Free Printable Algebra 2B Final Review

1.

Evaluate 3x + 5y for x = -1 and y = 4.

a)

17

b)

11

c)

7

d)

7

2.

Simplify (by factoring): 3|x - 1| - 6|x - 1|

a)

-3|x - 1|

b)

3|x - 1|

c)

9|x - 1|

d)

6|x - 1|

3.

The Vertical Line Test is used to determine if a graph represents which of the following?

a)

A function

b)

A line

c)

A circle

d)

A parabola

4.

Define a function?

a)

A function is when each input has exactly one output.

b)

A function has multiple inputs that have more than one output.

c)

A function has outputs that have more than one input.

d)

A function has only one input and multiple outputs

5.

Solve the linear system: 2x - 2y = 8 3x + 2y = -13

a)

x = -1, y = -5

b)

x = 2, y = 3

c)

x = 1, y = 4

d)

x = -2, y = 1

6.

A minor league baseball team had a total attendance one evening of 1175. The tickets for adults and children sold for $5 and$ 3.50, respectively. The ticket revenue that night was $5087.50. Write a system of solutions and solve to find the number of adults and children that attended the game.

a)

Let a = number of adults, c = number of children. System: a + c = 1175, 5a + 3.5c = 5087.5. Solution: a = 725, c = 450.

b)

Let a = number of adults, c = number of children. System: a + c = 1175, 5a + 3.5c = 5087.5. Solution: a = 600, c = 575.

c)

Let a = number of adults, c = number of children. System: a + c = 1175, 5a + 3.5c = 5087.5. Solution: a = 800, c = 375.

d)

Let a = number of adults, c = number of children. System: a + c = 1175, 5a + 3.5c = 5087.5. Solution: a = 500, c = 675.

7.

Describe how the graph of the function $f(x) = -|x - 4|^2 + 1$ compares with its parent function $f(x) = x^2$ .

a)

It is reflected over the x-axis, shifted right by 4 units, and up by 1 unit.

b)

It is shifted left by 4 units and down by 1 unit.

c)

It is stretched vertically and shifted down by 1 unit.

d)

It is compressed horizontally and shifted up by 4 units.

8.

Given the graph to the right, name the parent function and compare it to the given graph.

a)

The parent function is $f(x) = x^2$ and the graph is shifted up.

b)

The parent function is f(x) = |x| and the graph is reflected over the x-axis.

c)

The parent function is f(x) = √x and the graph is shifted right.

d)

The parent function is f(x) = 1/x and the graph is shifted left.

9.

Use the functions for $f(x) = 3x - 1$ and $g(x) = x^2 + 4$ to find $f(3) + g(2)$ .

a)

f(3) = 8, g(2) = 8, so f(3) + g(2) = 16.

b)

f(3) = 9, g(2) = 6, so f(3) + g(2) = 15.

c)

f(3) = 7, g(2) = 9, so f(3) + g(2) = 16.

d)

f(3) = 8, g(2) = 6, so f(3) + g(2) = 14.

10.

Let f(x) = $3x^2 - 6x$ and g(x) = $7x - 5$ . What is g(f(x))?

a)

$g(f(x)) = 7(3x^2 - 6x) - 5 = 21x^2 - 42x - 5$

b)

g(f(x)) = $3(7x - 5)^2 - 6(7x - 5)$

c)

$g(f(x)) = 7x^2 - 5x$

d)

g(f(x)) = $21x^2 - 6x - 5$

11.

Let f(x) = 2x + 1 and g(x) = x - 5. Perform the indicated operation: f(g(2))

a)

0

b)

1

c)

-5

d)

-3

12.

Find the inverse of the following: f(x) = (1/7)x - 4

a)

f^(-1)(x) = (1/7)(x - 4)

b)

f^(-1)(x) = 7x - 4

c)

f^(-1)(x) = (1/7)(x + 4)

d)

f^(-1)(x) = 7(x + 4)

13.

Find the inverse of y = $(x+9)^{4^{ }}$

a)

y = x^4 - 9

b)

y = x^(1/4) - 9

c)

y = (x - 9)^{1/4}

d)

y = (x + 9)^{1/4}

14.

Solve ln(3x - 2) = ln(2x + 3)

a)

x=4

b)

x=5

c)

x=7

d)

x=3

15.

