Intermediate 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._________________________________________________________________________________________Solve the equation.

1) x + 44

-3x - 12

10= 1

A) 24 B) 6

C) - 24 D) -48

Solve the problem.

2) The difference of a number and 8 is the sameas 34 less the number. Find the number.

A) 21 B) -13

C) -21 D) 13

3) The population of a town is currently 22,000.This represents an increase of 80% from thepopulation 5 years ago. Find the population ofthe town 5 years ago. Round to the nearestwhole number if necessary.

A) 12,222 B) 4400

C) 17,600 D) 27,500

4) P = 2L + 2W for L

A) L =P - 2W

2 B) L = P - 2W

C) L =P - W

2 D) L = P - W

5) I =nE

nr + R for n

A) n = IR(Ir - E) B) n =-IR

Ir - E

C) n =IR

Ir + E D) n =-R

Ir - E

Solve.

6) The average price (in dollars) to rent a studioin a certain city can be approximated by theequation p = 34.0t + 646 where t is the numberof years since 1990. Solve this equation for tand use the new equation to determineapproximately what year it will be when theaverage price of a studio in this city reaches$1326.00.

A) 2012 B) 2013

C) 2010 D) 2011

Solve the linear inequality. Express the solution usingset-builder notation and interval notation. Graph thesolution set. NOTE: A square bracket, i.e. [, is the same asa filled in circle. A round bracket, i.e. (, is the same as anopen circle.

7) 3x - 9 < 4(x - 3)

A) {x|x < -3}; (- , -3)

B) {x|x > -21}; (-21, )

C) {x|x > 3}; (3, )

D) {x|x < 21}; (- , 21)

Solve the inequality. Graph the solution set, and state thesolution set in interval notation.

8) |x - 4| + 2 9

A) [-3, 9]

B) [-3, 11]

C) (-3, 11)

D)

List the intercepts of the graph.

9)

A) (0, -2), (0, 8), (4, 0)

B) (0, -2), (8, 0), (0, 4)

C) (-2, 0), (0, 8), (4, 0)

D) (-2, 0), (0, 8), (0, 4)

Find the domain of the function.

10) f(x) =2x - 3x + 6

A) {x|x 6} B) {x|x 32

}

C) {x|x -6} D) {x|x -6, 32

}

11) f(x) = x2 + 3

A) {x|x > -3} B) {x|- < x < }

C) {x|x -3} D) {x|x -3}

Find the slope of the line that goes through the givenpoints.

12) (-2, -1), (9, -1)

A) -211 B) -

27

C) 0 D) Undefined

Find an equation of the line with the given slope andcontaining the given point. Express your answer inslope-intercept form.

13) m = -3, (-6, 5)

A) y = -3x + 13 B) y = -3x - 13

C) y - 5 = x + 6 D) y - 5 = mx + 6

14) m = -23

, (5, 5)

A) y = -32

x -252 B) y =

23

x -253

C) y = -23

x +253 D) y = -

23

x -253

15) m is undefined, (5, -1)

A) y = 5 B) x = 5

C) x = -1 D) y = -1

Use the given conditions to write an equation for the linein slope-intercept form.

16) Passing through the point (2, 1) andperpendicular to y = 3x - 3

A) y = 3x +53 B) y = -3x +

53

C) y =13

x +53 D) y = -

13

x +53

Determine whether the ordered pair is a solution of thesystem of linear equations.

17) 4x = 18 - y3x = 7 - 4y

; (5, -2)

A) Yes B) No

Solve the system of equations using elimination.

18) 3x - 6y = -78x - 5y = -5

A) 4133

, 533 B) 5

33, -

4133

C) 533

, 4133 D) -

4133

, -533

Simplify the expression. All exponents should be positiveintegers.

19) -6a13b-3

3a7b-9

A) -2b6

a6 B) -2a6

b6

C) -2a6b6 D) -2a6b6

Simplify the expression.

