1. Write in symbols: (a) The quotient of -6 and the sum of 2 and -8. (b) Now Simplify the expression in part a. 2. Simplify. x 4, given x=-2 and y=4

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1 Sample problems for common Final Exam Math 115 LASC Directions: To receive credit show enough work so that your method of solution is clear. Box answers. Show all work on this test form. No Work=No Credit. 1. Write in symbols: (a) The quotient of -6 and the sum of and -8. (b) Now Simplify the expression in part a.. Simplify ( 5)( 1) ( ) ( 8). Simplify 0( 1 ) 9 ( ) 1( ). Evaluate y 5. Solve x Solve for t in r t d x, given x=- and y= 7. Solve 7 ( x ) x ( x 1) 8. Solve 0.6( x 0) 0.8( x 10) 6 9. In the 005 baseball season, the St. Louis Cardinals won the most games of any major league team. The Cardinals won less than twice as many games as they lost. They played 16 regular-season games. How many wins and losses did the Cardinals have? (a) Declare variables. (b) Box the equation (c) Solve. Write a sentence, include units. 10. Find the measure of an angle if its supplement measures 10 more than three times its complement (a) Declare variables. (b) Box the equation (c) Solve. Write a sentence, include units. 11. Given X-Y= (a) Find the x and y intercepts (b) Graph linear equation. 1. Graph y x by using the slope and y-intercept. Attention! Following directions for credit! 1. Find the slope of x+y=10 and the y-intercept.

2 For problems 1 & 15, write the equation of the line with the given information. Leave answer in the slope-inter form. 1. Through (0,) and M=- 15. Through (, -6) and (1,) For problems 16 & 17 solve each inequality and graph the solution set on the number line x+(x-) x-(+5x) <x Graph the following linear inequality on the plane, x + y Do not forget to show your test point. 19. Two cars leave from the same point, traveling in opposite directions. One travels at a constant rate of 50 mph, while the other travels at a constant rate of 65 mph. How long will it take for them to be 60 miles apart? (a) Set up the table and fill in the 6 boxes. (b) Write an equation using the table. (c) Solve the equation. x y 6 0. Solve the system by graphing x y 1. Solve the system by the substitution method x y x y 7 check your answer!. Solve the system by the Elimination method x 5y 8x 10y 6 check your answer!. Solve the system by the Elimination method x y 5x y 7 check your answer!. Jovan has a 5% solution of alcohol to mix with a 0% solution to get 50 liters of a final mixture that is 0% alcohol. How much of each of the original solutions should he use? 5. Graph the solution set of each system of linear inequalities: x 7y 1 Show your test points! Only shade the final answer! x y 1

3 For problems6-9 Simplify each the following expression: 6. ( ) ( x ) ( x ( xy ) 1 y) 0. Write 1,000,000,000,000,000 in scientific notation 1. Write.6 x 10 in standard notation (without exponents) 5 5. Subtract ( 9a b 1ab 5a b ) (6ab 1a b 10a b ) For problem -5, multiply each of the following:. ( x y)(x y). ( x y)(x y) 5. ( 5x y) 6. Divide 8y 6y y y 8x 7. Divide by using polynomial long division For problems #8- Factor completely, if possible. 8. 1x 0x 9. x y x y 5x y ax bx ay by 0. 10x x x 1 1. x 8xy 9y 81x 16y.. 6x 81x 5

4 . Solve by factoring x 11x 0 5. Solve by factoring y 1y 6 0 For problems 6 & 7 find the values for each of the following rational expressions which make it undefined. (Find the domain) 6. x 1 x x 8 x 7 7. x 1 For problems 8 & 9 write each of the following in lowest terms. (Simplify or reduce) 8. 6x x x x 1 y y 9. y Divide. (Write in lowest terms) x x 5 x x 9 x x A right triangle is such that one leg is meters shorter than the other leg. The triangle has area of5m. Find the lengths of the legs. (a) Declare variables. (b) Box the equation (c) Solve. Write a sentence, include units. 5. Multiply and simplify Multiply and simplify ab 6ab 5. Rationalize the denominator Simplify a 56. Divide and simplify 5x 80xy 57. Subtract and simplify Solve x Find the LCM of y y y y y 9, 10 1, Subtract and simplify if possible. 1 x 16 x x x

5 5x 1 5x 9x 61. Simplify: 6. Divide 9x 6x x x 1 9 y 1 y For problems 6 & 6 SOLVE y x x 6. The numbers on three raffle tickets are consecutive integers whose sum is 750. Find the integers. (a) Declare variable(s). (b) Write an equation which models problem. (c) Solve For problems 65 &66 solve the quadratic equation by the quadratic formula. 65. x x x 5x1 0 ANSWER KEY: 1. (a) ( 8) (b) 1 5. x 1or 1 6. d r t 7. No solution or 8. x 0 or games won and 6 games lost. 10. (b) 180-x=(90-x) +10 (c) x=50 degrees. 11. x-intercept=(,0), y-intercept=(0,-)

6 1. slope=/ and y-intercept=(0,-) Graph: TBA 1. slope=- and y-intercept=(0,10) 1. y=-x y=-9x x Graph TBA 17. -<x 6 Graph TBA 18. TBA 19. In hours the cars will meet. 0. (,-1) 1. (1,-6). No solution. Or Ø or empty set.. (-1,). 1 liters of the 5% solution must be mixed with 16 liters of the 0% solution. 5. Graph TBA x y x a b 7ab 5a b. 8x xy y. 5. x y 5x 0xy y 6. y y 7. x 7x 8. 6x (x 5) 9. x y(xy x 5y) 0. ( a b)(x y) 1. ( x 7y). (x y)(x y)(9x y )

7 . 9(x 5)( x 1).,8 5. 1,6 6. and - or Domain is all real numbers except and -. Or x, x 7. x 7 8. x x 1 9. y( y 1) or y y 50. x 5 x The measure of the short leg is 9 meters and the long leg is 1 meters ab a We assume that all variables are non-negative. 7 y Possible solution x=8, but it checks; therefore ( y )( y )( y 7) x 7x ( x )( x )( x 1)

8 y y 6. y=1 or 1 Possible solution checks. 6.,5 Both possible solutions check , 510, 511 are the three consecutive raffle tickets. 65.,

Math 46 Final Exam Review Packet

Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.