Simplify $(4x^3 y)^{-2}$

a)

$\frac{1}{16x^6 y^2}$

b)

$\frac{1}{8x^6 y^2}$

c)

$\frac{1}{16x^3 y^2}$

d)

$\frac{1}{8x^3 y^2}$

16.

Simplify $\frac{(2^{11}x^2y^4z^8)^0}{(3x^{-1}y^3)}$

a)

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

b)

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

c)

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

d)

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

17.

Mark had a goal of running for an average (mean) of 90 miles each week. The number of miles he ran each of the first four weeks were 87, 81, 92, and 95. Which value is the minimum number of miles he must run during the fifth week to meet his goal?

a)

95 miles

b)

90 miles

c)

100 miles

d)

85 miles

18.

Factor the expression completely: $16x^2 - 81y^2$

a)

(4x + 9y)(4x - 9y)

b)

(16x - 81y)(x + y)

c)

$(4x - 9y)^2$

d)

(8x + 9y)(2x - 9y)

19.

Which of the following is an example of an exponential growth equation?

a)

$y = 2^x$

b)

y = 2/x

c)

$y = x^2$

d)

y = |x|

20.

Solve: $6x^2 = 5x - 1$

a)

x = 1, x = -1/6

b)

x = 2, x = -1/3

c)

x = 1/2, x = -1/2

d)

x = 3, x = -1/2

21.

Solve the equation. $x^2 + 6x = -15$

a)

x = -3 ± 2i

b)

x = -6 ± i√15

c)

x = 3 ± i√6

d)

x = -3 ± i√6

22.

What are the solutions of the following equation? $x^2 - 10x - 9 = 0$

a)

x = 11, x = -1

b)

x = 9, x = 1

c)

x = -9, x = -1

d)

x = 10, x = -9

23.

Factor completely: $5x^4 - 625x$

a)

$5x(x - 5)(x^2 + 5x + 25)$

b)

$5x(x^3 - 125)$

c)

$5(x^4 - 125x)$

d)

$5x(x^2 - 25x + 25)$

24.

Perform the indicated operation and simplify the result: $\frac{x^2 - 4}{x + 3} \cdot \frac{x^2 + 4x + 3}{2x - 4}$

a)

[(x - 2)(x + 2)(x + 3)] / [(x + 3)(2(x - 2))] = (x + 2)/(2)

b)

$(x^2 - 4x + 3)$ / $(2x - 4)(x + 3)$ = $(x - 1)/(2)$

c)

$(x^2 + 4x + 3)$ / $(x + 3)(x^2 - 4)$ = $(x + 3)/(x - 2)$

d)

$[(x^2 - 4)(x^2 + 4x + 3)]$ / $[(x + 3)(2x - 4)]$ = $(x^2 + 2x - 3)/(2x - 4)$

25.

24. Divide: $\frac{x^2 + 9x + 20}{x^2 - 16}$ ÷ $\frac{x + 5}{x - 5}$

a)

1/(x - 4)

b)

(x + 4)/(x - 4)

c)

(x - 4)/(x + 4)

d)

1/(x + 4)

26.

What are all solutions of the equation? $5(x - 2)^2 - 4 = 26$

a)

x = 2 ± 3

b)

x = 2 ± 2

c)

x = 2 ± 4

d)

x = 2 ± 5

27.

Give the correct factorization: $6x^2 - 7x - 5$

a)

(3x + 1)(2x - 5)

b)

(2x + 1)(3x - 5)

c)

(3x - 5)(2x + 1)

d)

(6x + 1)(x - 5)

28.

Factor. $x^3 - 4x^2 - 4x + 16$

a)

$(x^2 - 4)(x - 4)$ = $(x - 2)(x + 2)(x - 4)$

b)

$(x^2 + 4)(x + 4) = (x + 2)(x - 2)(x + 4)$

c)

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

d)

$(x^2 + 4x + 16)(x - 1)$ = $(x + 2)(x + 2)(x - 1)$

29.

Simplify: $(-4 + 2i)^2$

a)

12 - 16i

b)

-12 + 16i

c)

20 - 8i

d)

-8 + 20i

30.

29. Simplify. i/(3 + i)

(a)

31.

What is the x-coordinate of the vertex for the function f(x) = $4x^2 - 8x + 5$ ?

a)

1

b)

2

c)

-1

d)

0

32.

Simplify: $\frac{(24x^3y^{-1})}{(4xy^2)}$

a)

$6x^2/y^3$

b)

$8x^3/y$

c)

$12x^2/y^2$

d)

$4x/y^2$

33.

