Free Printable Algebra 2 Fall Final Review

1.

Solve for x:

(x + 6)²= 49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

2.

What should you do first to solve this equation using quadratic formula?

x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

3.

What number goes in the blank to complete the square for this trinomial?

x² – 8x + ___

a)

-4

b)

-16

c)

4

d)

16

4.

When solving the equation x² - 12x + 4 = 20

by completing the square , what values would go in the two blanks?

(________)² = ______

a)

x - 12; 52

b)

x - 6; 16

c)

x - 6; 52

d)

x - 6; 56

5.

Why do we get imaginary numbers?

a)

When a square root has a positive on the outside

3x^2\sqrt{14x}

b)

When a square root has a negative on the outside $-3x^2\sqrt{14x}$

c)

When a square root has a positive on the inside $\sqrt{14}$

d)

When a square root has a negative on the inside $\sqrt{-14}$

6.

Evaluate i²⁴

a)

-1

b)

1

c)

i

d)

-i

7.

What is the simplifies form of (11 – 7i) – (–3 + 12i)

a)

8 – 19i

b)

8 + 5i

c)

13 – 19i

d)

14 –19i

8.

What is the simplified form of (–3x + 2i)(x– 4i)

a)

–3x² + 6xi – 8

b)

–3x² + 6xi + 8

c)

–3x² + 14xi – 8

d)

–3x² + 14xi + 8

9.

a)

A

b)

B

c)

C

d)

D

10.

Fully Factor the Following
216x³+125

a)

6(x+5)³

b)

(6x+5)³

c)

(6x+5)(6x²-30x+25)

d)

(6x+5)(36x²-30x+25)

11.

Factor completely:
5n³ - 10n² + 3n - 6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

12.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

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

13.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

14.

x⁴ - 81

a)

(x² - 9)(x² + 9)

b)

(x - 3)²(x + 3)²

c)

(x - 3)(x + 3)(x² + 9)

d)

(x - 3)⁴

15.

Factor completely:
x⁴-10x²+9

a)

(x-9)(x-1)

b)

(x²-9)(x²-1)

c)

(x-3)(x+3)(x²-1)

d)

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

16.

How many real solutions does x²-8x+16 = 0 have?

a)

0

b)

1

c)

2

d)

infinitely many

17.

Find the value of the discriminant: 4x²-7x+8

a)

√79

b)

√-79

c)

-79

d)

-7±i√79/8

18.

Write the equation 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

19.

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

20.

The quadratic whose roots are -3 and 4.

a)

x²+x-12

b)

x²-x + 12

c)

x²+x+12

d)

x²-x-12

21.

What is the value: √-9 ⋅ √-16

a)

-12

b)

12i²

c)

12i

d)

-12i

22.

Simplify: (2i¹⁰)(-4i¹²)(-5i⁷)

a)

-40

b)

40i

c)

-40i

d)

40

23.

Simplify:
(2+3i)/(5+2i)

a)

(11 + 16i)/29

b)

(16 + 11i)/29

c)

16/29

d)

(4 + 11i)/29

24.

What is the vertex:
y = 2(x-3)²+18

a)

(-3,-18)

b)

(3,-18)

c)

(-3,18)

d)

(3,18)

25.

Which equation is perpendicular to y = 2x + 5?

a)

y = -1/2x + 7

b)

y = 1/2x + 7

c)

y = 2x + 7

d)

y = -2x + 7

26.

What is the equation of the line that passes through (0,4) and (5,0)?

a)

y = -4/5x + 0

b)

y = -4/5x + 5

c)

y = -4/5x + 9

d)

y = -4/5x + 4

27.

Given f(x) = 3x - 2 and g(x) = x²-5. Find: f(2) - g(2)

a)

5

b)

0

c)

4

d)

2

28.

Solve: x²+x+1=0

a)

(1 ± i√3)/2

b)

(1±i√2)/2

c)

(-1±i√3)/2

d)

-1±i√2)/2

29.

Evaluate:
∣-6∣⋅2³ - (5-7)²

a)

32

b)

52

c)

44

d)

48

30.

Which quadratic is the widest?

a)

y = -3/4x²+4x+1

b)

y=2x²-3x+7

c)

y=-4x²+9

d)

y=7/5x²-5x+1

31.