20) (-5)2 · 100

A) -25 B) 125

C) -125 D) 25

Perform the indicated operation. Express the solution inscientific notation.

21) (8 × 10-5) · (6.1 × 10-3)

A) 4.88 × 10-7 B) 4.88 × 1015

C) 488 × 10-8 D) 48.8 × 10-7

22) 12.74 × 107

4.9 × 108

A) 2.6 × 10-1 B) 2.6 × 1015

C) 5.2 × 1015 D) 5.2 × 10-1

Factor the difference of two squares completely.

23) 25 - 16x2

A) (5 + 4x)(5 - 4x) B) (5 + 4x)2

C) (5 - 4x)2 D) Prime

24) ab4 - 121a3b2

A) a(b2 + 11ab)(b2 - 11ab)

B) ab2(b + 11a)(b - 11a)

C) ab2(b - 11a)2

D) Prime

Find the product.

25) -5x6(11x7 + 6x4 + 12)

A) -55x7 - 30x4 - 60

B) -55x13 - 30x10

C) -55x13 + 6x4 + 12

D) -55x13 - 30x10 - 60x6

Solve the system of equations using substitution.

26) x - 6y = -42-5x - 5y = -35

A) (0, 7) B) (-7, 0)

C) (1, 6) D) no solution

Factor the sum or difference of two cubes completely.

27) x3 + 27

A) (x + 3)(x2 + 9)

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

C) (x - 27)(x + 1)(x - 1)

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

28) 64y3 - 1

A) (64y - 1)(y2 + 4y + 1)

B) (4y - 1)(16y2 + 1)

C) (4y - 1)(16y2 + 4y + 1)

D) (4y + 1)(16y2 - 4y + 1)

Factor completely, or state that the polynomial is prime.

29) 40x2 + 2x - 24

A) (5x + 4)(8x - 6)

B) 2(5x + 4)(4x - 3)

C) (2x + 8)(4x - 3)

D) 2(5x - 4)(4x + 3)

30) 2x3 + 2000

A) 2(x + 10)3

B) 2(x3 + 1000)

C) 2(x + 10)(x2 - 10x + 100)

D) Prime

Find the special product.

31) (7x + 12)2

A) 7x2 + 168x + 144

B) 49x2 + 144

C) 49x2 + 168x + 144

D) 7x2 + 144

32) (6x - y)2

A) 36x2 - 12xy - 2y2

B) 36x2 + y2

C) 36x2 - 12xy + y2

D) 36x2 - 6xy + y2

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

33) x2 - 5xy - 24y2

A) (x - 3y)(x + y) B) (x + 3y)(x - 8y)

C) (x - 3y)(x + 8y) D) Prime

34) 10x2 + 7x - 12

A) (2x - 3)(5x + 4) B) (10x + 3)(x - 4)

C) (2x + 3)(5x - 4) D) Prime

Factor completely, or state that the polynomial is prime.

35) x3 - 4x2 - 36x + 144

A) (x + 4)(x + 6)(x - 6)

B) (x - 4)(x + 6)(x - 6)

C) (x - 4)(x - 6)2

D) Prime

Find the intercepts of the graph of the function.

36) g(t) = t2 + 6t - 16

A) (8, 0), (2, 0), (0, - 16)

B) (-8, 0), (2, 0), (0, - 16)

C) (-8, 0), (1, 0), (0, - 16)

D) (8, 0), (-2, 0)

Factor the polynomial completely.

37) x4 - 8x2 + 7

A) (x2 - 1)(x2 - 7) B) (x2 + 1)(x2 + 1)

C) (x2 + 1)(x2 - 7) D) Prime

Find the values of x such that the given function has thestated value.

38) f(x) = x2 + 8x; f(x) = 48

A) x = 12 or x = 4 B) x = -12 or x = 4

C) x = 12 or x = -4 D) x = -12 or x = 1

Multiply the rational expression. Express the product as arational expression in lowest terms.

