Free Printable College-Prep Math Final Exam Review

1.

Which graph represents 2x + 4y = 12?

a)

b)

c)

d)

2.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=(-1/3)x-1

d)

y= -3x-3

3.

On Ryan’s last social studies test, there were two types of questions: true/false worth 2 points each and multiple choice questions worth 4 points each. If Ryan earned 86 points on the test and answered 18 multiple choice questions correctly, how many true/false questions did he answer correctly?

a)

8

b)

6

c)

12

d)

7

4.

For commission as a realtor, Michelle earns $349 plus 3% of the purchase price for each home she helps buy or sell. If she earned $8,965 in commission on a certain home, find its purchase price.

a)

$2,872,000

b)

$28,720

c)

$287,200

d)

There is not enough information to answer this question

5.

Write the equation in slope-intercept form for a graph that passes through (-7, -3) and (5, 6)

a)

$y\ =\ \frac{3}{4}x+\frac{9}{4}$

b)

$y\ =\ 4x+6$

c)

$y\ =\ -\frac{3}{4}x\ +2$

d)

$y\ =\ -4x+\frac{9}{4}$

6.

Write the equation in slope-intercept form for a graph that passes through (-8, 3) with a slope of -2

a)

$y\ =\ -2x+13$

b)

$y\ =\ -2x-19$

c)

$y\ =\ -2x-13$

d)

$y\ =\ -2x+19$

7.

Find the x-intercept of: $y\ =\ -5x-3$

a)

$\left(-\frac{3}{5},\ 0\right)$

b)

$\left(\frac{3}{5},\ 0\right)$

c)

$\left(\frac{12}{5},\ 0\ \right)$

d)

$\left(-3,\ 0\right)$

8.

Find the y-intercept for:

$4y=10x-24$

a)

$(0,\ -6)$

b)

$(0,\ 6)$

c)

$\left(\frac{12}{5},\ 0\right)$

d)

$\left(0,\ -\frac{12}{5}\right)$

9.

Write an equation that is perpendicular to:

y = -3x + 4

a)

$y\ =\ 3x+4$

b)

$y=-\frac{1}{3}x+4$

c)

$y\ =\ \frac{1}{3}x-5$

d)

$y\ =\ -\frac{1}{3}x-7$

10.

Which equation is parallel to this line?

$9x+6y=−6$

a)

$y\ =\ -\frac{2}{3}x-4$

b)

$y\ =\ -\frac{3}{2}x+6$

c)

$y\ =\ \frac{3}{2}x+4$

d)

$y=-\frac{2}{3}x+2$

11.

Write the equation in slope-intercept form

$12x=4y−28$

a)

$12x+3y=-7$

b)

$y=-3x+7$

c)

$y=3x+7$

d)

$12x-4y=-28$

12.

Write the equation in standard form:

$\frac{5}{8}x+\frac{3}{4}y=-1$

a)

$5x+6y=-8$

b)

$5x+3y=-8$

c)

$5x+3y=-32$

d)

It is already in standard form

13.

Use $f(x)=-4x+1$ , $g(x)=x^2-8x+21$ , and $h(x)=|9-3x|$

If $h(x)=39$ , find x

a)

No Solution

b)

x = 16

c)

x = -10

d)

x = -10 & 16

14.

Use $f(x)=-4x+1$ , $g(x)=x^2-8x+21$ , and $h(x)=|9-3x|$

Find $g(-5)$

a)

-44

b)

86

c)

36

d)

6

15.

Which situation can be represented by the inequality
15 + 6x ≤ 100?

a)

Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

b)

Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

c)

Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

d)

Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

16.

Solve the system of inequalities by graphing.

$x-2y\le-4$

$2x+y\ge-3$

a)

b)

c)

d)

17.

On Friday, 3247 people attended the county fair. The entrance fee was $5 for adults and $3 for children 12 or under. The fair collected a total of $14,273. How many adults and how many childern attended the fair?

a)

870 Adults

2027 Children

b)

2266 Adults

981 Children

c)

2027 Adults

870 Children

d)

981 Adults

2266 Children

18.

Solve:
3 | 2x + 7| - 7 < -4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

19.

Solve:
$3x+2<-4\ or\ 4x+4>24$

a)

x < -2 or x > 5

b)

x < 2 or x > 5

c)

x < -2 and x > 5

d)

x < 2 and x > 5

20.

Solve by graphing:

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

21.

Solve by graphing

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

22.

Solve by graphing:

$y=2x^2-16x+33$

23.

Solve
x² + 9x + 20 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

24.

Simplify:
√45

a)

9√5

b)

3√5

c)

5√9

d)

3√15

25.

$\sqrt{18}$

a)

3 $\sqrt{2}$

b)

$2\sqrt{3}$

c)

5 $\sqrt{5}$

26.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Prime

27.

Factor 4x²-9

a)

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

b)

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

c)

2x-3

d)

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

28.

Factor completely: 16x²-24x+9

a)

(16x-3)(x-3)

b)

(16x+9)(x+1)

c)

(4x-3)(4x-3)

d)

(4x+3)(4x+3)

29.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

30.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

31.

Factor completely: x²-13x+40

a)

(x-5)(x-8)

b)

(x+5)(x+8)

c)

(x-4)(x-10)

d)

(x-2)(x-20)

32.

A rectangle has an area of 4x²+19x + 12 and a length of (x + 4). What is the width?

a)

4x - 3

b)

4x + 3

c)

2x + 6

d)

2x + 3

33.