Use Synthetic Division to perform the given operation: $(4x^3 - 11x^2 - 9x - 5) ÷ (x + 4)$

a)

$4x^2 - 27x + 99$ , remainder -401

b)

4x^2 + 5x + 11, remainder 3

c)

4x^2 - 27x - 99, remainder 401

d)

$4x^2 + 27x - 99$ , remainder -401

34.

How many zeroes does the given function have? f(x) = $-4x^7 + 4x^5 - 8x^3 + 16$

a)

7

b)

0

c)

3

d)

5

35.

Factor completely: $3x^4 - 24x$

a)

$3x(x^3 - 8) = 3x(x - 2)(x^2 + 2x + 4)$

b)

$3x(x^3 + 8)$ = $3x(x + 2)(x^2 - 2x + 4)$

c)

$3x(x^3 - 8) = 3x(x - 8)$

d)

$3x^4 - 24x = 3(x^4 - 8x)$

36.

Find the product. $y^4\left(y+5\right)\left(y^2-2\right)$

a)

$y^7+5y^6-2y^5-10y^4$

b)

$y^7 - 5y^6 + 2y^5 + 10y^4$

c)

$y^7 + 2y^6 - 5y^5 - 10y^4$

d)

$y^7 + 5y^6 + 2y^5 - 10y^4$

37.

Estimate the real zeros of the function graphed to the right:

a)

Approximately x = -3, x = 0, x = 2

b)

Approximately x = -2, x = 1, x = 3

c)

Approximately x = -1, x = 1, x = 4

d)

Approximately x = -4, x = 0, x = 3

38.

Rewrite the expression in exponential form. $\sqrt[3]{x^5}$

a)

x^{5/3}

b)

x^{5/2}

c)

x^{6/3}

d)

x^{3/5}

39.

Rewrite the expression in radical form. $x^{9/4}$

a)

$\sqrt[4]{x^9}$

b)

$\sqrt[9]{x^4}$

c)

$x^{\frac{2}{1}^{+\frac{1}{4}}}$

d)

$x^2+x^{\frac{1}{4}}$

40.

Simplify the expression. $\sqrt[3]{27x^7 y^9 z^4}$

a)

$3x^{7/3} y^3 z^{4/3}$

b)

$3x^{2} y^3 z^{4}$

c)

$9x^{7/3} y^3 z^{4/3}$

d)

$3x^{7/3} y^2 z^{4/3}$

41.

Add: $\frac{5}{x+3} + \frac{6}{x-3}$

a)

$\frac{11x+3}{x^2-9}$

b)

$\frac{11x-3}{x^2-9}$

c)

$\frac{5x+6}{x^2-9}$

d)

$\frac{5}{x+3} + \frac{6}{x-3}$

42.

Simplify. $\frac{2}{x+4} \div \frac{3}{x-2}$

a)

$\frac{2(x-2)}{3(x+4)}$

b)

$\frac{2(x+4)}{3(x-2)}$

c)

$\frac{3(x+4)}{2(x-2)}$

d)

$\frac{3(x-2)}{2(x+4)}$

43.

Solve the equation: $\frac{-15}{x} = \frac{x+16}{4}$ Fill in the blank with the value of x.

a)

x=-6, x=-10

b)

x=5, x=3

c)

x=4, x=-4

d)

x=8, x=-2

44.

Expand $\log \frac{a^2b^2}{c^3}$ ?

a)

$2\log a + 2\log b - 3\log c$

b)

$\log a + \log b - 3\log c$

c)

$2\log a + 2\log b + 3\log c$

d)

$2\log a - 2\log b - 3\log c$

45.

What is the solution of this equation? $5\sqrt[3]{x}-1=25$ Fill in the blank with the value of x.

a)

140.608

b)

64

c)

27

d)

216

46.

Evaluate $\log_3 11$ Fill in the blank with the answer (exact or rounded to 3 decimal places).

a)

$\log_3 11 \approx 2.183$

b)

$\log_3 11 \approx 1.041$

c)

$\log_3 11 \approx 3.462$

d)

$\log_3 11 \approx 0.958$

47.