39) 80xx2 - 25

·10x - 50

8x2

A) 100xx + 5 B) 10

x(x + 5)

C) 100x(x + 5) D) 64

x(x + 5)

40) 6w - 36w2 + 1w

·w2 + 8w + 7

w2 - 13w + 42

A) 6(w - 7)w(w + 7) B) 6(w + 7)

w - 7

C) 6(w + 7)w(w - 7) D) 6

w

Determine the domain of the rational function.

41) R(x) =2

x - 7

A) {x|x 7} B) {x|x -7}

C) {x|x 0} D) {x|x 0, x 7}

Perform the indicated operation and simplify the result.

42) 4x2 - 17x + 5x2 - 15x + 54

-3x2 - 9x - 7x2 - 15x + 54

A) x - 2x + 9 B) x2 - 8x + 12

x2 - 15x + 54

C) x - 2x - 9 D) x + 2

x - 9

43) 2xx - 5

+7

5 - x

A) 2x + 7x - 5 B) -5x

x - 5

C) 2x - 75 - x D) 2x - 7

x - 5

Add or subtract, as indicated, and simplify the result.

44) 910a3b

-8

15ab2

A) 27b - 16a2

30a3b2 B) 27b - 8a2

30a3b2

C) 27b - 16a2

30a2b3 D) 27b + 16a2

30a3b2

45) y + 9y + 2

-y + 9y - 9

A) 11(y + 9)(y + 2)(y - 9) B) -11(y + 9)

(y + 2)(y - 9)

C) -7(y + 9)(y + 2)(y - 9) D) 0

Multiply, and then simplify if possible. Assume allvariables represent positive real numbers.

46) 2( 50 + 10)

A) 10 + 2 5 B) 20

C) 100 + 2 5 D) 10 + 4 5

Use the product rule to simplify the expression. Assumethat the variables can be any real number.

47) 405k7q8

A) 9q4 5k7 B) 9k3q4 5k

C) 9k3q4 5 D) 9k7q8 5k

Divide and simplify.

48) 3 250x132x

A) 5x4 x B) x4 35

C) x4 32 D) 5x4

Simplify the radical expression. Assume that all variablesrepresent positive real numbers.

49) 75k7q8

A) 5q4 3k7 B) 5k3q4 3

C) 5k3q4 3k D) 5k7q8 3k

Simplify the radical.

50)3

(-6)3

A) -18 B) -6

C) 18 D) 6

51)5

(x - 1)5

A) -x + 1 B) |x - 1|

C) -|x - 1| D) x - 1

Evaluate the expression, if possible.

52) 64-4/3

A) 256

B) 1256

C) -1

256

D) not a real number

Multiply, and then simplify if possible. Assume allvariables represent positive real numbers.

53) ( 2 + 5)2

A) 10 + 2 10 B) -3 + 2 10

C) 7 + 2 10 D) 7 - 2 10

Add or subtract. Assume all variables represent positivereal numbers.

54) 2 125 - 3 20 - 4 45

A) -8 5 B) 7 5

C) -7 5 D) 2 5

Rationalize the denominator and simplify. Assume that allvariables represent positive real numbers.

55) 57 - 9

A) 5 7 - 4574

B) -5 7 + 45

74

C) -5 7 - 45

74D) 5 7 + 45

74

Simplify the complex rational expression.

56)

4a

+ 1

4a

- 1

A) 4 - a2 B) a2

4 - a2

C) 4 D) 4 + a4 - a

Solve for x.

57) 11x = 1

A) x = 1 B) x =111

C) x = 0 D)

Solve the equation by completing the square.

58) x2 + 10x + 15 = 0

A) {5 - 15, 5 + 15}

B) {5 + 10}

C) {-5 - 10, -5 + 10}

D) {-10 + 15}

Solve the rational inequality.

59) x +60x

< 16

A) (0, 6) (10, ) B) (- , 0) (6, 10)

C) (- , 0) (10, ) D) (0, 6) (6, 10)

Solve for x.

