In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics:

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Christiana West
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1 MATH 080: Review for the Final Exam In order to prepare for the final exam, you need to understand and be able to work problems involving the following topics: I. Simplifying Expressions: Do you know how A. to use the order of operations to simplify an expression? B. to combine like terms? C. to remove parentheses and combine like terms? D. to use the laws of exponents for both positive and negative exponents? Simplify: 1. ( 1) + ( )( ). x y + x y xy 8x y. ( a 1) ( a + ). 7 ( 1) ( x 5 ) 7. 8 a b 5 8a b 8. ( x )( x)( x ) 9. ( a b )( ab) 10. ( x y ) 11. ( x ) 1. x y 1. x y

2 II. Perform the indicated operations. Do you know how to A. add polynomial? B. subtract polynomials? C. multiply polynomials? D. divide a polynomial by a monomial? Perform the indicated operations: 1. ( 5x x + x 1) + ( x 5x 8x 1) 15. ( 6x ) ( 8x + ) 16. x y xy xy + x y 17. x ( x x + 5) 18. ( 5x )( 5x + ) 19. ( b + )( b 8) 0. ( 8 y)( + y ) 1. ( 5a + ). ( a ). ( 5x )( x ). ( x )( x 6x + 1) 5. ( 6x 8x x) x III. Factor Completely. Do you know how to factor A. a common factor out? B. the difference of two squares? C. a trinomial square? D. a polynomial of the type x + bx + c? E. a polynomial of the type ax + bx + c? F. a four-term polynomial? Factor completely: 6. 6x y 9x y + x y 7. 6x 1x 10x + 5

3 8. x 5x 1 9. x + x x + 6x x 15 x. 81x. 9x x x 50y 5. x x + 8 IV. Evaluating expressions. Do you know how to evaluate an expression if given the value(s) of the variable(s)? 6. Evaluate x x y 5x 8y if x = 1, y = V. Solving equations: Do you know how to solve A. linear equations? B. quadratic equations? C. rational equations? D. formulas for a specified variable? Solve: 7. 5( t ) = ( d + ) = 7( d ) x = x 8x ( 5+ m ) 8 = 88

4 1. x 7x 18 = 0. 1y 5y = y = 5 y x + = 5 x 5. x x = 9 8x 6. ( t + 1)( t 1) = 1 VI. Solving inequalities. Do you know A. what to do when you divide both sides of an inequality by a negative number? B. how to graph the solutions of an inequality? C. how to indicate the solutions of an inequality using set-builder notation? Solve the following linear inequalities. Indicate the solutions using set-builder notation and graph the solutions. 7. y + 8 > x 1y VII. Graphing linear equations in two variables. Do you know how to graph equations of the form A. Ax + By = C? B. y = mx + b? C. x = a? D. y = b?

5 Graph the following linear equations: 9. y = x x y = x = 1 5. y = VIII. Do you know how to A. find the x-intercept and y-intercept of a graph if given the equation? B. determine the slope of a line if given 1. the graph of a line?. two points on the line? C. find the slope and y-intercept of a line if given the equation in the form 1. y = mx + b?. Ax + By = C? D. determine if two lines are parallel if given their equations? E. draw the graph of a line if given its slope and y-intercept?

6 Answer each of the following questions: 5. Find the coordinates of the x-intercept and y-intercept for x y = Find the slope of the line pictured below. 55. Find the slope of the line containing the points (, 1 ) and ( 8, 5 ). 56. Find the slope and y-intercept of the following lines: a. y = x b. x y = Determine if the following lines are parallel: y = x + 1 and x + 5y = 6. Explain your reasoning.

7 IX. Solving word problems. In solving word problems, do you know that you must A. indicate what the variable represents? B. write an equation translating the word in the proble C. solve the equation from step B? D. write your answer in sentence form? E. check your answer with the words of the problem? Solve the following word problems: 58. It costs $1.50 plus 5 cents per mile for Mary to rent a car for her vacation. If her budget for car rental is $100, how many miles can she drive? 59. Bill borrowed money from a friend at the rate of 8% simple interest. After 1 year, $68 paid off the loan. How much did Bill borrow? 60. The length of a rectangle is 9 inches more than the width. If the area of the rectangle is 6 in, find the dimensions of the rectangle. 61. The lengths of the sides of a triangle are consecutive integers. If the perimeter of the triangle is 18 cm, what are the lengths of the sides?

8 6. The measure of the first angle of a triangle is 1 degrees less than the measure of the second angle and the measure of the third angle is twice the measure of the second angle. Find the measures of the angles of the triangle. 6. Find the length of the missing side in the right triangle pictured below. x 0 in. 16 in.

9 Answers: x y xy. 9a x 7 9. a 6 b x 6 y x x x y a 6 b 1. x y x 7x 5x 15. x x y xy 17. 6x + x 10x x b 1b 0. 6y + y a + 0a +. 9a 1a x x + 6. x 1x + 1x 5. x x 1 6. x y( x y + y ) 7. ( x 7)( x 5) 8. ( x 7)( x + ) 9. ( x )( x + 5) 0. ( 5x + 1)( x + 5) 1. ( x + 5)( x ). ( 9x )( 9x + ). ( 7x ). ( x + 5y)( x 5y) 5. ( x 8)( x ) t = x = m = 9 1. x = 9 or x =. y = or y = 5. x = or x = 1 5. x = or x = 1 6. t or t = = 7. { y y < } 8. { x x } 8. d = 17. y =

11 5. x- intercept: ( 0) 56. a. slope =, ; y- intercept: 0, 9 5. slope = 55. slope = ; y-intercept: ( 0, ) b. slope = ; y-intercept: 7 0, 57. The lines are not parallel because their slopes are not equal. One line has slope 6 5, and the other line has slope. 58. She can drive up to 50 miles. 59. Bill borrowed $, The width is inches and the length is 1 inches. 61. The sides of the triangle have lengths of 5 cm, 6 cm, and 8 cm. 6. The measures of the angles of the triangle are 6, 8, and 96 degrees 6. The length of the missing side is 1 in.

My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.