Evaluate: a. $\log_7 49$ b. $\log_{25} 5$ c. $\log_2 1/4$ Fill in the blank with the answers.

a)

a. 2 b. 0.5 c. -2

b)

a. 1 b. 2 c. -1

c)

a. 3 b. 0.2 c. -3

d)

a. 0 b. 5 c. 2

48.

Solve the equation: $5+\ln x=7$ Fill in the blank with the value of x.

a)

$x=e^2 \approx 7.389$

b)

x=2

c)

x=1

d)

x=10

49.

What type of function is $f(x) = 2(4)^x$ ?

a)

Linear

b)

Quadratic

c)

Exponential

50.

Condense $2(\log_3 20 - \log_3 4) + 0.5\log_3 4$

a)

$\log_3 50$

b)

$\log_3 10$

c)

$\log_3 40$

d)

$\log_3 5$

51.

You deposit $2200 in a bank account. Find the balance after 4 years for the following situation: a. The account pays 3.5% compounded continuously.

a)

$3146.13

b)

$2500.00

c)

$3000.00

d)

$2800.00

52.

You deposit $2200 in a bank account. Find the balance after 4 years for the following situation: b. The account pays 3.5% compounded quarterly.

a)

$3142.13

b)

$2500.00

c)

$3000.00

d)

$2800.50

53.

You buy a boat for $20,000. The value decreases by 15% each year. What is the value after 3 years?

a)

$12,282.50

b)

$10,000.00

c)

$15,000.00

d)

$8,500.00

54.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

55.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

56.

Find the inverse of the equation

a)

2^(x-9)+5=y

b)

2^(x+9)-5=y

c)

5^(x-9)-5=y

57.

Which function matches the graph?

a)

A

f(x) = √(x - 4) - 2

b)

B

f(x) = √(x + 2) - 4

c)

C

f(x) = √(x - 2) - 4

d)

D

f(x) = √(x + 4) - 2

58.

Which function matches the graph?

a)

A

f(x) = ∛(x + 3) + 2

b)

B

f(x) = − ∛(x - 3) + 2

c)

C

f(x) = ∛(x - 3) + 2

d)

D

f(x) = ∛(x - 2) + 3

59.

What type of function is shown?

a)

cube root

b)

square root

c)

logarithm

d)

exponential

60.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

61.

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

62.

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

63.

What is the inverse of the points
(1,3)(2,4)(6,8)

a)

(3,1)(4,2)(8,6)

b)

(-3,-1)(-4,-2)(-8,-6)

c)

(1,3)(2,4)(6,8)

d)

(-1,-3)(-2,-4)(-6,-8)

64.

Are these inverse functions?

a)

no

b)

yes

c)

no way to tell

65.

Given the function above:

What is the domain?

a)

x >= 1

b)

x > -1

c)

y >= 1

d)

x >= 0

66.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

67.

What transformations has the function undergone?

a)

reflect over y, vertical compress by 2, right 5, up 1

b)

reflect over x, horizontal compression by 2, left 5, up 1

c)

reflect over x, vertical stretch by 2, right 5, up 1

d)

reflect over y, horizontal stretch by -2, right 5, up 1

68.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

69.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

70.

Solve by cross-multiplying.

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

71.

Calculate:
(1 − 2i) + (-4 + 2i)

a)

-3

b)

-3 − 4i

c)

5 − 4i

d)

5

72.

Simplify $\left(2+3i\right)^2$

a)

$-5+12i$

b)

$4+6i+3i^2$

c)

$4-12i+9i^2$

73.

Solve: $2x^2-5x-6\ =\ 0$

a)

$x\ =\frac{5\pm\sqrt[]{73}}{4}$

b)

$x\ =\frac{5+\sqrt[]{73}}{4}$

c)

$x\ =\frac{5-\sqrt[]{73}}{4}$

d)

$x\ =\frac{7\pm\sqrt[]{53}}{4}$

74.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

75.

$\sqrt{x-3}+6=5$

a)

4

b)

22

c)

2

d)

no solution

76.

Factor:
56a³-8a

a)

8a²(56a³-8a)

b)

8a(7a²-1)

c)

8a(7a³-a)

d)

8a²(35a²-a)

77.

Factor 4x²-9

a)

(4x-9)(4x+9)

b)

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

c)

2x-3

d)

(2x-4.5)(2x+4.5)

78.

Simplify each expression.

Answers should have only positive exponents

and no rational exponents in the denominator.

a)

12

b)

10

c)

2√30

d)

4√30

79.