Which function is graphed?

a)

f(x) = 2|x - 5|

b)

f(x) = |x - 5|

c)

f(x) = |x - 5| + 5

d)

f(x) = |x| + 5

32.

When do you use the plus or minus symbol?
±

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

33.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

34.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

35.

Does this parabola have a maximum or minimum?

a)

Maximum

b)

Minimum

36.

What is the Range of the function?

a)

[1, ∞)

b)

[-2, ∞)

c)

(-∞, ∞)

d)

[-∞, ∞]

37.

What is the domain of the function?

*Hint: Domain is the set of all x-values included in the function.

a)

x≥3

b)

x≤3

c)

All real numbers

d)

-1≤x≤5

38.

a)

A

b)

B

c)

C

d)

D

39.

Solve x² - 5x + 10 = 0

a)

(5 - i√15)/2 , (5 + i√15)/2

b)

(5 - √15)/2 , (5 + √15)/2

c)

(5 - i√65)/2 , (5 + i√65)/2

d)

(5 - √65)/2 , (5 + √65)/2

40.

When f(x) = 9-3x and g(x) = 5x-7 , find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

41.

When f(x) = x²+9 and g(x) = x-9, find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

42.

Solve for r.
−2|−2r − 4| = -12

a)

{5,1}

b)

{-5,-1}

c)

{-5,1}

d)

No Solution

43.

What is the domain of the absolute value function?

a)

(4, 0)

b)

(0, 4)

c)

(-infinity, infinity)

d)

[4, infinity)

44.

| x + 3 | ≤ 2

a)

No Solution

b)

All Real Numbers

c)

-5 ≤ x ≤ -1

d)

1 ≤ x ≤ 5

45.

If $f\left(x\right)\ =\ 9x\ -9\ and\ g\left(x\right)\ =\ \sqrt{x\ -\ 2},\ what\ is\ the\ value\ of\ \ f\left(g\left(18\right)\right)?$

a)

27 and -45

b)

27

c)

-45

d)

-27 and 45

46.

If $f\left(x\right)\ =\ \frac{1}{2}x+3$ and $g\left(x\right)=\ 2x\ -\ 6$ , what is the value of $f\left(g\left(x\right)\right)$ ?

a)

x

b)

2x

c)

$\frac{1}{2}x$

d)

-2x

47.

Solve the absolute value inequality:

|2x + 3| - 4 > 5

a)

x<-6 or x>3

b)

x<3 or x>-6

c)

x<3

d)

x>-6

48.

$\left|\frac{x+7}{10}\right|-15>8$ Solve the absolute value inequality:

a)

x<-237 or x>223

b)

x<223 or x>-237

c)

x<223

d)

x>-237

49.

Change the following equations to vertex form.

$f\left(x\right)\ =\ x^2+14x+48$

a)

$f\left(x\right)\ =\ \left(x+7\right)^2-1$

b)

$f\left(x\right)=\ \left(x+14\right)^2-1$

c)

$f\left(x\right)\ =\ \left(x-7\right)^2+1$

d)

$f\left(x\right)=\ \left(x+14\right)^2+1$

50.

Given the parabola that has a vertex of (2, -4) and another point at (0, -16) and it opens downwards, write the quadratic equation in vertex form.

a)

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

b)

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

c)

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

d)

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

51.

What are the coordinates at the minimum point of $f\left(x\right)\ =\ x^2-4x+3$ ?

a)

(-1, -2)

b)

(-1, 2)

c)

(2, -1)

d)

(2, 1)

52.

Which function represents this graph?

a)

$f\left(x\right)=\ -\frac{1}{4}x^2-2$

b)

$f\left(x\right)=\ \frac{1}{4}x^2-2$

c)

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

d)

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

53.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

54.

a)

x = 5

b)

x = 10

c)

x = -9

d)

x = -5

55.

Solve.

a)

no solution

b)

6

c)

3

d)

4

56.

a)

{ 1 }

b)

{ 1, 9 }

c)

{ 9 }

d)

No Solution

57.

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at least $254 each week to pay your bills. Write a system to represent the situation.

a)

x+y≤254
5x+8y≥41

b)

x+41≤y
5x+8y≥254

c)

x+y≤41
5x+8y≥254

d)

x+y>41
5x+8y<254

58.

