Free Printable Alg 2_S2_FinalExamReview

1.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

2.

Reduce, or simplify

the rational expression.

a)

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

b)

( x - 5 ) / ( x - 2 )

c)

( x + 5 ) / ( x - 2 )

d)

-25 / ( 3x - 10 )

3.

Divide and Simplify

a)

A

b)

B

c)

C

d)

D

4.

Simplify: $\frac{3x\ +\ 5xy}{12x^2}\ +\ \frac{9x\ +\ 7xy}{12x^2}$

a)

$\frac{12x\ +\ y}{x^2}$

b)

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

c)

$\frac{12x\ +\ y}{x}$

d)

$\frac{12x\ +\ 12xy}{12x^2}$

5.

What factor is the second fraction missing in its denominator? $\frac{x}{\left(x-1\right)\left(x+1\right)}-\frac{4}{\left(x+1\right)}$

a)

$\left(x+1\right)\left(x-1\right)$

b)

$\left(x-1\right)$

c)

$x^2-1$

d)

$x$

e)

$\left(x+1\right)$

6.

If you were going to subtract the fractions, what would you do first? $\frac{2}{\left(x+7\right)}-\frac{3}{\left(x+3\right)\left(x+7\right)}$

a)

Subtract the numerators.

b)

Multiply out the second denominator.

c)

Make the denominators match by multiplying the left fraction by $\frac{\left(x+7\right)}{\left(x+7\right)}$

d)

Make the denominators match by multiplying the left fraction by undefined

e)

Make the denominators match by multiplying the left fraction by $\frac{\left(x+3\right)}{\left(x+3\right)}$

7.

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

8.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

9.

Find the hole of the function.
x²- 9x+20
___________
4x² - 12x- 40

a)

x =5

b)

x=0

c)

x=4

d)

x=-2

10.

A hole occurs when....

a)

You wear pants that are too tight.

b)

A factor from the numerator cancels with a factor in the denominator.

c)

The degree of the numerator is one more than the degree of the denominator.

d)

The denominator cannot be factored.

11.

Consider the function

$g\left(x\right)=\frac{x-4}{x^2-4}$

Does the function have any holes?

a)

Yes, when $x=4$

b)

Yes, when $x=2$

c)

Yes, when $x=-2\ or\ 2$

d)

The function does not have any holes.

12.

Select all the options below that are equivalent to 15y + 60.

a)

3(5y + 20)

b)

15(y + 4)

c)

-15(-y - 4)

d)

15(y + 60)

e)

15y(y + 4)

13.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

14.

(x-3)(x²+2x+7)

a)

x³-x²+x-21

b)

x³+5x+13x-21

c)

x³-3x²+7x-21

d)

x²+2x-3

15.

Which expression with a fractional exponent best represents √7 ?

a)

7^½

b)

7¼

c)

7⅓

d)

2⁷

16.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a)

a negative real number

b)

a positive real number

c)

an even real number

d)

an odd real number

17.

Based on the end behavior of the polynomial, what is the degree of the polynomial?

a)

a negative real number

b)

a positive real number

c)

an odd real number

d)

an even real number

18.

Which point does not represent a zero of a polynomial?

a)

(-2, 0)

b)

(-1, 0)

c)

(0, 4)

d)

(2, 0)

19.

Multiply and Simplify

a)

a

b)

b

c)

c

d)

d

20.

What are the linear terms of the polynomial function?

a)

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

b)

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

c)

(x-2)(x-1)(x+1)(x+2)(x-4)

d)

(x-2)(x-1)(x+1)(x+2)(x+4)

21.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

22.

What is the least degree of the polynomial?

a)

2

b)

4

c)

3

d)

5

23.

What are the zeros of the polynomial?

a)

X=5, x=-3(multiplicity of 2)

b)

x=-3, x=5(multiplicity of 2)

c)

x=3, x=-5

d)

x=5

24.

Classify the polynomial by degree.

a)

quartic

b)

quintic

c)

6th degree polynomial

d)

7th degree polynomial

25.

What is the remainder?
(6x² + 19x + 13) ÷ (2x + 5)

a)

0

b)

3

c)

5

d)

-5/2

26.

