Free Printable College Algebra Final Review

1.

In the equation, y = mx + b, the letter b is the ___________.

a)

y-intercept

b)

x-intercept

c)

slope

d)

rate of change

2.

What is the simple definition of slope?

a)

line

b)

run/rise

c)

undefinied

d)

rise/run

3.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

4.

What is the slope of the equation?
y = -3x + 4

a)

-3

b)

3

c)

4

d)

-4

5.

What type of slope does the following graph have?

a)

Postive

b)

Negative

c)

Zero Slope

d)

Undefined

6.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

7.

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

a)

m=4, b=-x

b)

m=-x, b=4

c)

m=1, b=4

d)

m=-1, b=4

8.

How would you write the equation with a slope of 2/3 and a y-intercept of -3

a)

y=3/2x+3

b)

y=2/3-3

c)

y=2/3x-3

9.

Bob has $150 in his savings account and saves $40 per month. Which function models his savings?

a)

y = 150 + 40

b)

y = 40x + 150

c)

y = 150x + 40

10.

Write a rule: A plumber charges $50 for a house call plus $12 per hour for labor.

a)

y = 50 x + 12

b)

y = 50 + 12 x

c)

y = 62 x

d)

x = 50 + 12y

11.

Write a rule : Miles has joined a weight loss program. His weight is 225 lbs and he is losing weight at a rate of 3 lbs per week.

a)

y = 222 x

b)

y = 225 + 3 x

c)

y = 225 - 3x

d)

y=225x - 3

12.

Which is the graph of y=-x+2?

a)

A

b)

B

c)

C

d)

D

13.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2

d)

-2

14.

Which equation represents the graph?

a)

x = 2

b)

y = 2

c)

y = 2x

d)

y = undefined

15.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

16.

Consider the equation $3x^2=-2x^2-8x-5$

Use the quadratic formula to determine the solution(s).

a)

$\frac{-4\pm6i}{5}$

b)

$-\frac{4}{5}\pm\frac{3i\sqrt{3}}{5}$

c)

$-\frac{1}{5},\ -\frac{7}{5}$

d)

$-\frac{4}{5}\pm\frac{i\sqrt{41}}{5}$

e)

$-\frac{4}{5}\pm\frac{3i}{5}$

17.

Consider the following function.
$f\left(x\right)\ =\ x^2+4x+3$
Find the vertex.

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

18.

What is the domain of this function?

a)

Domain: (-∞, ∞)

b)

Domain: (-1, ∞)

c)

Domain: [-1, ∞)

d)

none of the above

19.

Rewrite in exponential form:

log₃(9)=2.

a)

3⁹=2

b)

3²=9

c)

x²=9

d)

3^x=2

20.

Rewrite in logarithmic form:

6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

21.

Rewrite in logarithmic form:

5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

22.

log ₃9 =

a)

1/2

b)

2

c)

1/3

d)

3

23.

log ₂₅ 5 =

a)

1/2

b)

2

c)

1/5

d)

5

24.

Find the domain.

a)

(-∞, 1)

b)

(-∞, ∞)

c)

(-∞, 0)

d)

(1,-∞)

25.

Which equation has a domain of $\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)$ ?

a)

$f\left(x\right)=\frac{x+10}{x-4}$

b)

$f\left(x\right)=\frac{x-6}{x+4}$

c)

$f\left(x\right)=\frac{x+4}{x-6}$

d)

$f\left(x\right)=\frac{x+4}{x+4}$

26.

What is the solution to the system of equations?

a)

No Solution

b)

Infinitely Many Solutions

c)

(7, -2)

d)

(-5, -5)

27.

Solve 6x²-36=0

a)

x=6

b)

x=√6

c)

x=6, x=-6

d)

x=√6, x=-√6

28.

Solve x²-2x-3=0

a)

x=-3, x=-1

b)

x=-3, x=1

c)

x=-1, x=3

d)

x=1, x=3

29.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

30.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

31.

Solve by factoring. (HINT: Factor GCF 1st)

a)

x = 3, x = -6

b)

x = 0, x = 2

c)

x = 2, x = 3

d)

x = -2, x = 1

32.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

33.

Solve by the Extraction of Roots method: -5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

34.

Solve by the Square Root method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

35.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

36.

Simplify:
3√-81

a)

-27

b)

3i√3

c)

27i

d)

9i

37.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

d)

$x=\frac{by}{v}$

38.

Rewrite this formula and solve for the variable h. $A=\frac{bh}{2}$

a)

h = 2A / b

b)

h = A - ½b

c)

h = 2A - b

d)

h = A / b

39.

30% of the 1200 Wilson students are 7th graders. How many Wilson students are 7th graders?

a)

360 students

b)

300 students

c)

800 students

d)

840 students

40.