-|−2r − 1| = 11

a)

{-6,5}

b)

{5,-6}

c)

-6

d)

No Solution

59.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-3,-1}

c)

{-3}

d)

No Solution

60.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

61.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

62.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

63.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

64.

What does the discriminant tell you?

a)

the solutions

b)

the number of solutions

c)

the kinds of solutions

65.

Why is the equation -1/2x+4y=6 not considered to be standard form?

a)

There can't be fractions

b)

"x" can't be negative

c)

"y" is not by itself

66.

How do you find the vertex of y=2x²-4x+6

a)

b²-4ac

b)

transformations

c)

-b/2a

67.

Factor completely

a)

A

b)

B

c)

C

d)

D

68.

a)

A

b)

B

c)

C

d)

D

69.

a)

A

b)

B

c)

C

d)

D

70.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

2 seconds

c)

6 seconds

d)

9 seconds

71.

Simplify

a)

2x²yz² ⁵√(xy³)

b)

2x²yz⁴ ⁵√(xy³)

c)

2xyz ⁵√(xy³z)

d)

2x²yz⁴ ⁵√(xy³z)

72.

Simplify. You should only have positive exponents.

a)

((4x+1)(x-1)/x

b)

(16(x+1)(x-1))/x

c)

((4x+4)²)/2x

d)

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

73.

Calculate(Divide, multiply by conjugate):

a)

-3/4 − 1/4i

b)

3/4 + 1/4i

c)

-3/4 + 1/4i

d)

3/4 − 1/4i

74.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

75.

a)

-25/3

b)

4

c)

-6

d)

25/3

76.

Solve for x:
$x^2-x\le6$

a)

$\left(-2,3\right)$

b)

$\left[-2,3\right]$

c)

$\left(-\infty,-2\right)\cup\left(3,\ \infty\right)$

d)

$\left(-\infty,-2\right]\cup\left[3,\ \infty\right)$

77.

What movie has the line "Hakuna Matata" in it?

a)

Lilo and Stitch

b)

Toy Story

c)

The Jungle Book

d)

The Lion King

78.

What is the/are the y-intercepts of
f(x)=3x² - 8x + 2

a)

(0, 2)

b)

(0, -2)

c)

(2, 0)

d)

(-2, 0)

79.

Solve the following absolute value inequality:
∣ 2x - 3 ∣ ≤ 5

a)

- 1 < x < 4

b)

-1 ≤ x ≤ 4

c)

x ≤ -1 or x ≥ 4

d)

x < -1 or x ≥ 4

80.

Simplify. You should only have positive exponents.

a)

2(x-1)(x²+x+1)

b)

2/5x

c)

2x(x-1)(x²+x+1)/(x³-1)(5x²)

d)

2(x²+x+1)/5x²

81.

Simplify each expression.

Answers should have only positive exponents

and no rational exponents in the denominator.

a)

4x²y⁴∜(x³)

b)

4y∜(x¹¹)

c)

3xy∜(2x³)

d)

4x²y∜(x³)

82.

Simplify

a)

b)

c)

d)

83.

a)

b)

c)

d)

84.

a)

b)

c)

d)

85.

a)

b)

c)

d)

86.

a)

0

b)

1

c)

d)

87.

What is the simplified form of -2√-24

a)

-4i√6

b)

4i

c)

24i

d)

-8i√3

88.

Rationalize the denominator. Simplify the answer. $\frac{4\ +\sqrt{6}}{\sqrt{2}\ +\sqrt{3}}$

a)

$\sqrt{3}\ -\sqrt{2}$

b)

$2\sqrt{3}\ -\ \sqrt{2}$

c)

$\sqrt{3}+2\sqrt{2}$

d)

$2\sqrt{3}+\sqrt{2}$

89.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

90.

Simplify the expression:

a)

25x²y³

b)

-5xy² ∛5x

c)

5ixy² ∛5x

d)

-125x³y⁶ ∛5x

91.

Multiply and simplify.

a)

2x²∜14

b)

8x³∜7

c)

2x⁸∜112

d)

224x⁸

92.

Simplify this expression.

a)

√18x⁵y

b)

3x²√2xy

c)

√18x³⁶y⁵⁶

d)

3√2x¹³y¹⁵

93.

