Elementary Algebra problems you can use for practice. Remember, you may not use a calculatorwhen you take the assessment test. Use these problems to help you get up to speed._____________________________________________________________________________________

Perform the indicated operation. Write in lowest terms ifnecessary.

1) 45

- -14

A) -920 B) 9

100

C) 2120 D) -

2120

2) 157

·16

A) 2 142 B) 1 5

14

C) 514 D) 3

14

3) 26 ÷ -133

A) -7 B) -6 C) 6 D) -5

4) 19 - (-19) + 14 + (-14)

A) -28 B) 28

C) 38 D) -10

5) -18.4 + 13.1

A) 5.3 B) 31.5

C) -31.5 D) -5.3

6) (-1)(-3)(-7)

A) -11 B) -42

C) -21 D) 21

7) 87 ÷ 0

A) 0 B) 1

C) 87 D) undefined

8) -86 divided by - 2

A) 2 B) -43

C) 43 D) -2

Evaluate the expression.

9) 8 · 5 - 5(4)3 ÷ (-8)

A) 80 B) 1040

C) 35 D) -280

10) Evaluate (x - 4y)3 for x = -5 and y = 6.

A) -87 B) 17,576

C) -24,389 D) -6859

Simplify the algebraic expression.

11) 4(9a + 10b) - (10a - 7b)

A) 26a + 33b B) 26a + 47b

C) 26a + 17b D) 46a + 47b

Solve the inequality and express the solution set ininterval notation. Graph the solution set on the realnumber line. NOTE: A square bracket, i.e. [, is the sameas a filled in circle. A curved bracket, i.e. (, is the same asan open circle.

12) 42x + 54 > 6(6x + 5)

A) (-4, )

B) (- , -4]

C) (- , -4)

D) [-4, )

13) -4(3x + 10) -16x - 32

A) (2, )

B) [2, )

C) (- , 2]

D) (- , 2)

Solve the problem.

14) After a 17% price reduction, a boat sold for $21,580. What was the boat's price before thereduction? (Round to the nearest cent, ifnecessary.)

A) $126,941.18 B) $25,248.60

C) $3668.60 D) $26,000

15) A 12-ft. board is cut into 2 pieces so that onepiece is 8 feet longer than 3 times the shorterpiece. If the shorter piece is x feet long, find thelengths of both pieces.

A) shorter piece: 1 ft.; longer piece: 11 ft.

B) shorter piece: 24 ft; longer piece: 44 ft.

C) shorter piece: 6 ft; longer piece: 36 ft.

D) shorter piece: 28 ft; longer piece: 36 ft.

16) A rectangular carpet has a perimeter of 264inches. The length of the carpet is 96 inchesmore than the width. What are the dimensionsof the carpet?

A) 114 by 18 inches

B) 123 by 132 inches

C) 75 by 93 inches

D) 114 by 132 inches

17) 40.3 is 155% of a number. Find the number.

A) 6246.5 B) 0.26

C) 26 D) 62.465

Solve the equation. Check your solution.

18) 6x + 1.6 = -33.2

A) {-4.8} B) {-7.2}

C) {-5} D) {-5.8}

19) 34

-13

x =1912

A) -52 B) 5

2

C) 103 D) -

103

20) 7(9p + 2) = 8p

A) 74 B) 14

55

C) -1455 D) 55

14

21) 45

t =67

A) -1514 B) 14

15

C) 307 D) 15

14

22) x - 19 = 12

A) {-31} B) {7}

C) {31} D) {-7}

Evaluate the expression for the given value of the variable.

23) z2 - 4z - 5 for z = -4

A) 37 B) 27 C) -5 D) 5

Combine.

24) (4x3 + 10x2 + 11) - (9x3 - 7x + 6)

A) -5x3 + 10x2 - 7x + 5

B) -5x3 + 10x2 + 7x + 5

C) -5x3 + 10x2 + 7x + 17

D) -5x3 + 17x2 + 5

Multiply.

25) 11x5(12x3 + 2x2 + 3)

A) 132x8 + 2x2 + 3

B) 132x8 + 22x7

C) 132x3 + 22x2 + 33

D) 132x8 + 22x7 + 33x5

Find the product.

26) (5x - 8)2

A) 5x2 - 80x + 64 B) 5x2 + 64

C) 25x2 - 80x + 64 D) 25x2 + 64

Multiply.

27) (4y + x)(4y - x)

A) 16y2 + 8xy - x2 B) 16y2 - 8xy - x2

C) 16y2 - x2 D) 8y2 - x2

Perform the division.

28) 35x2 + 30x - 115x

A) 7x - 5 B) 7x + 6 -115x

C) 35x + 30 -115x D) 7x2 + 6x -

115

Simplify the expression. All exponents should be positiveintegers.

29) (8x2y3)-1 · (2x2y)3

A) 1x0 B) 2x0

C) 2x4 D) 1x4

Perform the indicated computation. Write the answer inscientific notation.

30) (6.9 × 109)(2 × 10-1)

A) 1.38 × 108 B) 1.38 × 109

C) 1.38 × 107 D) 13.8 × 108

Perform the indicated computations. Write the answer inscientific notation.