Write the equation of the polynomial function
zeros: 0, -2, 4
degree: 5
0 has a multiplicity 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)

27.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

28.

Fill in the value based on the graph...

As x → -∞ f(x)→

a)

-∞

b)

∞

29.

How many real roots are in the graph?

a)

2

b)

3

c)

4

d)

5

30.

Give the equation of the 4th degree polynomial with zeros: 1 with multiplicity 2,-i and i.

a)

x² - 4x + 4

b)

x³ - 4x² + 4x +ix² -4ix + 4i

c)

x⁴ - 4x³ + 5x²-4x + 4

d)

x⁴ - 4x³ + 5x²-4x + 4i

31.

Factor 4v² − 4v − 8

a)

4(v + 1)(v − 2)

b)

(v− 10)(v − 5)

c)

4(v-1)(v-2)

d)

None of the Above

32.

(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

33.

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.

34.

Find all real solutions of the polynomial equation x³- x²- 7x + 3 = 0 given x= 3 is a zero.

a)

x = 3, ± √2

b)

x = -3, -1 ± √2

c)

x = -1 ± √2

d)

x = 3, 1 ± √2

35.

a)

(2, - 3)

b)

(- 2, 1)

c)

(-2, 3)

d)

(3, 2)

36.

a)

(-2, -3)

b)

(-2, 3)

c)

(2, -3)

d)

(2, 3)

37.

What is the solution to the systems of equations?

a)

(-7, -9)

b)

(-10, 5)

c)

No Solution

d)

Infinitely Many Solutions

38.

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

39.

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

a)

4

b)

5

c)

6

d)

7

40.

Look at the equation below.

$x^2+2x-5=2$

Which values of x satisfy the equation? Write your answers in simplest radical form.

a)

$-1\pm2\sqrt{2}$

b)

$1\pm2\sqrt{2}$

c)

$-1\pm2i\sqrt{2}$

d)

$1\pm2i\sqrt{2}$

41.

Look at the equation below.

$x^2+5x+7=0$

What are the solutions of the equation? Write your answers in simplest radical form.

a)

$\frac{-5\pm\sqrt{3}}{2}$

b)

$\frac{-5\pm i\sqrt{3}}{2}$

c)

$\frac{-5\pm\sqrt{53}}{2}$

d)

$\frac{-5\pm i\sqrt{53}}{2}$

42.

What is the value of the expression below?

$8\left(5-3i\right)+i\left(3+2i\right)$

a)

$42-21i$

b)

$38-21i$

c)

$42+27i$

d)

$40-19i$

43.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

44.

Consider the function y<2x+3. Which is true?

a)

The line would be solid with shading above.

b)

The line would be dashed with shading above.

c)

The line would be solid with shading below.

d)

None of these.

45.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

46.

Is the point (2, 1) a solution to the inequality shown?

a)

Yes

b)

No

47.

Which correctly shows the inequality $y\ge-x^2+2x+1$ ?

a)

b)

c)

d)

48.

How many real solutions does this graph have?

a)

one

b)

two

c)

none

d)

cannot be determined

49.

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

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

50.

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

a)

(1, 4)

b)

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

c)

(1, 3) and (4, 6)

d)

(1, 4) and (3, 6)

51.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

52.

Solve for b:
4^{3b - 3} = 1/16

a)

7

b)

-1/4

c)

1/2

d)

1/3

53.

Solve the following exponential equation:
$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

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

d)

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

54.

Solve the following exponential equation:

3^3=3^{4x+2}

a)

$x=\frac{1}{4}$

b)

$x=-\frac{1}{4}$

c)

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

d)

$x=-\frac{1}{2}$

55.

Write in exponential form: ∛4⁵

a)

4^3/5

b)

4^5/3

c)

4^1/5

d)

4^1/3

56.

Solve: 7^-x = 49

a)

1

b)

-1

c)

2

d)

-2

57.

A pair of classic Nike shoes was worth $125 when bought new in 2018 and are now only worth about $93.50. What is the multiplier (percent decrease)

a)

0.93

b)

0.85

c)

0.94

d)

0.9

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.