Simplify $\frac{8n}{n-3}+\frac{3n}{5n-6}$

a)

$\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$

b)

$\frac{11n}{6n-9}$

c)

$\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$

d)

$\frac{8n+3n}{n-3+5n-6}$

94.

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

a)

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

b)

$\frac{x+1}{x\left(x+2\right)}$

c)

$\frac{2x+2}{x\left(x+2\right)}$

d)

$\frac{1}{x}$

95.

$\frac{1}{5n^2}+\frac{2}{5n}=\frac{n+5}{n^2}$ Solve. Check for extraneous solutions.

a)

$n\ =\ 4$

b)

$n\ =\ 8$

c)

$n\ =\ 2$

d)

$n=-8$

96.

Subtract

$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

b)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

d)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

97.

a)

A

b)

B

c)

C

d)

D

98.

A passenger train travels at 80 mph. A freight train travels at 30 mph. If they travel in opposite directions, how long will it be before they are 275 miles apart?

a)

1.5 hours

b)

2 hours

c)

2.5 hours

d)

3 hours

e)

None of these

99.

Bella drove to her cabin on the lake and back. The trip there took five hours and the trip back took three hours. She averaged 14 km/h faster on the return trip than on the outbound trip. Find Bella's average speed on the outbound trip.

a)

35 km/h

b)

21 km/h

c)

10 km/h

d)

25 km/h

100.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

101.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

102.

The perimeter of a rectangle is 30 cm. Its area is 54 cm² . Find the dimensions of this rectangle.

a)

5 cm by 10 cm

b)

6 cm by 9 cm

c)

7 cm by 8 cm

d)

11 cm by 4 cm

103.

One number is 3 more than another. The sum of their squares is 149. Find the numbers.

a)

4 and 7; -4 and -7

b)

5 and 8; -5 and -8

c)

6 and 9; -6 and -9

d)

7 and 10, -7 and -10

104.

Liza can paint the kitchen in 5 hours. David can paint the same kitchen in 3 hours. If they work together, how long will it take to paint the kitchen?

a)

$1\ \frac{5}{8}\ hours$

b)

$1\ \frac{7}{8}\ hours$

c)

$\frac{1}{5}\ hours$

d)

$\frac{8}{15}\ hours$

105.

Working together Sal and Joe paint the house in in 4.95 hours. Alone Sal can do it in 9 hours. How long would it take Joe to paint the house alone?

a)

15 hours

b)

8.5 hours

c)

13.95 hours

d)

11 hours

106.

A plane flies 1225 miles with a tailwind in the same time it can go 1100 miles against the wind. The speed of the plane in still air is 575 miles per hour. Which equation would you use to find the speed of the wind?

a)

$\frac{1225}{575-x}=\frac{1100}{575+x}$

b)

$\frac{1225}{575+x}=\frac{1100}{575-x}$

c)

$\frac{1225}{x+575}=\frac{1100}{x-575}$

d)

$\frac{1225}{x-575}=\frac{1100}{x+575}$

107.

George can build a laptop twice as fast as Kurt. Working together, it takes them 3 hours. Which equation would you use to determine how long it will take Kurt working alone?

a)

$2t+t=3$

b)

$\frac{1}{3}+\frac{1}{6}=\frac{1}{t}$

c)

$\frac{1}{t}+\frac{1}{3}=\frac{1}{2t}$

d)

$\frac{1}{t}+\frac{1}{2t}=\frac{1}{3}$

108.

The time it takes for a canoe to go 4 miles upstream and back 4 miles downstream is 5 hours. The current in the lake is 2 mile per hour. Find the average speed (rate) of the canoe in still water.

a)

$\frac{4}{x+2}+\frac{4}{x-2}=5$

b)

$\frac{4}{2+x}+\frac{4}{2-x}=5$

c)

$\frac{4}{x+2}=\frac{5}{x-2}$

d)

$\frac{4}{2+x}=\frac{5}{2-x}$

109.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

110.

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.

a)

-9, 7

b)

√75

c)

9, -7

d)

15, -5

111.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

a)

4 seconds

b)

-2 seconds

c)

-6 seconds

d)

9 seconds

112.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

Algebra 2 Fall Final Review

Total questions: 112

Worksheet time: 7hrs 35mins

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