31) 7 × 10 -7

14 × 103

A) -1.2 B) 1.4 x 103

C) 3.5 x 104 D) 5.0 x 10-11

Factor the polynomial completely. If the polynomialcannot be factored, say it is prime.

32) x4 - 81

A) (x2 - 9)2

B) (x2 + 9)2

C) (x2 + 9)(x + 3)(x - 3)

D) prime

33) xy + 10x - 6y - 60

A) (x + 10)(y - 6) B) (y - 10)(x + 6)

C) (x - 10)(y + 6) D) (y + 10)(x - 6)

34) x2 + 4x - 45

A) (x - 9)(x + 1) B) (x - 9)(x - 5)

C) (x + 9)(x - 5) D) prime

35) 4 - m2

A) (2 - m)(2 + m) B) (2 - m)2

C) (2 + m)2 D) prime

36) 25x2 + 64

A) (5x - 8)2 B) prime

C) (5x + 8)(5x - 8) D) (5x + 8)2

37) 15(a + 12) - y(a + 12)

A) (a - 12)(y - 15) B) (a + 12)(15 - y)

C) (a + 12)(15 + y) D) prime

38) 5x2y - 10xy - 400y

A) 5y(x - 10)(x + 8)

B) 5y(x - 10)(x - 8)

C) y(5x - 50)(x + 8)

D) 5y(x + 10)(x - 8)

39) x2 - x - 63

A) (x - 7)(x + 9) B) (x + 7)(x - 9)

C) (x - 63)(x + 1) D) prime

40) 8x2 + 18x + 9

A) (8x + 3)(x + 3) B) (2x + 3)(4x + 3)

C) (2x - 3)(4x - 3) D) prime

41) 10m - 25mn + 10n

A) 5(2m - 5mn + 2n)

B) 5(-3m + 2n)

C) 5(2m + 5mn - 2n)

D) prime

Evaluate the expression for the given values.

42) 4m - 2n28p

when m = 2, n = -4, and p = -1

A) 1 B) 5 C) 3 D) 4

Simplify the rational expression.

43) m2 - 5m - 5040 - 4m

A) -m + 5

4 B) m - 5536

C) m2 - 5536

D) m + 54

Perform the indicated operation. Simplify if possible.

44)

21x4

7x3

9x2

28x5

A) 3x428

B) 28x43

C) 28x83

D) 189x2196

45) 3y - 245y + 40

·3y + 245y - 40

A) 0 B) 15

C) 35 D) 9

25

46) x2x + 6

+6x

x + 6

A) 1x B) x

2 C) x D) 2

47) x2

x2 - 64-

10x - 16x2 - 64

A) 0 B) x + 8x - 2

C) x - 2x + 8 D) undefined

48) 4s - t

+12

t - s

A) -8s - t B) 0

C) -16s - t D) 8

s - t

49) 3x

+6

x - 7

A) 3(3x - 7)x(x - 7) B) 3(3x + 7)

x(x - 7)

C) 9x(x - 7) D) 9

2x - 7

Simplify the complex rational expression.

50)

14

-1x2

12

+1x

A) x - 22x B) x + 2

2x

C) 2xx + 2 D) 2x

x - 2

Solve the equation.

51) 1 +1x

=20x2

A) 5, -4 B) -5, 4

C) 5, 4 D) -15

, 14

Solve the rational equation. Check your answer.

52) 7x + 21

+3

x - 7=

3x + 21x2 + 14x - 147

A) {1} B) { }

C) {0} D) {-1}

Solve the equation for the indicated variable.

53) 1a

+1b

=1c

for b

A) b =a - c

ac B) b =ac

a - c

C) b =a + c

ac D) b =ac

a + c

Solve the proportion.

54) 5x + 2

=4

x - 4

A) {-6} B) {6}

C) {28} D) {-28}

Given that the pair of triangles is similar, find the missinglength.

55)12

8

16

A) x = 16 B) x = 30

C) x = 23 D) x = 24

Solve.

56) If 5 apples cost $2.50, how much would 20apples cost?

A) $0.03 B) $40.00

C) $0.50 D) $10.00

Solve the problem.

57) Determine whether the ordered pair (-4, 3)satisfies the equation 4x - 6y = -34.

A) Yes B) No

58) If m varies directly as p, and m = 15 when p =

3, find m when p is 9.

A) m = 3 B) m = 81

C) m = 25 D) m = 45

Solve the equation.

59) 5x2 = 4x + 9

A) 59

, 0 B) 59

, -1

C) 95

, -1 D) 59

, 1

60) 8x3 + 64x2 + 120x = 0

A) {0, 5, 3} B) {-5, -3}

C) {0, -5, -3} D) -15

, -3

Simplify the square root. Assume all variables representpositive real numbers.