Find the vertex y = (x - 5)(x - 1)

a)

(5, 1)

b)

(-5, - 1)

c)

(3, -4)

d)

(-3, 32)

34.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

35.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

36.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

37.

What is a, b, and c in 3x² + 4 = 5x?

a)

a = 3, b = -5, c = 4

b)

a = 3, b = 5, c = 4

c)

a = 3, b = 5, c = -4

d)

a = 3, b = -5, c = -4

38.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

39.

Solve:
3 | 2x + 7| - 7 < -4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

40.

Solve for p
$A\ =\ \frac{1}{2}pa$

a)

$A-\frac{1}{2}a\ =\ p$

b)

$\frac{2A}{a}=p$

c)

$\frac{A}{2a}=p$

d)

$2A-a\ =\ p$

41.

Solve for p
$SA\ =hp\ +\ 2B$

a)

$\frac{SA-2B}{h}=p$

b)

$\frac{SA}{h}-2B=p$

c)

$\frac{SA-h}{2B}=p$

d)

$SA-2B-h=p$

42.

Simplify

$2\sqrt[]{-147}$

a)

$14i\sqrt[]{3}$

b)

$14\sqrt[]{3}$

c)

$-14\sqrt[]{3}$

d)

$-14i\sqrt[]{3}$

43.

Simplify

$(21+9i)-(13-2i)$

a)

$112i+46$

b)

$11i+8$

c)

$57i+8$

d)

$34+11i$

44.

Simplify

$(1+5i)(4-2i)$

a)

$-6-18i$

b)

$5-7i$

c)

$14+18i$

d)

$5+3i$

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

A

b)

B

c)

C

d)

D

47.

Solve by using the quadratic formula

$4x^2+32x-36=0$

a)

$x=4,\ 8$

b)

$x=-9,\ 16$

c)

$x=14,\ 9$

d)

$x=-9,\ 1$

48.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

49.

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

50.

(f - g)(x)

a)

5x² + 3x

b)

-3x² - 13x

c)

3x² + 3x

d)

-3x² + 3x

51.

(f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

52.

Find g(5)

a)

3375

b)

375

c)

25

d)

45

53.

g[h(-2)]

a)

30

b)

624

c)

13

d)

286

54.

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

55.

Simplify

$\left(12x^2-20x+3\right)\div\left(2x-3\right)$

a)

$8x-4$

b)

$6x-1$

c)

$3x+1$

d)

$x+6$

56.

Simplify

$\left(n^2-9n+17\right)\div\left(n-2\right)$

a)

$n-7+\frac{3}{n-2}$

b)

$n-3+\frac{1}{n-2}$

c)

$n-7+\frac{3}{n+2}$

d)

$n-6+\frac{1}{n-2}$

57.

a)

A

b)

B

c)

C

d)

D

58.

a)

A

b)

B

c)

C

d)

D

59.

Rewrite the following as a radical. Simplify if possible.

a)

A

b)

B

c)

C

d)

D

60.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

61.

Simplify:

a)

2

b)

4

c)

8

d)

16

62.

Simplify: 64 ^-2/3

a)

16

b)

-16

c)

1/16

d)

1/512

e)

-512

63.

a)

11√5

b)

11√10

c)

5√5

d)

12√10

64.

Simplify
-2√2 - 3√8 - √5

a)

-8√2-√5

b)

-8√2-√9

c)

-14√3-√7

d)

-2√4-√3

65.

Simplify
3√2 - 3√18

a)

-4√8

b)

4√9-6√3

c)

5√12

d)

-6√2

66.

a)

A

b)

B

c)

C

d)

D

67.

Solve.

a)

-1/2

b)

2

c)

7

d)

no solution

68.

Solve.

a)

-2/3

b)

-2

c)

2

d)

no solution

69.

Solve.

a)

x = -7

b)

x = 7

c)

x = -11

d)

no solution

70.

$\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}$

a)

$\frac{2}{m-64m^2}$

b)

$\frac{16m^2}{8m^2\left(m-8\right)}$

c)

$\frac{2}{64m^4\left(m-8\right)}$

d)

$\frac{2}{m-8}$

71.

$\frac{2a-20}{6a}\times\frac{a-9}{a-10}$ Simplify

a)

$\frac{2a^2-180}{6a^2-60a}$

b)

$\frac{2\left(a-9\right)}{6a}$

c)

$\frac{a-9}{3a}$

d)

$\frac{3a-29}{7a-10}$

72.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

73.

Add

$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$

a)

$\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}$

b)

$\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}$

c)

$\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}$

d)

An $\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}$ swer 4

74.

Subtract

$\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}$

a)

$\frac{-2x-10}{3x+4}\ ,\ -\frac{4}{3}$

b)

$\frac{-2x}{3x+4}\ ,\ x\ne-\frac{4}{3}$

c)

$-2x\ ,\ x\ne0$

d)

$-2x-10\ ,\ x\ne0$

75.

Subtract

$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$

a)

$\frac{x^2-2x-8}{2x+7}\ ,\ x\ne-\frac{7}{2}$

b)

$x^2-2x-8\ ,\ x\ne0$

c)

$x^2-2x+2\ ,\ x\ne0$

d)

$\frac{x^2-2x+2}{2x+7}\ ,\ \ x\ne-\frac{7}{2}$

76.

$\frac{\frac{2x}{x+1}}{\frac{3}{x+1}}$

a)

$\frac{2x\left(x+1\right)}{3}$

b)

$\frac{2x}{3}$

c)

$\frac{3}{2x}$

d)

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

College-Prep Math Final Exam Review

Total questions: 76

Worksheet time: 6hrs 20mins

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