Free Printable College Algebra Unit 1 Review

1.

What is the equation of this graph?

a)

y=(3/4)x+3

b)

y=(-3/4)x+3

c)

y=(-4/3)x+3

d)

y=(4/3)x+3

2.

What is the equation of this graph?

a)

y=-4x+5

b)

y=5x+4

c)

y=5x-4

d)

y=-4x+1

3.

What does "m" represent in y=mx+b?

a)

y-intercept

b)

slope

c)

macaroni

d)

nothing

4.

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

d)

y=2/3x+3

5.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

6.

Name the x- and y-intercepts for the equation:
2x + y = 6

a)

(0, 3) and (6, 0)

b)

(0, -3) and (-6, 0)

c)

(3, 0) and (0, 6)

d)

(-3, 0) and (0, -6)

7.

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

8.

For the equation
y + 1 = -3(x - 5),
the line contains the point (5, -1) and has a slope of?

a)

-1

b)

1

c)

-3

d)

5

9.

Solve by factoring:

x²+ x - 6 = 0

a)

x= 4 and -1

b)

x= -3 and 2

c)

x= -6 and 1

d)

x= -2 and 3

10.

Solve:
2(a + 4) = 2a - 8 + 4a

a)

3

b)

-3

c)

-4

d)

4

11.

Solve (x+2)²=5

a)

x=-2+√5

b)

x=-2+√5, x=-2-√5

c)

x=√3

d)

x=√3, x=-√3

12.

Write as a single complex number: (3+4i)(2-i)

a)

10+5i

b)

10-5i

c)

2+5i

d)

10+3i

13.

$\frac{1-i}{6+2i}$ Simplify!

a)

1/10 - 1/5 i

b)

1/2 + 1/4 i

c)

1/4 - 1/4 i

d)

1/32 - 1/4 i

14.

Solve for x

a)

5

b)

4/5

c)

1

d)

- 4

15.

Solve for x

a)

6

b)

17/5

c)

19/2

d)

- 6

16.

Solve.

a)

no solution

b)

6

c)

3

d)

4

17.

Solve

a)

-9

b)

-2,3

c)

5

d)

0

18.

a)

a

b)

b

c)

c

d)

d

e)

e

19.

An executive invests $15,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $1090, how much is invested at each rate?

a)

$11,000 in 8%, $4000 in 7%

b)

$266.67 in 8%, $14,733.33 in 8%

c)

$320 in 8%, $770 in 7%

d)

$4000 in 8%, $11,000 in 7%

20.

a)

a

b)

b

c)

c

d)

d

e)

e

21.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

22.

a)

10

b)

-10

c)

10i

d)

-10i

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

b)

c)

d)

26.

a)

b)

c)

d)

27.

a)

9/19

b)

19/9

c)

1/2

d)

2

28.

One crew can seal a parking lot in 14 hours and another in 18 hours. How long will it take to seal the parking lot if the two crews work together?

a)

32 hours

b)

7.875 hours

c)

12 hours

d)

10.5 hours

29.

One morning, Santiago drove 5 hours before stopping to eat lunch at Chic-Fil-A. After lunch, he increased his speed by 10mph. If he completed a 310-mile trip in 9 hours of driving time, how fast did he drive in the morning?

a)

60 mph

b)

33 mph

c)

40 mph

d)

30 mph

30.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

31.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

32.

When you graph an inequality, you used a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

33.

Solve: 5x - 14 = 8x + 4

a)

6

b)

-6

c)

-18/13

d)

10/3

34.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

35.

Solve the equation, if possible.
(3x − 2) ÷ (5x - 1) = 3/4

a)

x=-2/3

b)

x=-3/2

c)

x=-5/3

d)

x=-3/5

36.

Solve by factoring.
6x²=5x+4

a)

(6x - 2)(x + 2) = 0, x = 1/3 or x = -2

b)

(2x - 4)(x + 1) = 0, x = 2 or x = -1

c)

(2x - 1)(3x + 4) = 0, x = 1/2 or x = -4/3

d)

(3x - 4)(2x + 1) = 0, x = 4/3 or x = -1/2

37.

