Elementary Algebra problems you can use for practice ...

[Pages:9]Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. _____________________________________________________________________________________

Perform the indicated operation. Write in lowest terms if

necessary.

1)

4 5

-

-

1 4

A)

-

9 20

B)

9 100

C)

21 20

D)

-

21 20

2)

15 7

?

1 6

A)

2

1 42

C)

5 14

B)

1

5 14

D)

3 14

3)

26 ?

-

13 3

A) -7

B) -6

C) 6

D) -5

4) 19 - (-19) + 14 + (-14) A) -28 C) 38

B) 28 D) -10

Evaluate the expression. 9) 8 ? 5 - 5(4)3 ? (-8) A) 80 C) 35

B) 1040 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 C) 26a + 17b

B) 26a + 47b D) 46a + 47b

Solve the inequality and express the solution set in interval notation. Graph the solution set on the real number line. NOTE: A square bracket, i.e. [, is the same as a filled in circle. A curved bracket, i.e. (, is the same as an open circle.

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

A) (-4, Q)

5) -18.4 + 13.1 A) 5.3 C) -31.5

B) 31.5 D) -5.3

B) (-Q, -4]

6) (-1)(-3)(-7) A) -11 C) -21

7) 87 ? 0 A) 0 C) 87

B) -42 D) 21

B) 1 D) undefined

C) (-Q, -4) D) [-4, Q)

8) -86 divided by - 2 A) 2 C) 43

B) -43 D) -2

13) -4(3x + 10) L -16x - 32 A) (2, Q) B) [2, Q) C) (-Q, 2] D) (-Q, 2)

Solve the problem.

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

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 one piece is 8 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths 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 264 inches. The length of the carpet is 96 inches more than the width. What are the dimensions of 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)

3 4

-

1 3

x

=

19 12

A)

5 -2

C)

10 3

B)

5 2

D)

10 -3

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

A)

7 4

C)

14 - 55

21)

4 5

t

=

6 7

A)

15 - 14

C)

30 7

B)

14 55

D)

55 14

B)

14 15

D)

15 14

22) x - 19 = 12 A) {-31} C) {31}

B) {7} 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 C) 25x2 - 80x + 64

B) 5x2 + 64 D) 25x2 + 64

Multiply. 27) (4y + x)(4y - x) A) 16y2 + 8xy - x2 C) 16y2 - x2

B) 16y2 - 8xy - x2 D) 8y2 - x2

Perform the division.

28)

35x2 + 30x - 11 5x

A) 7x - 5

C)

35x

+

30

-

11 5x

B)

7x

+

6

-

11 5x

D)

7x2

+

6x

-

11 5

Simplify the expression. All exponents should be positive integers.

29) (8x2y3)-1 ? (2x2y)3

A) 1x0

B) 2x0

C) 2x4

D) 1x4

Perform the indicated computation. Write the answer in scientific 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 in

scientific notation.

31)

7 ? 10 -7 14 ? 103

A) -1.2 C) 3.5 x 104

B) 1.4 x 103 D) 5.0 x 10-11

Factor the polynomial completely. If the polynomial cannot 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) C) (x - 10)(y + 6)

34) x2 + 4x - 45 A) (x - 9)(x + 1) C) (x + 9)(x - 5)

35) 4 - m2 A) (2 - m)(2 + m) C) (2 + m)2

36) 25x2 + 64 A) (5x - 8)2 C) (5x + 8)(5x - 8)

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

B) (x - 9)(x - 5) D) prime

B) (2 - m)2 D) prime

B) prime D) (5x + 8)2

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

B) (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) C) (x - 63)(x + 1)

40) 8x2 + 18x + 9 A) (8x + 3)(x + 3) C) (2x - 3)(4x - 3)

B) (x + 7)(x - 9) D) prime

B) (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 - 2n2 8p

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

A) 1

B) 5

C) 3

D) 4

Simplify the rational expression.

43)

m2 - 5m - 50 40 - 4m

A)

-

m+ 4

5

C)

m2 36

55

B)

m - 55 36

D)

m+ 4

5

Perform the indicated operation. Simplify if possible. 21x4 7x3

44) 9x2 28x5

A)

3x4 28

C)

28x8 3

B)

28x4 3

D)

189x2 196

45)

3y - 24 5y + 40

?