The start up cost to join eTunes music is $7.95 plus $0.95 per song downloaded. If Will spent $26, write and solve a linear equation to find how many songs he downloaded.

a)

32 songs

b)

33 songs

c)

19 songs

d)

36 songs

41.

Factor:

2n²-8n³

a)

2n²(n-4n²)

b)

-2n²(4n²-1)

c)

2n³(10-8n²)

d)

3n(1-4n)

42.

Factor the Polynomial

x³- x² + 2x - 2

a)

(x² + 2) (x - 1)

b)

(x² - 2) (x + 1)

c)

(x² + 1) (x - 2)

d)

(x² - 1) (x + 2)

43.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

44.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

45.

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)

46.

Factor

3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

47.

Simplify √-4

a)

2i

b)

-2i

c)

2

d)

4i

48.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

49.

Solve by factoring.

2x² - 13x - 70 = 0

a)

7/2, -10

b)

-5/7, -2

c)

-7/2, 10

d)

-7, -10

50.

Find the slope of the line through the pair of points.

(-16, 20) and ( -6, -12)

a)

-16/5

b)

16/5

c)

5/16

d)

-5/16

51.

Write the slope-intercept form equation for the line.

a)

y = -3x - 7

b)

y = -1/3x - 7

c)

y = 3x - 3

d)

y = -3x - 5

52.

Find the slope of the line through the points (18, 5) and (18, -2).

a)

0

b)

undefined

c)

-1/2

d)

1/2

53.

Write the equation of the line through the points (4, -4) and (6, -4).

a)

y = -4x

b)

x = -4

c)

y = -4

d)

x = 6

54.

2x + 3x = ?

a)

x+5

b)

5x

c)

55x

d)

5x5

55.

4s + 8s =

a)

12s

b)

s+12

c)

s

d)

4s

56.

10y + 10x =

a)

20xy

b)

10y + 10x

57.

5a + b - 4a + b

a)

a + 2b

b)

a

c)

9a - 2b

d)

9a + 2b

58.

9x - 3 + x + 15

a)

27x

b)

10x +18

c)

12x + 15x

d)

10x +12

59.

a)

8y+5

b)

3y+3

c)

7y+5

d)

7y+4

60.

Combine like terms
3x + 2x + 11y - 7y

a)

5x + 10y

b)

5x - 4y

c)

5x + 4y

d)

5x -10y

61.

If y = 4, find the value of 3y+5.

a)

27

b)

12

c)

17

d)

18

62.

If a = 4 and b = 6, what is the value of 3a + 5b?

a)

40

b)

42

c)

44

d)

46

63.

If a = 6 and b = 7,find the value of 15-a-b.

a)

2

b)

3

c)

4

d)

5

64.

If a = 6 and b = 7,find the value of 15-a-b.

a)

2

b)

3

c)

4

d)

5

65.

If a = 4, b = 5 and c = 6, find 2c-a-b

a)

4

b)

3

c)

6

d)

5

66.

4 $-$ 3 $+$ 2 + 5 $\cdot$ 3

a)

40

b)

17

c)

24

d)

18

67.

$5^2-10\div2\times4$

a)

4

b)

5

c)

80

d)

160

68.

Identify the vertex and intercepts of the graph of the equation:
f(x) = (x + 3)² − 2

a)

Vertex: (−3, −2); y-intercept: (0, 7); x-intercepts: (−3±√2, 0)

b)

Vertex: (3, 2); y-intercept: (0, 1); x-intercepts: (±3, 0)

c)

Vertex: (2, −3); y-intercept: (0, 4); x-intercepts: (−2±√3, 0)

d)

Vertex: (−3, −2); y-intercept: (0, −2); x-intercepts: (−3, 0), (−7, 0)

69.

Rewrite the following equation in vertex form:
f(x) = 3x² − 12x + 11

a)

f(x) = 3(x − 4)² + 3

b)

f(x) = 3(x − 2)² − 1

c)

f(x) = 3(x − 4)² − 8

d)

I'm not sure. Lately, my dog has been eating my homework.

70.

Find the quadratic function that has the indicated vertex and whose graph passes through the given point.
Vertex: (−4, −2); point: (−3, −5)

a)

f(x) = −3(x − 4)² − 2

b)

f(x) = −(x − 4)² + 2

c)

f(x) = −3(x + 4)² − 2

d)

f(x) = 3(x + 4)² − 2

71.

A manufacturer has daily production costs of
C = 20,000 − 40x + 0.055x²
where C is the total cost in dollars and x is the number of units produced. Graphically estimate the number of units that should be produced to yield a minimum cost.

a)

58

b)

127

c)

364

d)

652

College Algebra Final Review

Total questions: 71

Worksheet time: 18hrs 45mins

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