Solve the equation. Use your calculator if necessary.
34x² − 296x +47 = 0

a)

x ≈ -18.244 or x ≈ 2.552

b)

x ≈ 0.752 or x ≈ 9.235

c)

x ≈ 0.162 or x ≈ 8.544

d)

x ≈ -11.587 or x ≈ 2.337

38.

Solve the equation using factoring.
x⁴ − 5x² + 4 = 0

a)

x = 0, 1, 4, 5

b)

x = 0, ±1, 2

c)

x = ±1, ±2

d)

x = ±2, ±4

39.

Solve the inequality.
3(x − 1) < 2x + 8

a)

x < 11

b)

x ≥ 11

c)

x < 4

d)

x > -4

40.

Solve the inequality.
∣x + 10∣ + 3 < 5

a)

-12 < x < -8

b)

x < -8 or x > 8

c)

x < -12 or x > 8

d)

x < 8

41.

Solve 6x²-36=0

a)

x=6

b)

x=√6

c)

x=6, x=-6

d)

x=√6, x=-√6

42.

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

43.

Solve |4y-3|=5

a)

y=2

b)

y=2, y=-2

c)

y=-1/2

d)

y=2, y=-1/2

44.

What value do you need to add to both sides of the equation x²+4x=1 to complete the square?

a)

4

b)

2

c)

-4

d)

-2

45.

Solve |x+3|≤4

a)

[-7,1]

b)

(-∞,-7]∪[1,∞)

c)

(-∞,1]

d)

[1,∞)

46.

Solve |x+5|>2

a)

(-7,-3)

b)

(-∞,-7)∪(-3,∞)

c)

(-∞,-3)

d)

(-3,∞)

47.

Write as a single complex number: (1-i)÷(6+2i)

a)

1/10 - 1/5 i

b)

1/2 + 1/4 i

c)

1/4 - 1/4 i

d)

1/32 - 1/4 i

48.

The hypotenuse of a right triangle is 50 ft. One leg is 10 ft longer than the other. What are the lengths of the legs?

a)

30 ft and 40 ft

b)

20 ft and 30 ft

c)

-40 ft and -30 ft

d)

20√5 ft and 10+20√5 ft

49.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

50.

Given the rational expression, which of the following values of x are excluded values?

I. x = -1

II. x = -3/2

III. x = 5

a)

I and II only

b)

II only

c)

II and III only

d)

I, II and III

e)

III only

51.

Solve the equation.

a)

x = 2

b)

x = 4

c)

x = 8

d)

No solution

52.

If the solutions to this given equation are a and b,

find |a - b|.

a)

3

b)

9

c)

12

d)

15

53.

Suppose the quadratic equation 3x²- 7x + 8 = 0 was solved by completing the square. What constant would be added to both sides of the equation to create a perfect square?

a)

7/6

b)

49/9

c)

49/36

d)

49/4

54.

Solve the equation (3x - 2)²+9 = 0

a)

2/3 ± i

b)

2/3 ± 3i

c)

2 ± 3i

d)

2/3 ± 3i/2

55.

Simplify the complex expression: (3 - 2i)² - 3i(-1 - 3i).

a)

-4 + 9i

b)

22 - 9i

c)

4 + 9i

d)

-4 - 9i

56.

For a particular quadratic equation in the form ax²+ bx + c, the value of b²- 4ac = 20. Which of the following statements is correct about the roots of the function?

a)

There will be two imaginary roots.

b)

There will be two rational roots.

c)

There will be two irrational roots.

d)

There will be one rational root.

e)

No conclusion can be made about the roots without specifically knowing the values of a, b and c.

57.

Which of the following statements correctly describes the roots of the quadratic equation (3x - 1)(4x + 1) = 0?

a)

There will be two imaginary roots.

b)

There will be two rational roots.

c)

There will be two irrational roots.

d)

There will be one rational root.

58.

Solve the equation by using the quadratic formula:

x² + 3x + 5 = 0

a)

-3/2 ± i√(11)

b)

3/2 ± i√(11)/2

c)

-3 ± i√(11)/2

d)

-3/2 ± i√(11)/2

59.

Which of the following quadratics is/are factored correctly and completely?

