# 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:

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

 Prev Next

Start solving your Algebra Problems in next 5 minutes!

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of July 6th you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!