Math Final Examination STUDY GUIDE Fall Name Score TOTAL Final Grade

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1 Math Final Examination STUDY GUIDE Fall 010 Name Score TOTAL Final Grade The Use of a calculator is permitted on this exam. Duration of the test is 13 minutes and will have less number of questions than this study guide. This study guide does not necessarily contain questions from every possible topic covered by the final exam. Any topic covered in the course may be represented in the final. It is recommended that students study all topics of the course. We also recommend studying chapter tests and chapter exercises. All questions are the property of Math Department at Kent - Trumbull. Final Exam composition is in TWO PARTS as follows. PART 01. Approximately 0-0% of the Final Exam is to come from First Book (1001 Book). Please study Math Test 01 (= Math 1001 Midterm) Study Guide and Math Test 0 (= Math 1001 Final) to prepare you for this part of the test. Both of these STUDY GUIDEs have been circulated before. Breakdown of the Final exam is Approximately 0-% from each study guide. PART 0. Approximately 0-60% of the Final Exam is to come from Second Book (100 Book). Please study Math Test 03 (= Math 100 Midterm) Study Guide circulated before and the attached questions that cover the latter part of the book (material covered after the Test 03) to prepare you for this part of the test. Breakdown of the Final exam is Approximately 0-% from each study guide. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the GCF for the list. 1) 6, 10, 3 A) 7 B) C)1 D) 1) ) x7y8, x6y7, xy8, x3y A) xy B) x3y3 C) xy D) x3y ) 3) 6a8b3, 6a6b8 A) 8a8b8 B) 8a8b8 C) ab D) 8a6b3 3) Factor out the GCF from the polynomial. ) 7x8y8 + 3xy - 8xy A) 8(9x8y8 + xy - 6xy) B) xy(7x6y6 + 3y3-8x) C)8xy(9x6y6 + y3-6x) D) 8x(9x6y8 + y - 6xy) ) ) 1y3-6y + 1y A) 3y(7y - y + ) B) y(1y - 6y + 1) C)3(7y3 - y + y) D) 3y(7y3 - y + y) ) 6) s(t - 6) + 7(t - 6) A) (t - 6)(s + 7) B) (t - 6)(s - 7) C)(st - 6s) + (7t - ) D) 7s(t - 6) 6) 1

2 Factor the four-term polynomial by grouping. 7) 0x6 - x3-8x A) (x6 - )(x - ) B) (x3 + )(x3 + ) C)(0x3 + )(x3 + ) D) (x3 - )(x3 - ) 8) 6x xy - 1y A) (x- 1y)(6 + y) B) (x- 1)(6 + y) C)(y - 1)(6x + y) D) (y - 1)(x + 6) 7) 8) 9) x3 + 7x + x + 7 A) (7x + 7)(x + 1) B) (x + 1)(7x + 7) C)(x + 7)(x + 1) D) (x + 1)(x + 7) 9) 10) 8x - 0xy + 10xy - y A) (8x + y)(x - y) B) (x + y)(x - y) C)(x - y)(x - y) D) (x + )(x - ) 10) Multiply. 11) (x + 9y) A) 16x + 7xy + 81y B) x + 81y C)x + 7xy + 81y D) 16x + 81y 11) 1) (10a - 9) A) 100a - 180a + 81 B) 10a + 81 C)100a + 81 D) 10a - 180a ) (p + 8q)(p - 8q) A) p - 6q B) p - 16pq - 6q C)p + 16pq - 6q D) p - 16q 1) 13) 1) z 1-3 z 1) A) 1-9 z B) z - 9 z C)1-6 z D) 1-7 z - 9 z Determine whether the trinomial is a perfect square trinomial. 1) x - 9x + 81 A) Yes B) No 1) 16) 6x - 11xy + 9y A) Yes B) No 16) Factor the trinomial completely. 17) x - 1x + 1 A) (x + 1)(x - 1) B) (x + 1) C)(x - 1) D) prime 17)