I. x² - 5x + 6 = (x - 3)(x - 2)

II. -2x² + 50 = -2(x - 5)(x + 5)

III. 6x² + 7x - 3 = (3x - 1)(2x + 3)

a)

I, II and III

b)

I and III

c)

II and III

d)

I and II

60.

a)

a

b)

b

c)

c

d)

d

61.

a)

a

b)

b

c)

c

d)

d

62.

a)

a

b)

b

c)

c

d)

d

63.

a)

a

b)

b

c)

c

d)

d

64.

a)

a

b)

b

c)

c

d)

d

65.

a)

a

b)

b

c)

c

d)

d

66.

a)

a

b)

b

c)

c

d)

d

67.

a)

a

b)

b

c)

c

d)

d

68.

Use substitution to solve:

a)

a

b)

b

c)

c

d)

d

69.

Use substitution to solve:

a)

a

b)

b

c)

c

d)

d

70.

What is the x-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(0, 3)

d)

(3, 0)

71.

What is the y-intercept?

a)

(0, 5)

b)

(5, 0)

c)

(0, 3)

d)

(3, 0)

72.

What are the x-intercepts?

a)

(0, -2), (0, -10)

b)

(-2, 0), (-10, 0)

c)

(2, 0), (-10, 0)

d)

(0, 2), (0, -10)

73.

√20

a)

2√5

b)

4√5

c)

5√2

d)

3√6

74.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

75.

Solve the literal equation for the given variable.

a)

2A/h

b)

2/(h)

c)

2Ah

d)

Ah/2

76.

E = mc² solve for m

a)

m = sqrt(E/c)

b)

m = sqrt(E)/c

c)

m = E/c²

d)

m = money

77.

Factor
k²+7k+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

78.

Factor:
x² + 7x + 6

a)

(x + 6) (x + 1)

b)

(x + 3) (x + 2)

c)

(x + 4) ( x + 3)

d)

(x - 6) ( x -1)

79.

Multiply:
(x - 1)(x - 8)

a)

x² + 9x + 8

b)

x²+ 9x - 8

c)

x² - 9x - 8

d)

x² - 9x + 8

80.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

81.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

82.

a)

a

b)

b

c)

c

d)

d

83.

a)

a

b)

b

c)

c

d)

d

84.

a)

a

b)

b

c)

c

d)

d

85.

a)

a

b)

b

c)

c

d)

d

86.

a)

a

b)

b

c)

c

d)

d

87.

Solve (looks like a good problem to use substitution)

a)

a

b)

b

c)

c

d)

d

88.

a)

a

b)

b

c)

c

d)

d

89.

a)

a

b)

b

c)

c

d)

d

90.

Change the following equation to standard form
x²+y²-4x+12y-8=0

a)

(x+2)²+(y-6)²=48

b)

(x-2)²+(y+6)²=48

c)

(x-6)²+(y-2)²=48

d)

(x+2)²+(y-6)²=48

91.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

92.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

93.

What is the equation of a circle with radius 2 and center (3, 4)?

a)

(x+3)² + (y+4)² = 2

b)

(x-3)² + (y-4)² = 2

c)

(x+3)² + (y+4)² = 4

d)

(x-3)² + (y-4)² = 4

94.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

95.

Write the equation of the circle with a radius of 3 and a center of (4, 2).

a)

( x - 4)² + (y - 2)² = 3

b)

( x - 2)² + (y - 2)² = 3²

c)

( x - 4)² + (y - 2)² = 3²

d)

( x + 4)² + (y + 2)² = 3²

96.

Simplify:

a)

A

b)

B

c)

C

d)

D

97.

Simplify

a)

A

b)

B

c)

C

d)

D

98.

Simplify:

a)

A

b)

B

c)

C

d)

D

99.

Simplify:

a)

A

b)

B

c)

C

d)

D

100.

What is (12x³y⁵z⁷)/ (144x^-4 y⁷z^-3)

a)

12(x⁷z¹⁰)

b)

(x⁷z¹⁰)/12y²

c)

1

d)

(x⁷y^-2z¹⁰)/12

College Algebra Unit 1 Review

Total questions: 100

Worksheet time: 8hrs 20mins

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