\ \ f\left(x\right)=-0.1x^2+43x-3520$ represents a company’s profit, where x is number of items sold. Find the number of items sold that will give the maximum profit. What is the maximum profit? Select all that apply.

a)

$110

b)

$215

c)

$1103

d)

$320

89.

$The\ \ f\left(x\right)=-0.1x^2+43x-3520$ represents a company’s profit, where x is number of items sold. How many items should be sold for the company to break even? Select all that apply.

a)

110 items

b)

215 items

c)

1103 items

d)

320 items

90.

What could be the equation for this graph?

a)

y = -2x³+ 1x + 3

b)

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

c)

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

d)

y = -2x² + 1x + 3

91.

Which of these represents a CUBIC function?

a)

b)

c)

d)

92.

What is the standard form of a CUBIC function?

a)

$y=ax^3+bx^2+cx+d$

b)

$y=mx+b$

c)

$y=ax^2+bx+c$

d)

$y=b\left(r\right)^x$

93.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

94.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

95.

All imaginary roots comes in pairs.

a)

True

b)

False

96.

A rectangular fence is constructed around a backyard so that one side is bounded by a wall of a barn. Determine the equation for the area enclosed if the total fencing is 80 m.

a)

A(x) = x^2(80-2x)^2

b)

A(x) = x(80-2x)

c)

A(x) = x(80-2x)^2

d)

A(x) = x(80-x)^2

97.

The function, A(x)=x(20-2x), represents a rectangular fence being constructed around a backyard so that one side is bounded by a wall of a barn. Determine the max area enclosed if the total fencing is 20 m.

a)

0 m^2

b)

5 m^2

c)

10 m^2

d)

50 m^2

98.

If the polynomial $x^2-5x+9$ is divided by (x-3), then the remainder is

a)

4

b)

5

c)

2

d)

3

99.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

100.

What are the three factors for
(x³ -3x² -4x +12) ÷ (x + 2)?

a)

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

b)

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

c)

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

d)

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

101.

The value of p for which the polynomial $2x^3+px^2-5x-6\$ is divisible by 2x -3 is

a)

p=3

b)

p=2

c)

p=4

d)

p=6

102.

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.

103.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

104.

Which binomial is a factor of
f(x)= 6x³ -35x² +34x +40?

a)

2x - 3

b)

2x - 5

c)

3x - 2

d)

5x - 2

105.

What are the three factors for
(x³ +7x² +7x -15) ÷ (x -1)?

a)

(x-1) (x+5) (x-3)

b)

(x-1) (x+5) (x + 3)

c)

(x+1) (x+5) (x-3)

d)

(x+1) (x-5) (x-3)

106.

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

a)

g(1) = 2

b)

g(-1) = 2

c)

g(2) = 1

d)

g(2) = -1

107.

8r³ - 16r²

a)

4r²(2r - 4)

b)

8r²(r - 2)

c)

8(r³ - r²)

d)

4(r³ - 2r²)

108.

Factor Completely:

x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

109.

Factor Completely.
$4x^2+24x-64$

a)

$4\left(x+8\right)\left(x-2\right)$

b)

$4(x^2+6x-16)$

c)

$4\left(x^2+24x-16\right)$

d)

$4\left(x-8\right)\left(x+2\right)$

110.

When factored completely, $x^3-9x$ is equivalent to:

a)

$x\left(x-3\right)$

b)

$x\left(x+3\right)\left(x-3\right)$

c)

$\left(x+3\right)\left(x-3\right)$

d)

$x\left(x+3\right)$

111.

Factor p³- 3p² - 16p + 48

a)

p² ( p - 3) (p - 3)

b)

(p² - 16) (p - 3)

c)

(p + 4) (p - 4) (p - 3)

112.

Factor by Grouping:

x³ - 4x² -4x + 16

a)

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

b)

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

c)

(x+4)(x² - 4)

d)

(x+2)(x-2)

113.

Factor Completely:

x² + 16

a)

(x + 8)(x - 2)

b)

(x - 4)(x + 4)

c)

(x - 8)(x + 2)

d)

(x + 4i)(x - 4i)

114.

Fully Factor the Following
25x²-81

a)

(5x-9)²

b)

(5x+9)(5x-9)

c)

25(x-9)²

d)

(9x+5)(9x-5)

115.

Which type of regression model does the scatter plot appear to show?

a)

linear

b)

exponential

c)

quadratic

116.

Which scatterplot would best fit a cubic function?

a)

b)

c)

d)

117.

Solve the inequality.

2x³+ 3x²- 17x - 30 < 0

a)

(-2.5,-2) U (3,∞)

b)

(-∞,-2.5] U [-2,3]

c)

(-∞,-2.5) U (-2,3)

d)

[-2.5,-2] U [3,∞)

118.

On what intervals is

x^2-7x+10<0

?

(Select all that apply)

a)

x<2

b)

2<x<5

c)

x>5

December 2022 Alg 2H Final Exam

Total questions: 118

Worksheet time: 6hrs 18mins

Similar Resources on Wayground