A student used $f\left(x\right)=500\left(1.012\right)^x$ to show how the balance in a savings account will increase over time. What does the 500 represent?

a)

The interest the account earned for the first year

b)

The annual interest rate of the savings account

c)

The number of years the savings account has earned interest

d)

The starting balance of the savings account

60.

Scientists are studying the coronavirus very carefully. The function $f\left(x\right)=10000\left(1.05\right)^x$ gives the number of infected people in the world at the end of x weeks. Which of the following statements is the best description of one of the values in the function?

a)

The initial number of infected people is 5

b)

The number of infected people decreases at a rate of 95% each week

c)

The number of infected people increases at a rate of 5% each week

d)

The number of infected people at the end of 1 week is 10,000

61.

There are 1,024 players in a Fortnite tournament. In each round, half the players are eliminated. Which function could be used to determine the number of players remaining at the end of x rounds?

a)

$f\left(x\right)=1,024\left(1.05\right)^x$

b)

$f\left(x\right)=1,024\left(0.95\right)^x$

c)

$f\left(x\right)=1,024\left(-2\right)^x$

d)

$f\left(x\right)=1,024\left(0.50\right)^x$

62.

The table represents some points on the graph of an exponential function. Which function represents the same relationship?

a)

$f\left(x\right)=15\left(\frac{5}{6}\right)^x$

b)

$f\left(x\right)=15\left(\frac{6}{5}\right)^x$

c)

$f\left(x\right)=18\left(\frac{5}{6}\right)^x$

d)

$f\left(x\right)=18\left(\frac{6}{5}\right)^x$

63.

Find the exponential equation that passes through (1, 125) and (4, 1)

a)

y=5(5)^x

b)

y=625(0.2)^x

c)

y=125(0.2)^x

d)

y=625(5)^x

64.

Find the exponential equation that passes through (2, 31.5) and (4, 283.5)

a)

y=3(3.5)^x

b)

y=10.5(3)^x

c)

y=3.5(3)^x

d)

y=283.5(0.33)^x

65.

Five years ago, Vanessa bought a car for $25,000. Each year since then, the value of the car has decreased by 12%. What is the approximate value of the car after 5 years?

a)

$44,000

b)

$13,200

c)

$650

d)

$15,000

66.

Find the exponential equation that passes through (2, 31.5) and (4, 283.5)

a)

y=3(3.5)^x

b)

y=10.5(3)^x

c)

y=3.5(3)^x

d)

y=283.5(0.33)^x

67.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

68.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

69.

Identify the parent function of the graph.

a)

Linear

b)

Logarithmic

c)

Exponential

d)

Square Root

70.

Which of the following parent functions has a range of $\left(0,\infty\right)$

a)

b)

c)

d)

71.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

72.

Write the equation of the quadratic in vertex form given the following:
vertex: (4, -2)
point: (0,-6)
opens down

a)

f(x)=(x-4)²-2

b)

f(x)=-4(x-4)²-2

c)

f(x)=1/4(x+4)²-2

d)

f(x)=-1/4(x-4)²-2

73.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

a)

(-2, 5)

b)

(-6, 5)

c)

(-4, 3)

d)

(-4, 7)

74.

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

a)

Shifted up 5 units
Shifted right 3 units
Stretched vertically by a factor of 3

b)

Shifted up 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

c)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

d)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 1/3

75.

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

a)

f(x - 3)

b)

f(x + 3)

c)

f(x) + 3

d)

f(x) - 3

76.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

77.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

78.

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

79.

Which is a function?

a)

A

b)

B

c)

C

d)

D

80.

Given f(x) = -4x - 10 and f(x) = 10. Find x

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

81.

What is the value of x when f(x) = 16?

a)

x = 4 only

b)

x = 4 and x = 8

c)

x = 16

d)

Not on the graph

82.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

83.

solve for x.

$3^{2x-1}\cdot3^4=3$

a)

1/2

b)

5/8

c)

-1

d)

8/5

Alg 2_S2_FinalExamReview_24-25

Total questions: 83

Worksheet time: 4hrs 57mins

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