Rewrite the logarithmic equation as an exponent.
log₄25 = x

a)

4^x = log

b)

4²⁵ = x

c)

4^x =25

d)

log = 4

80.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

81.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

82.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42

b)

$33,672.68

c)

$34,157.04

d)

$34,710.88

83.

Write the following parabola in vertex form: y = -2x²+16x+4

a)

y=-2(x-4)²+4

b)

y =-2(x+4)²+36

c)

y=-2(x+4)²+4

d)

y =-2(x-4)²+36

84.

Solve: (x-4)²-18 = 0

a)

x = 4 + 3√2

b)

x = 8.24, -.24

c)

x = 4 ± 3√2

d)

x = 4 ± √18

85.

What would you add to
x²-16x+___ to complete the square?

a)

4

b)

64

c)

16

d)

8

86.

Solve the following quadratic inequality:

$p^2-64>0$

a)

$p>8$ or $p>-8$

b)

$-8<x<8$

c)

$p<-8$ or $p>8$

d)

$p<-8$ or $p<8$

87.

Give the vertex of the equation.

a)

(1, -6)

b)

(-1, -6)

c)

(-6, 1)

d)

(1, 6)

88.

Factor:
5n³ - 10n² + 3n - 6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

89.

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

90.

Choose the best equation for the graph.

a)

A) y = mx + b

b)

B) y = ax^2 + bx + c

c)

C) y = sin(x)

d)

D) y = e^x

91.

If $f(x)=4x+1$ and $g(x)=4x-3$

Find $f(x).g(x)$

a)

$16x^2+8x-3$

b)

$16x^2-8x+3$

c)

$16x^2-8x-3$

92.

If $f(n)=x^2+1$ and $g(n)=2x-5$ Find $f(x)-g(x)$

a)

$x^2-2x+6$

b)

$-x^2+2x+4$

c)

$-x^2-2x-6$

d)

$x^2-2x-4$

93.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

94.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x) = x²

c)

f(x) =√(x)

d)

f(x) =∛(x)

95.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

96.

What is the equation of the graph below? You can click the picture to zoom in!

a)

f(x) = I x + 2 I

b)

f(x) = I x I + 2

c)

f(x) = I x I - 2

d)

f(x) = I x - 2 I

97.

Name the parent function.

a)

linear

b)

quadratic

c)

cube root

d)

cubic

98.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

99.

Write the equation of the graph.

a)

f(x)= $\sqrt[]{-x-4}+2$

b)

f(x)= $-\sqrt[]{x-4}+2$

c)

f(x)= $\sqrt[]{-x+4}+2$

d)

f(x)= $-\sqrt[]{x-2}+4$

100.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

101.

Identify the Parent Function

a)

Rational

b)

Exponential

c)

Logarithmic

d)

Cube Root

102.

$f\left(x\right)=\ -\frac{1}{x-4}-3$

a)

b)

c)

d)

103.

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

a)

Growth

b)

Decay

104.

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

a)

Growth

b)

Decay

105.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

106.

Is this exponential growth or decay?

a)

Growth

b)

Decay

107.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

108.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

109.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

110.

log(4x)

a)

log4-logx

b)

log4+logx

c)

4logx

d)

xlog4

111.

$\log\left(\frac{m^3}{n}\right)$

a)

logm-log3-logn

b)

3logm+logn

c)

3logm-logn

d)

3log(m-n)

112.

$\log\left(\frac{9}{4}\right)$

a)

log9+log4

b)

log(9-4)

c)

log9-log4

d)

4log9

113.

If $\log_BA=\frac{\log A}{\log B}$ , then $\log_{12}245=$

a)

$\log\frac{245}{12}$

b)

$\log\frac{12}{245}$

c)

None of these

114.

If $\log_BA=\frac{\log A}{\log B}$ , then $\log_8245=$

a)

$\log\frac{245}{8}$

b)

$\log\frac{8}{245}$

c)

$\frac{\log8}{\log245}$

d)

$\frac{\log245}{\log8}$

115.

If $\log_BA=\frac{\log_nA}{\log_nB}$ , then $\log_{25}3=$

a)

$\frac{\ln25}{\ln3}$

b)

$\ln\frac{25}{3}$

c)

$\frac{\ln3}{\ln25}$

d)

$\ln\frac{3}{25}$

Algebra 2B Final Review

Total questions: 115

Worksheet time: 29hrs 45mins

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