61) -2 75

A) -10 3 B) 3 10

C) -3 10 D) 10 3

62) 150x2y

A) 5xy2 6 B) 5x2 6y

C) 5xy 6 D) 5x 6y

63) 150x116x

A) 5x10 B) 5x5 6

C) 5x5 D) 5 x11

Simplify the expression. If necessary, express the resultthat is not a rational number as a decimal rounded to twodecimal places.

64) 42 - 4(3)(-15)

A) 53

B) 15

C) 14

D) not a real number

Perform the indicated operation and simplify. Assume allvariables represent positive real numbers.

65) 6 · 42

A) 6 B) 42

C) 6 7 D) 252

Graph the inequality.

66) y 3x + 4

A)

B)

C)

D)

Perform the indicated operation and simplify. Assume allvariables represent positive real numbers.

67) 6 2(3 6 - 7)

A) 18 12 - 42 2 B) 36 3 - 42 2

C) 36 3 - 7 D) 18 12 - 7

68) (8 11 + 8)2

A) 768 - 128 11 B) 768 + 128 11

C) 712 + 128 11 D) 640 + 128 11

69) 2750x9

10x7

A) x 275 B) 5x 11

C) 5x 110 D) 5x8 11

70) (5 7 + 4)(8 7 + 5)

A) 85 7

B) 20 + 40 72 + 25 7

C) 60 7 + 25

D) 300 + 57 7

71) 49 + 987

A) 7 - 2 B) 7 + 2

C) 49 + 2 D) 7 + 7 2

Solve the system of equations.

72)

y = -x2

y =x2

- 18

A) (-9, 18) B) (18, 9)

C) (2, 1) D) (18, -9)

Rationalize the denominator.

73) 1090

A) 103

B) 3

C) 13 D) 3 10

74) 45 + 2

A) 4 5 + 8 B) 4 5 + 810

C) 4 5 - 8 D) 4 5 - 2

Simplify the expression.

75)3

320x7

A) x2 34x B) 4

35x7

C) 4x2 35x D) 4x2 3

5

Simplify the square root, if possible.

76) 16-3/2

A) -64 B) -14

C) 164 D) 4

Solve the system of equations.

77) x - 4y = -244x + 16y = 0

A) (3, -12)

B) (-12, 3)

C) infinitely many solutions

D) no solution

Find the length of the unknown side of the right trianglewith sides a, b, and c, where c is the hypotenuse.

78) Two legs of a right triangle measure 14 inchesand 10 inches. Find the exact length of thehypotenuse and then find the decimalapproximation to the nearest tenth of an inch.

A) 2 74 17.2 in B) 2 35 11.8 in

C) 148 in D) 48 in

Solve.

79) 2x2 - 8 = 24

A) {-4, 4} B) {-8, 8}

C) {4} D) {-4}

80) x2 - 14x + 45 = 0

A) {9, 5} B) { 2, -1}

C) {40, 5} D) {-9, -5}

81) x2 + 18x + 59 = 0

A) {-18 + 59, -18 - 59}

B) {9 + 59, 9 - 59}

C) {-9 + 22, -9 - 22}

D) {9 + 22, 9 - 22}

Solve the quadratic equation by any method.

82) (x - 4)(x + 3) = 8

A) {-5, 4} B) {-4, 5}

C) {5} D) {-4}

Graph the solution set of the system of linear inequalities.

83)

-3x + y -3

y < -34

x

A)

B)

C)

D)

Solve the quadratic equation by any method.

84) 9p = 18 +6p

A) {1 - 15, 1 + 15}

B) 3 - 153

, 3 + 153

C) {1 - 5, 1 + 5}

D) -3 - 153

, -3 + 153

85) 12

y2 =14

+12

y

A) 1 - 32

, 1 + 32

B) 1 - 52

, 1 + 52

C) -1 - 32

, -1 + 32

D) no real solution

Solve the problem.

86) The sum of three consecutive integers is 387.Find the numbers.

A) 127, 128, 129 B) 129, 130, 131

C) 128, 129, 130 D) 127, 129, 131

87) Twice the sum of a number and -34 equals 12.Find the number.

A) 40 B) -11

C) -28 D) 23

88) The length of a rectangular room is 7 feetlonger than twice the width. If the room'sperimeter is 170 feet, what are the room'sdimensions?

A) Width = 26 ft; length = 59 ft

B) Width = 31 ft; length = 69 ft

C) Width = 52 ft; length = 118 ft

D) Width = 39 ft; length = 46 ft

89) The perimeter of a triangle is 48 centimeters.Find the lengths of its sides, if the longest sideis 8 centimeters longer than the shorter side,and the remaining side is 4 centimeters longerthan the shorter side.

A) 12 cm, 8 cm, 20 cm

B) 12 cm, 8 cm, 24 cm

C) 4 cm, 8 cm, 12 cm

D) 8 cm, 20 cm, 24 cm

Find the length of the unknown side of the right trianglewith sides a, b, and c, where c is the hypotenuse.

90) Two legs of a right triangle measure 35 inchesand 14 inches. Find the exact length of thehypotenuse and then find the decimalapproximation to the nearest tenth of an inch.

A) 7 29 37.7 in B) 147 in

C) 203 in D) 7 10 22.1 in