3 18) 6x + 11x + 9 A) (6x + 1)(x + 9) B) (8x + 7) C)(8x - 7) D) (8x + 7)(8x - 7) 18) 19) xy + 0xy + 16 A) (xy + ) B) (xy + 1)(xy + 16) C)(xy + )(xy - ) D) (xy- ) 19) 0) x3 + 1x + 36x A) x(x + 6) B) x(x + 6)(x - 6) C)x(x - 6) D) prime 0) Factor the binomial completely. 1) x - 9 A) x + 7 x - 7 B) x - 7 C) x x D) x + 7 1) ) 36 - xy A) (6 + xy) B) (6 - xy) C)(6 - xy)(6 + xy) D) prime ) 3) 9x - 6y A) (7x + 8y)(7x - 8y) B) (7x - 8y) C)(7x + 8y) D) prime 3) ) 81xy - 16x A) x(9y + ) B) x(9y - ) C)x(9y + )(9y - ) D) prime ) ) (6x + y) - A) (9x + y - ) B) (9x + y + ) C)(9x + y + )(9x + y - ) D) prime polynomial ) Factor the trinomial completely. If the polynomial cannot be factored, write "prime." 6) x - x - 3 A) (x- )(x + 7) B) (x + )(x - 7) C)(x - 3)(x + 1) D) prime 6) 7) 3y + 1y + 16 A) (y + 9)(3y + ) B) 3(y + 9)(y + 8) C)(3y + 9)(y + 8) D) 3(y - 9)(y - 8) 7) Factor the polynomial by grouping. 8) 16x + 16x + 3x3 A) x(3x + )(x + 3) B) 3x(x + )(x + ) C)x(x + )(3x + ) D) prime 8) Factor the trinomial completely. 9) 11x + 1x + 11 A) (11x - 1)(x - 11) B) (11x + 1)(x + 11) C)(11x + 11)(x + 1) D) prime 9) 3

4 30) 8x + 17x - 1 A) (x + 3)(8x - 7) B) (x- 3)(8x + 7) C)(x - 7)(8x + 3) D) prime 30) 31) 9x - 6xy - 8y A) (9x + y)(x - y) B) (3x + y)(3x - y) C)(3x - y)(3x + y) D) prime 31) 3) 1y - y + 8 A) (3y + )(y + ) B) (1y + )(y + ) C)(3y - )(y - ) D) prime 3) 33) 108x + 63xy + 9y A) 9(3x + y)(x + y) B) 9(3x - y)(x - y) C)(7x + 9y)(x + y) D) prime 33) 3) 30x3-63x - 30x A) 3x(x - )(x + ) B) x(x - )(1x + 6) C)3(x - )(x + ) D) x(3x - 1)(x + ) 3) Solve the equation. 3) x(3x + ) = 3) A) 0, - 3 B) 3, C) 3, - D) 0, 3 36) x - 13x = -0 A) -, 8 B) 8, C) -,-8 D) -8, 8 36) 37) 8y + 30y + = 0 37) A), B) - 8, - 1 C), - D) -, - 38) (x + 1) = -x + (x - 3) A) 1, - B), 1, C), -1, - D) -1, 38) 39) (x- )(x + 13x + ) = 0 A) B), -7,-6 C) - D) -, 7, 6 39) 0) x3 - x = -x + A) -, B) -1, 1, - C)1, -, D) 0) Find the root. Assume that all variables represent nonnegative real numbers. 1) 6x8y16 A) 6.33xy B) 16xy C)xy D) not a real number 1)

5 Find the cube root. ) 3 x 1 16y6 ) A) x 3 6y3 B) x 6y C) 6y x D) x 36y 3) - 3-1xy36 A) x8y1 B) -xy1 C) x8y18 D) x8y1 3) Find the square root. Assume that all variables represent nonnegative real numbers. ) 0.9 A) B) 7 C) 0.07 D) 0.7 ) ) 6z18 ) A) 8z 9 B) 8z 9 C) 6z 9 D) 8z 16 Find the root. Assume that all variables represent nonnegative real numbers. 6) 6 x8 A) x 7 B) x 7 C) x7 D) 6 x 7 6) 7) 3 A) B) 3 C)3 D) not a real number 7) Multiply, and then simplify if possible. Assume all variables represent positive real numbers. 8) 3( ) A) B) C) D) ) 9) ( ) A) 0 B) C)10 + D) ) 0) ( )( ) A) B) C)73 19 D) )

