Exam (elaborations) TEST BANK FOR PRECALCULUS Functions and Graphs BERNARD KOLMAN, ARNOLD SHAPIRO AND MICHAEL L. LEVITAN (Auth.)

TEST BANK FOR PRECALCULUS Functions and Graphs BERNARD KOLMAN, ARNOLD SHAPIRO AND MICHAEL L. LEVITAN PRECALCULUS: FUNCTIONS & GRAPHS Bernard Kolman & Arnold Shapiro by MICHAEL L. LEVITAN Villanova University Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers) Orlando San Diego San Francisco New York London Toronto Montreal Sydney Toyko Säo Paulo CHAPTER TEST 1A 1. Write explicitly the elements of the set of all integers 73 such that -2 n £ 3. 2. On the real number line, draw the graph of the set of real numbers x satisfying -2 x £ 3. In Problems 3 - 5 evaluate the following: 3. '* " y* when x = -3 and y = 2 4. 4 - 52 + 7(3 + 1) I 1 5 ^JU 5 6 In Problems 6 - 7 perform the indicated operations and simplify: 6. (x - 4x2 + 3) - (2 - 5x + 8x2) 7. (x - 3y) (y - 3x) In Problems 8 - 9 factor completely using only integer coefficients. 8. 4x3 - 9* 9. 16(y + 1) - x2(y + 1)3 In Problems 1 0 - 1 3 simplify: 10. 11. 12. 13. Write the following as the ratio of two polynomials: 4(x + 1)2 - 3x~2 sL· y 2 -3 • 6y ■ 2y 2x + 1 3 + 2_ _ X 2 X 2 - 7 Λ - 8 5 x - y2 - I7 "5 Ja 16 JiL In Problems 14 - 15 simplify: 14. 8 /3 »· Φ* 16. Rationalize the denominator: 5 1 CHAPTER TEST 1A 17. Simplify and combine: /TF + Λ8" - 2 V§T 18. Write the following in the form a + bi: (3 + li) (2 - i) 19. Find the values of x satisfying the inequality 2x + 3 5 and draw the solution set on the real line. 20. Find the set of x such that: x2 - 6x + 8 ^ 0 2 CHAPTER TEST 1B 1. Write explicitly the elements of the set of all integers n such that n 4.1 and x ^ 7.5. 2. On the real number line, draw the graph of the set of real numbers x satisfying x 4.1 and x ^ 7.5. - In Problems 3 - 5 evaluate the following: 3. xy when x = 2 and y = -1 Ixl - M 4. 9 + 4(32 - 5) 5. ^ — i 1-i In Problems 6 - 7 perform the indicated operations and simplify: 6. 2(3xy + 4t - 5) + 3(7 - xy + t) 7. (x2 + 2x + 3) Cx - 1] In Problems 8 - 9 factor completely using only integer coefficients. 8. xk - 6x2 + 5 9. 3(3z + 6) - z2(z + 2) In Problems 1 0 - 1 3 simplify: a2 + 2ab + b2 A a2 - 2?2 2a2 - a£ - b2 ' 2a2 + 3a2 + b2 n 2x . 4x + 1 x - 1 x + 1 12. 2 Χ + Γ 4 Τ i 3x x - 1 13. Write the following as the ratio of two polynomials: x2 - 5x~3 + Ar 3 CHAPTER TEST 1B In Problems 14-15 simplify: M "3/2 15. (8) 16. Rationalize the denominator: Λ- 2 17. Simplify and combine: -2/32 - /Ϊ8" + ι/ξδ" 18. Write the following in the form a + bi: (4 - 7i) (2 + i) 19. Find the values of x satisfying the inequality -3x + 2 1 and draw the solution set on the real line. 20. Find the set of x such that: x2 - 8x + 15 0 4 CHAPTER TEST IC 1. Write explicitly the elements of the set of all positive integers n such that n. ^ A. 2. On the real number line, draw the graph of the set of positive numbers x satisfying x ^ A. 1 , In Problems 3 - 5 evaluate the following: 3. .slffc ~ 5l when s = 3 and t = 2 - |-A| A. 7 v 4 + 9(52) li - I '5 10 In Problems 6-7 perform the indicated operations and simplify: 6. (9t - 5t2 + s - st) - (125 + st2 - i*s - st + 9t) 7. (z + 1)2(2z + 3) In Problems 8 - 9 factor completely using only integer coefficients. 8. 3x2 + Ax - 20 9. w2x2(y + 3) + 8t2(-6 - 2y) In Problems 1 0 - 1 3 simplify: m g2 " z " 6 · z2 * z " 2 lu# z* - 1 T z2 + Az + 3 11 * + 1 2(x - 1) 11 . , + rx - A 3 - x 1 1 12. x " x + 1 3 _ 1 x + 1 x 13. Write the following as the ratio of two polynomials: 5 CHAPTER TEST 1C In Problems 14 - 15 simplify 14. (64) k »· UP 16. Rationalize the denominator: 6 3/Γ+ 5 17. Simplify and combine: 21/3 + 2Va + 2? / 3 18. Write the following in the form a + bi: (3 - i) (2 + i) 19. Find the values of x satisfying the inequality 5x - 1 * -2 and draw the solution set on the real line. 20. Find the set of x such that x2 + 3x - 4 0 6 CHAPTER TEST 1D 1. Write explicitly the elements of the set of all natural numbers n such that 1.4 n 3.8. 2. On the real number line, draw the graph of the set of real numbers x such that 1.4 x ^ 3.8. In Problems 3 - 5 evaluate the following: 3# st - t when s = _3 a n d t = 5 t t - s I 4. 6 - 4 T (2 + 2 · 3) JL 1 5. 10 " 7 _L 1 14 + 5 In Problems 6 - 7 perform the indicated operations and simplify: 6. (x + 9x2 + 5x3 - 4) - 2(4 + 8x - 9y) 7. (-3w - 1) (-2* + 1) In Problems 8 - 9 factor completely using only integer coefficients. 8. 2x2 - 3x - 9 9. 4x yz3 + 3yz x - yz In Problems 10-13 simplify: 4z2 + 3z - 1 A 4z2 - z z + 2z + 1 z - z - 2 11. 2 3x_ 2x2 + 3x x + 1 A x 12. * + x2 - 1 7 CHAPTER TEST ID 13. Write the following as the ratio of two polynomials: 2x3 - 3X-1 x-2 + 1 In Problems 14 - 15 simplify: 14. (32) /s 16. Rationalize the denominator: *2 -y x + /y 17. Simplify and combine: 1/ 6/ 1 1/ 3/5 + 3A _ 3 /5 18. Write the following in the form a + bi: (4 - 2i) (6 - i) 19. Find the values of x satisfying the inequality 3x + 2 * -7 and draw the solution set on the real line. 20. Find the set of x such that x2 + 4x - 12 * 0 8 CHAPTER TEST 1E 1. Write explicitly the elements of the set of all integers