60) 4-x =164

A) x =116 B) x = 3

C) x = -3 D) x =13

Simplify the radical expression. Assume that all variablesrepresent positive real numbers.

61)3

6 ·3

-36

A) -6 B) -216

C) 6 D) 6 6

Complete the square for the binomial. Then factor theresulting perfect square trinomial.

62) x2 - 14x

A) x2 - 14x - 49 = (x - 7)2

B) x2 - 14x + 196 = (x - 14)2

C) x2 - 14x - 196 = (x - 14)2

D) x2 - 14x + 49 = (x - 7)2

Add or subtract, as indicated, and simplify the result.

63) 3y2 - 3y + 2

+5

y2 - 1

A) 8y - 7(y - 1)(y + 1)(y - 2)

B) 30y - 7(y - 1)(y + 1)(y - 2)

C) 8y - 7(y - 1)(y - 2)

D) 7y - 8(y - 1)(y + 1)(y - 2)

Solve the equation.

64) log3 (2x + 2) = log3 (30)

A) x = 56 B) x = 14

C) x = 16 D) x = 64

65) log2 (x + 4) - log2 (x + 3) = 1

A) x = 2 B) x = - 2

C) x = 1 D) no solution

66) log2 (x + 1) + log2 (x - 5) = 4

A) x = 8 B) x = 7

C) x = -3 D) x = 7, x = -3

Solve the equation. Give an exact solution.

67) e4x = 6

A) 4 ln 6 B) 32

e

C) ln 46 D) ln 6

4

68) 2x + 7 = 3

A) log 3log 2

- 7

B) log 3 - log 2 - log 7

C) log 2log 3

+ log 7

D) log 2log 3

+ 7

Rationalize the denominator. Assume that all variablesrepresent positive real numbers.

69) 47

A) 4 77

B) 53

C) 16 7 7

D) 4 7

Solve the equation.

70) x4 - 20x2 + 64 = 0

A) {2, 4} B) {4, 16}

C) {-2i, 2i, -4i, 4i} D) {-2, 2, -4, 4}

Simplify the complex rational expression.

71)x9

-1x

1 +3x

A) 9x + 3 B) x - 3

9

C) 9x - 3 D) x + 3

9

Evaluate the expression, if possible.

72) 278

-1/3

A) -23 B) -

32

C) 32 D) 2

3

Solve the equation.

73) 2x + 1 = x - 3

A) {2, 8} B) {8}

C) {-4, 43

} D) {-4}

74) 10x - 9 - 9 = 0

A) {81} B) {9}

C) {365

} D) no real solution

Solve the rational inequality.

75) x - 1x + 3

> 0

A) (-3, 1) B) (- , -3) (1, )

C) (1, ) D) (- , -3)

Solve the equation.

76) 1 +1y

=42y2

A) y = -7 or y = 6

B) y = 7 or y = -6

C) y = 7 or y = 6

D) y = -17

or y =16

77) m -3m

= 2

A) m = -3 or m = 1

B) m = -13

or m = 1

C) m = -1 or m =13

D) m = -1 or m = 3

78) 6x + 4

-9

x - 4=

3x2 - 16

A) x = 67 B) x = 63

C) x = -21 D) x = 21

Solve.

79) A ladder that is 26 feet long is 10 feet from thebase of a wall. How far up the wall does theladder reach?

A) 24 ft B) 4 ft

C) 576 ft D) 2 194 ft

Use the quadratic formula to solve the equation.

80) 8x2 + 24x = - 17

A) -6 - 704

, -6 + 704

B) -24 - 24

, -24 + 24

C) -6 - 216

, -6 + 216

D) -6 - 24

, -6 + 24

81) 8x2 + 1 = 3x

A) -3 - i 2316

, 3 + i 2316

B) 3 - i 2316

, -3 + i 2316

C) 3 - i 2316

, 3 + i 2316

D) -3 - i 2316

, -3 + i 2316