BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH 05 Review Sheet Go to http://www.cun.edu/testing for more information on the CUNY Elementar Algebra final eam, including sample finals such as http://www.cun.edu/academics/testing/sample-ceafe-a.pdf I. Operations with signed numbers and fractions 1. Evaluate: d) 5 95) ) 1 e) 6 8 9 ) 1 ) c) 5 f) ) + 1 ). Evaluate: b ac when a = 1, b = 7, c = 6. b ac when a = 1, b = 1, c = 1. c) b a when a =, b = d) 1 1 when 1 =, =, 1 =, = 9. e) when =, =. Solve: II. Linear equations and sstems 6 = 18 5 + ) = + c) t ) t + 5 = 5t 7 d) 10z ) = z + 1). Solve for the indicated variable: e) 5 = + 7 + 6 f) 6 w + w = 1 6 I = P r t for t F = 9 C + for C c) = 8 for 5 5. Sketch the graphs of the following linear equations: = 6 + = 8 c) = 1 + d) = 6. Find the slope of the lines described b the following information: With equation = + With equation = 8 c) Passing through the points, ) and 5, 1) d) Perpendicular to the line with equation = 1
7. Write an equation of the line described b the following information: With slope 1 and passing through the point, ) Passing through the points, 1) and, ) c) Parallel to the line with equation = and passing through 1, 9). d) Parallel to the line with equation 5 = and having the same intercept as the line with equation 8 = 0. 8. Solve the sstems: { + = 1 = 8 { 5 = 10 7 = 1 c) { + = = 1 9. Write an algebraic equation in order to solve the following questions: Ojana has 9 coins. If she has a total of $6.0 and the coins are onl dimes and quarters, how man of each tpe of coin does she have? The length of a rectangle is three centimeters more than twice its width. The perimeter is 5 cm. Find the length and the width of the rectangle. c) One number is si more than three times another number. Their sum is 75. Find the two numbers. d) Find two consecutive integers such that three times the first is seven more than two times the second. e) Three consecutive integers have the propert that the sum of the first two is 1 less than three times the third. Find the three integers. 10. Solve and graph the solution set of the inequalities: > 7 5 1. Graph the solution set of the following inequalities: 5 + 10 < 6 1. Perform the indicated operations: 1) + 5) ) c) 1) + ) d) + 5) + 5) e) 7 16 5 + 1. Factor completel: III. Inequalities IV. Operations with polnomials p q 5 1p q 15 + 56 c) + 1 d) 6 e) 16 f) 6 5 + 1 g) + 10 6 15 Page
V. Operations with radicals rational eponents and comple numbers 1. Simplif the following radical epressions: 75 5 c) 9 d) 1 e) 8 7 f) 1 15. Perform the indicated operations and epress the answers in simplest radical form: 50 + 7 + 8 8 7 ) c) 5 ) 5 + ) VI. Quadratic Equations 16. Solve. Write all solutions in simplest radical or standard comple form a + bi: + 10 = 0 6 = 16 c) + = 0 d) + = 1 e) 5 + = 0 f) = + 17. Graph the following parabolas. Make a table of values showing at least five solutions. = 5 = + c) = 18. Solve the following problems b writing and using an algebraic equation: A rectangle has perimeter 8 feet and area 80 square feet. Find the dimensions of the rectangle. One leg of a right triangle measures three inches more than the other leg. Find the length of both legs if the hpotenuse is 15 inches long. c) The product of two consecutive integers is 9 more than their sum. Find the two integers. Page
1. A. 7 0. A. 5 B.. A.. A. t = I pr B. 1 6 C. 17 5 D. 79 6 C. D. E. 6 Answers E. F. 7 B. 10 C., ), i.e., all real numbers D. 5F 160 B. C = 9 C. = 8 8 7 E., i.e., no solution F. 10 6. A. 5. B. c) C. D. d) 7. A. + = 1 B. = 5 C. = + 6 D. = 5 8. A., ) B. ) 1, 50 1 C. 1 8, ) 9. A. dimes and 16 quarters. B. The length is 19cm; the width is 8cm. C. E. 16, 17, and 18 69 and 1 D. 9, 10 A. B. 0 10. 0 Page
. 1. A. 1 + 5 B. 1+ 9 C. + 5 D. + 10 E. + 6 1. A. p q q ) B. 7) 8) C. +1) 1) D. +) ) E. +) ) +) F. + ) ) G. 5 + ) ) 1. A. 5 B. C. i D. i E. F. 15. A. 1 + 6 B. 1 C. 16. A. 5 and B. 8 and C. + i and i D. 1 + 5 and 1 5 E. 1 and F. 1 + 5 and 1 5 17. c) 18. A. 0 feet b feet B. 9 inches b 1 inches. C. 6, 7 or 5, Revised 10/010, AM, NEA, 5/01, 6/016 CO S Page 5