6 1) ( )( 3 7-1) 1) A) 0 B) C) D) ) ( )( 7-10) A) 17 B) -3 C)7-7 D) 7-10 ) 3) ( 3x - 7 )( 3x - 7 7) A) 9x - 7 1x - 7 6x B) 3x - 7 1x - 7 6x C)3x - 7 1x - 7 6x + 9 D) 3x - 7 x ) ) ( + ) A) 8-3 B) C) D) ) Simplify. Assume that all variables represent positive real numbers. ) 3 79xy ) A) 9xy 3 xy B) 9xy xy C)3xy 3 xy D) 9xy 3 xy 6) xy A) 3xy 6 B) 3x 6y C)3xy 6 D) 3x 6y 6) 7) 3 6 7) A) B) C) 3 D) 3 8) 10 x y17 8) A) xy3 x y B) xy x3 y C)y3 x y D) y x y 9) 3 81x 17y1 3 3x 8y 9) A) 6x3y B) 3xy3 3 xy C)3x3y3 3 y D) 9xy 3 y 60) 3-7a11b10 60) A) 3ab 3 ab B) 3 a10b11 C)3ab 3 a3b3 D) -3a3b3 3 ab 61) 3 108a b6 3 a 61) A) 3ab 3 3ab B) 3ab 3 3a C)3ab D) 3ab 6

7 Add or subtract. Assume all variables represent positive real numbers. 6) x - 0x + 6 0x A) x 63 B) 11x 63 C)11x D) x 6) 63) A) B) C) D) ) 6) A) B) C)17 6 D) ) 6) 3 x3y13 + xy 3 8y10 6) A) xy 3 y B) xy 3 8y C)6xy 3 y D) 6 xy 3 y 66) ) A) 3 3 B) C)0 3 9 D) Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. 67) a 3 67) A) a B) a a C) a3 a D) a a 68) ) A) B) C) D) ) 9-69) A) B) 9 - C) D) ) 33x 70) A) x 7x B) 8x 9x C) 33x 33x D) 7x 9x 71) A) B) + 6 C) 6 - D) ) 7

8 7) ) A) B) C) D) ) 7 73) A) 1 B) 7 C) 1 D) 1 Use the properties of exponents to simplify. Write with positive exponents. 7) (r1/9 s1/9) A) r1/81s1/81 B) rs C) r1/18s1/18 D) r/9s/9 7) 7) x-1/y/8 (xy-) -1/ 7) A) x1/y1/8 B) y 1/8 x1/ C) x 1/ y1/8 D) - x 1/ y1/8 Use rational exponents to write as a single radical expression. 76) 1 x 3 x 76) A) x3 B) x7 C) 1 x3 D) x3 Use rational exponents to simplify. Assume that all variables represent positive real numbers. 77) ( 10 xy ) 77) A) xy B) (xy) C)xy D) xy Write with positive exponents. Simplify if possible. 78) (- 1) -/3 A) 1 B) - C) - 1 D) ) 79) 16-/ A) 1 3 B) 3 79) C) D) not a real number Use radical notation to write the expression. Simplify if possible. 8 /3 80) 7 80) A) 3 B) 9 C) - 9 D) 13 8

9 Answer Key Testname: MATH10006_FINAL_EXAM_STUDYGUIDE 1) C ) C 3) D ) C ) A 6) A 7) D 8) B 9) D 10) B 11) A 1) A 13) A 1) A 1) B 16) A 17) D 18) B 19) A 0) A 1) A ) C 3) A ) D ) C 6) D 7) B 8) C 9) B 30) A 31) B 3) C 33) A 3) A 3) C 36) B 37) D 38) D 39) B 0) B 1) C ) B 3) A ) D ) A 6) C 7) A 8) C 9) C 0) A 9

10 Answer Key Testname: MATH10006_FINAL_EXAM_STUDYGUIDE 1) C ) B 3) B ) B ) D 6) B 7) C 8) C 9) C 60) D 61) D 6) C 63) A 6) C 6) D 66) D 67) B 68) D 69) C 70) D 71) C 7) B 73) D 7) D 7) C 76) D 77) B 78) A 79) A 80) B 10