Math Review Guide

Part III: Elementary Algebra

Elementary Algebra covers the following topics: linear and quadratic equations, inequalities, exponents, polynomials, graphing, and systems of equations in two variables .

Graphing of Linear Equations
39. Graph 2x – y = 6. Indicate x- and y-intercepts (if any).

Polynomials
40. Subtract the following polynomials: (x⁵ – 3x² + 2x – 1) – 2(x³ – 3x² – 2x + 1)
a. x⁵ + 2x³ + 9x² – 6x + 3
b. x⁵ – 2x³ – 9x² – 2x + 1
c. x⁵ – 2x³ + 3x² + 6x – 3
d. x⁵ + 2x³ – 3x² – 6x + 3

41. Subtract (2x + 1) from the sum of (3x – 7) and (5x + 2)
a. 6x – 6
b. –6x + 6
c. 4x + 10
d. 4x – 10

42. Multiply: (x + 3) (5x – 1)
a. 5x² + 14x – 3
b. 5x² + 15x – 3
c. 5x² – x – 3
d. 5x² + 16x – 3

43. If x = -3 and y = 1, evaluate: x² + 2xy + 7
a. 10
b. –5
c. 11
d. –8

44. Factor completely : 9x² – 25
a. (9x – 5) (9x + 5)
b. (3x – 5) (3x – 5)
c. (3x – 5) (3x + 5)
d. (3x – 5)²

45. Factor completely: x² – 5x – 14
a. (x + 7) (x – 2)
b. (x – 7) (x – 2)
c. (x – 14) (x + 1)
d. (x – 7) (x + 2)

46. Factor completely: 6x² + 19x + 10
a. (6x + 5) (x + 2)
b. (3x + 2) (2x + 5)
c. (6x + 1) (x + 10)
d. cannot factor

47. Multiply and simplify :

48. Add and simplify (if possible):

49. Use long division and divide: (2x² – 5x + 1) ) (x – 3)
a
d. none of the above

Inequalities
50. Solve: 2x – 1 < 5x – 13
a. {x | x < 4}
b. {x | x < -4}
c. {x | x > -4}
d. {x | x > 4}

Exponents
51. Simplify: (3x^-2 y)³ (2xy)

52. Simplify:

Quadratic Equations
53. Solve: x² – 4x = 12
a. x = 12 or x = 16
b. x = 6 or x = -2
c. x² = 4x + 12
d. x = 0

Linear Equations
54. Find the slope and the y-intercept of the line: x + 3y = 9
a. slope = 1; y-intercept = 9
b. slope = -3; y-intercept = 9
c. slope = -1; y-intercept = 3
d. slope = -1/3; y-intercept = 3

55. Find the slope- intercept equation of the line passing through the points (1, -3) and (3, 5)
a. y = 4x – 7
b. y = x – 4
c. y = 4x + 13

56. Solve for P : P = A – Prt

Systems of Equations in Two Variables
57. Solve the following linear system: 3x + 2y = 9 and 4x + 5y = 5
a. x = 0, y = 1
b. x = -5, y = 3
c. x = 3, y = 0
d. x = 5, y = -3

58. Michael has a number of dimes and quarters totaling $12.05. The number of quarters is five more than twice the number of dimes. How many coins of dimes does he have?
a. 20 dimes
b. 18 dimes
c. 100 dimes
d. 5 dimes

Part IV: Intermediate Algebra Review Guide

Intermediate Algebra covers the following topics: algebraic operations and concepts, solving equations and inequalities, algebraic fractions, exponents, roots and radicals , graphing of linear and quadratic functions and equations, and introduction to logarithms.

59. Find the slope of the line pictured below.

60. Below is the graph of a function showing y = ƒ(x). Use it to answer the following questions.

a. What is ƒ(−4)?
b. What is x if ƒ(x) = 1?

61. Find the equation in slope-intercept form of the straight line containing the point (1,−3) and having the slope -5/2.

62. Let ƒ(x) = 2x + 3. Find and simplify ƒ(t − 1).

63. Factor the following polynomial or determine that the polynomial is prime: 2a² − 16a + 32

64. Which of the following are graphs of functions?

65. Solve the given inequality and graph the solution set on a number line: 2x − 3 ≥ 9 + 3x

66. Solve the given inequality and write the solution set in interval notation: |2x + 5| > 10

67. Write using rational exponents (in lowest terms):

68. Simplify. Assume that b represents a non- negative number .

69. Rationalize the denominator :

70. Simplify. Do not assume that x represents a non-negative number.

71. Solve for a:

72. A bookcase is 1 foot taller than it is wide. A diagonal brace, 1 foot longer than the height of the bookcase, is needed for support. What is the length of the brace?

73. Simplify. Express your answer in the form a + bi. (2 + i)(3 − 2i) − (i + 1)

74. Solve for x: x² + 6x = 1 + x²

75. Let ƒ(x) = −x² + 6x − 8. Find the vertex and x− and y−intercepts of the graph of ƒ.

76. Solve for t:

77. A ball is tossed in the air. Its distance in feet above ground t seconds later is given by the formula d (t) = 6 + 96t −16t². What is the ball's maximum height?

78. Let  . Find g(−3).

Math Placement Review Guide Answer Key