3y + 24 5y - 40

A) 0

C)

3 5

B) 15

D)

9 25

46)

x2 x+6

+

6x x+6

A)

1 x

B)

x 2

C) x

D) 2

47)

x2 x2 - 64

-

10x - 16 x2 - 64

A) 0

C)

x x

+

2 8

B)

x x

+ -

8 2

D) undefined

48)

4 s-t

+

12 t- s

A)

-8 s-t

C)

-16 s-t

B) 0

D)

8 s-

t

49)

3 x

+

6 x- 7

A)

3(3x - 7) x(x - 7)

C)

9 x(x -

7)

B)

3(3x + 7) x(x - 7)

D)

9 2x -

7

Simplify the complex rational expression. 11 4 - x2

50) 1 1 2+x

A)

x-2 2x

C)

2x x+2

B)

x+2 2x

D)

2x x-2

Solve the equation.

51)

1

+

1 x

=

20 x2

A) 5, -4

C) 5, 4

B) -5, 4

D)

-

1 5

,

1 4

Solve the rational equation. Check your answer.

52)

7 x + 21

+

3 x- 7

=

3x + 21 x2 + 14x - 147

A) {1} C) {0}

B) {+} D) {-1}

Solve the equation for the indicated variable.

53)

1 a

+

1 b

=

1 c

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)

5 x+2

=

x

4 -4

A) {-6} C) {28}

B) {6} D) {-28}

Given that the pair of triangles is similar, find the missing length.

55) 12

Solve.

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

5 9

,

0

C)

9 5

,

-1

B)

5 9

,

-1

D)

5 9

,

1

60) 8x3 + 64x2 + 120x = 0 A) {0, 5, 3}

C) {0, -5, -3}

B) {-5, -3}

D)

-

1 5

,

-3

Simplify the square root. Assume all variables represent positive real numbers.

61) -2 75

A) -10 3

B) 3 10

C) -3 10

D) 10 3

8

A) x = 16 C) x = 23

16 B) x = 30 D) x = 24

62) 150x2y A) 5xy2 6 C) 5xy 6

63)

150x11 6x

A) 5x10 C) 5x5

B) 5x2 6y D) 5x 6y

B) 5x5 6 D) 5 x11

Simplify the expression. If necessary, express the result

C)

that is not a rational number as a decimal rounded to two

decimal places.

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

A)

5 3

B) 15 C) 14 D) not a real number

Perform the indicated operation and simplify. Assume all

variables represent positive real numbers. D)

65) 6 ? 42

A) 6

B) 42

C) 6 7

D) 252

Graph the inequality. 66) y L 3x + 4 A)

Perform the indicated operation and simplify. Assume all variables 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

B)

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 C) 5x 110

B) 5x 11 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 + 7

98

A) 7 - 2 C) 49 + 2

Solve the system of equations.

y

=

-

x 2

72)

y

=

x 2

-

18

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

Rationalize the denominator. 73) 10 90

A)

10 3

C)

1 3

B) 7 + 2 D) 7 + 7 2

B) (18, 9) D) (18, -9)

B) 3 D) 3 10

74) 4 5+2 A) 4 5 + 8 C) 4 5 - 8

B) 4

5+8 10

D) 4 5 - 2

Simplify the expression. 75) 3 320x7 A) x2 3 4x C) 4x2 3 5x

B) 4 3 5x7 D) 4x2 3 5

Simplify the square root, if possible.

76) 16-3/2 A) -64

B)

-

1 4

C)

1 64

D) 4

Solve the system of equations. 77) x - 4y = -24 4x + 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 triangle with sides a, b, and c, where c is the hypotenuse.

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

A) 2 74 Y 17.2 in

B) 2 35 Y 11.8 in

C) 148 in

D) 48 in

Solve. 79) 2x2 - 8 = 24 A) {-4, 4} C) {4}

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

80) x2 - 14x + 45 = 0 A) {9, 5} C) {40, 5}

B) { 2, -1} 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.

D)

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.

-3x + y L -3

83)

y

<

-

3 4

x

A)

Solve the quadratic equation by any method.

84)

9p

=

18

+

6 p

A) {1 - 15, 1 + 15}

B)

33

15 ,

3+ 3

15

C) {1 - 5, 1 + 5}

D)

-3 3

15 ,

-3

+ 3

15

B)

85)

1 2

y2

=

1 4

+

1 2

y

A)

12

3,

1

+ 2

3

B)

12

5,

1

+ 2

5

C)

-1 2

3

,

-1

+ 2

3

D) no real solution

C)

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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download