Elementary Algebra Review for Eam 4 ) The length of a rectangular picture frame is 9 cm more than the width. The area inside the frame is 90 square cm. Find the dimensions of the frame. ) A 0-ft ladder is leaning against a building. If the bottom of the ladder is 6 ft from the base of the building, how high does the ladder reach? List all numbers for which the rational epression is undefined. 9 ) a - 7 4) ) - + + - 49 - - 40 Simplify, if possible. 6) m 6p 4m9p 7) ) 9) 0) + 4 0 + 0-4 + - b - a a - b 7t - 4 - t + ) + + 6 ) y - 6y - 6 y - y - 4 a - 6 ) a + 0a + 4 Provide an appropriate response. 4) What is wrong with the following? 4 + = 4 + = 4 Multiply and, if possible, simplify. ) 4 6) - 9 4-4 7-7 4 + 9 7) m - 6 m ) 9) m m + m - 4 + 0 - - 6 + - 4-7 ( + ) - 4 - (- 7) 0) + - 4 - - 9 - ) k + k + k + k + 4 k + 7k k + 6k + Divide and, if possible, simplify. )
Elementary Algebra Review for Eam 4 Page ) 0 y9 4 y ) 6 + y y - 4-6y y 4) 9 y - - y 4) + - - ) p - p p - p 6) z + z + 4 z + 6z + 6 z + 6z z + z + ) 6 + 4 + Solve. If no solution eists, state this. 6) 6-9 0 = 7) (y + ) y + 0y - y + y + 7) + -4 = Perform the indicated operation. Simplify, if possible. 4 ) a) + 7 4m m - + - m - c) m - 6m m - d) 9) a) c) + m - - 0 + + 6 + 9-4 + + 6 q - 9 - q - 9 a + a - - a + 7 a - + + - 4 - + 6 + - 4 ) t + 7 t = 9) - + = 6 40) + = - 6 4) For the pair of similar triangles, find the value of b. 6 4 0) 4 + 7 4 ) 0 + 9 4 4 ) z + z - z - z
Elementary Algebra Review for Eam 4 Page Solve. 4) To determine the number of deer in the Great Gulf Wilderness, a game warden catches and tags deer and then lets them loose. Later, 6 deer are caught; 6 of them have tags. Estimate the number of deer in the preserve. Provide an appropriate response. 4) Describe the three possible outcomes when graphing a system of equations, and include the number of solutions that each system has. Decide whether or not the ordered pair is a solution of the system. 44) a) (4, -) 4 + y = + 4y = - Solve the system of equations by graphing. If there is no solution or an infinite number of solutions, state this. 4) + y = 0 + y = 4 46) y = + - y = 7 47) - y = 6 = y + 0 Solve the system using the substitution method. If there is no solution or an infinite number of solutions, state this. 4) y = - - + y = - Solve the system using the elimination method. If there is no solution or an infinite number of solutions, state this. ) - 4y = 9-4y = 4 ) - y = -7 4y = 7-6 4) - - 6y = 4-4 - y = ) -4 + y = - - + y = 6 6) The sum of two angles is 94. One angle is less than twice the other. Find the angles. 7) Two angles are supplementary (they sum to 0 ), and one is 40 more than three times the other. Find the measure of each angle. Solve. ) One rental agency rents a van for $7.00 per day plus $0.6 per mile. A competitor rents a truck for $.00 per day plus $0. per mile. For what mileage is the cost the same for renting the van one day? 9) Ron and Kathy are ticket sellers at their class play, Ron selling student tickets for $.00 each and Kathy selling adult tickets for $4.0 each. If their total income for 64 tickets was $7.0, then how many of each type of ticket was sold? 49) - 7y = -49-7 - 6y = -4 0) y - = y - = 7 60) In a local high school basketball game, the winning team scored 7 of their points on a combination of two- and three-pointers. How many shots of each type did the team make? ) + y = 9 + y = 7
Elementary Algebra Review for Eam 4 Page 4 6) Don runs a charity fruit sale, selling boes of oranges for $ and boes of grapefruit for $0. If he sold a total of 76 boes and his total income was $, then how many boes of oranges did he sell? 6) Ellen wishes to mi candy worth $.40 per pound with candy worth $.00 per pound to form 4 pounds of a miture worth $.40 per pound. How many pounds of each type of candy should she use? 6) For small jobs, a contractor mies concrete with 9% cement and concrete with 0.% cement. How many bags of each should be used if the contractor needs bags of concrete with 0 % cement? Simplify. Do not use negative eponents in your answer. 64) a) y7 y - - -6 Solve the equation. 70) - = 4 7) + = -0 7) -4 + (- - 6) = - - 7 Find the intercepts, then graph the equation. 7) - + y = 0 Find the following. 74) a) Find the slope of the line containing the points ( -, -6 ) and (, -). Write the slope-intercept equation of the line containing the points given in part a). 6) a) c - -4 y -7 z - 66) a) p 4 p - z- z -4 c) 7-6 y - z 67) a) ( - yz) -4 ( -9 yz)( -4 y -4 z6) 6) An employee earned $,96 this year. This was a raise of 4% over last year. What was his salary last year? 69) In a local election, 7,96 people voted. This was a decrease of % over the last election. How many people voted in the last election?
Answer Key Testname: EAEXAM4REVIEW_SP0 ) width = 6 cm, length = cm ) ft ) a = 7 4) = - and -4 ) = - and 6) 7p m 7) 4 ) - 9) - 0) -7 ) + ) y + y + ) a - 6 a + 4 4) You can only cancel factors, and is not a factor of 4 +. The has to be divided out of both terms, not just the last. ) 6) 7) ) 9) 0) ) ) - 7 4( + ) m(m + 4) (m + 6) ( - ) - + ( + 4)( + ) k k + 4 6 ) 6 y4 4) - ) 6p 6) z + z 7) ) a) 9) a) 0) 4 ) ) (y + )(y + ) y - 4 c) m - 4 d) - 7 + 6 q - 9 + 4 70 z + 7 0z a + a - ) - + 4y + y y - 4) - 9 ) 6) 0 + ( + 4) 7) -, 7 ) 7 9) 7 40) - 9 c) - 4 4) 4) 94 deer 4) () The graphs intersect at one point, and the system has one solution. () The graphs are parallel, and the system has no solution. () The equations have the same graph, and the system has an infinite number of solutions. 44) Yes
Answer Key Testname: EAEXAM4REVIEW_SP0 4) (, 6) y 0-0 - 0 46) No solution - -0 y 4 - -4 - - - 4 - - -4-47) Infinite number of solutions y 4 6) 0 boes 6) pounds of $.00 candy 9 pounds of $.40 candy 6) 0 bags of 0.% cement bags of 9% cement 64) a) y 4 6) a) c or 4 c 66) a) p 9 67) a) y4z0 6) $,60 69),700 people 70) 60 7) - 7) 7) (-, 0), (0, ) 74) a) - y = - - 7 z4 y7 z y7 z 4 c) 7y 6z - -4 - - - 4 - - -4-4) (-6,-0) 49) (0, 7) 0) - 7, ) No solution ) (, -) ) (, ) 4) Infinite number of solutions ) No solution 6) 7 and 7), 4 ) 40 9) student tickets 79 adult tickets 60) Two-pointers: ; three-pointers: