Review Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the order of operations to find the value of the expression. 1) -7(-9) - 4(-2) 1) A) 71 B) -118 C) -55 D) 55 2) 3-6(-2 + 4) 2) A) 19 B) -9 C) 39 D) -6 3) 6-3(9-7) - 7 3) A) -7 B) 13 C) 5 D) -1 4) 4 2-8 2 2 4-4 4) A) 12 B) 4 C) 0 D) -2 5) 5 2-25 5 2 + 1 5) A) 1 B) 14 C) 0 D) 16 Solve and check the equation. 6) 7y - 2 = -8 + 5y 6) A) - 6 1 B) - 3 C) D) - 1 5 3 3 7) 7x - (5x - 1) = 2 7) 1 A) B) - 1 1 C) D) - 1 12 12 2 2 8) 5(2y - 4) = 9(y + 2) 8) A) {-2} B) {38} C) {2} D) {3} 9) 3(2x - 9) - 4 = 3(x - 4) + (-1) 9) A) {8} B) {1} C) {3} D) {6} 10) -4.8x + 1.4 = -9.4-1.2x 10) A) {-14} B) {2.5} C) {3} D) {2.3} 11) 0.50x - 0.20(70 + x) = 0.10(70) 11) A) {60} B) {70} C) {35} D) {80} 12) 3x - 6 + {9x - [6(x + 4) - 9]} = 9(x + 3) 12) 22 A) - 22 B) 6 C) D) - 18 3 1
Solve the inequality and graph the solution set. 13) 7x - 4 2x + 11 13) A) {x x 3} B) {x x > 4} C) {x x -3} D) {x x 4} 14) -8x + 4-5x < 2-15x + 8 14) A) {x x < 7} B) {x x < 3} C) {x x > 7} D) {x x > 3} 2
15) 25x + 30 > 5(4x + 1) 15) A) {x x > -5} B) {x x -5} C) {x x < -5} D) {x x -5} 16) 2x - 2 < 3(x - 9) 16) A) {x x < 29} B) {x x > -29} C) {x x < -25} D) {x x > 25} 3
17) 9-8(x - 2) < 3(2-4x) 17) A) {x x < - 19 2 } B) {x x > - 19 2 } C) {x x < - 19 4 } D) {x x > - 19 4 } 18) -3(6y + 3) < -21y - 18 18) A) {y y < -3} B) {y y -3} C) {y y -3} D) {y y > -3} 4
19) -14x + 2-2(6x + 6) 19) A) {x x < 7} B) {x x > 7} C) {x x 7} D) {x x 7} Find the indicated sum. 20) 5 i = 1 (i - 9) 20) A) -12 B) -26 C) -4 D) -30 21) 6 (2i - 5) 21) i = 3 A) 16 B) 21 C) 13 D) 15 22) 4 i = 1 1 4i A) 1 16 B) 11 24 C) 5 16 D) 25 48 22) 23) 6 i = 3 1 i + 5 A) 1691 3960 B) 38 C) 200 81 D) - 17 12 23) 24) 4 i = 1 2 i 24) A) 20 B) 18 C) 14 D) 30 5
25) 5 i = 3 (i 2 + 1) 25) A) 15 B) 53 C) 27 D) 60 26) 4 k = 2 k(k - 5) 26) A) 3 B) -10 C) -20 D) -16 Find the indicated function value. 27) Find f(4) when f(x) = 3x 2-2x - 3. 27) A) 43 B) 5 C) 37 D) 53 28) Find f(2) when f(x) = 2. 28) A) -10 B) 0 C) -5 D) 2 29) Find f(-1) when f(x) = x2-2 x 3 + 7x. 29) A) 1 B) - 1 6 C) 1 8 D) - 1 8 30) Find f(4) when f(x) = x3-8 A) 8 13 x 2-3. 30) B) 56 13 C) 64 13 D) 7 2 31) Find g(a + 1) when g(x) = 1 x - 5. 31) 2 A) a + 9 2 B) a - 8 2 C) a - 19 2 D) a - 9 2 32) Find r(a + 3) when r(x) = 6 x + 8. 32) A) 6 a + 8 + 6 11 B) 9 a + 8 C) 6 a + 11 D) 3 4 a + 9 4 Find the slope of the line that goes through the given points. 33) (-9, -3), (-8, 2) 33) A) - 5 B) 1 17 C) 5 D) 1 5 34) (9, -6), (-9, -6) 34) A) 0 B) 12 C) 2 D) Undefined 0 3 6
35) (-7, -9), (-11, 5) 35) A) 2 9 B) 7 2 C) - 7 2 D) - 2 7 36) (-9, -5), (3, -5) 36) A) -2 B) 1 C) 0 D) 2 37) ( 3 5, -2) and ( 3, 1) 37) 5 A) 3 B) 1 3 C) - 1 D) Undefined 7
Use intercepts and a checkpoint to graph the linear function. 38) x + 3y = 6 38) A) (0, 2), (-2, 0) B) (0, 2), (-6, 0) C) (0, -6), (6, 0) D) (0, 2), (6, 0) 8
39) 2x - 8y = 6 39) A) (0, 3), - 3 4, 0 B) 0, - 3 4, (3, 0) C) 0, - 3 4, (-3, 0) D) 0, 3 4, (-3, 0) 9
40) 4x - 8y = 16 40) A) (0, 4), (-2, 0) B) (0, -2), (4, 0) C) (0, -2), (-4, 0) D) (0, -4), (2, 0) 10
41) -5x - 20y = 20 41) A) (0, -1), (-4, 0) B) (0, -1), (4, 0) C) (0, 4), (1, 0) D) (0, -4), (-1, 0) 11
42) y + 1 2 x = 4 42) A) (0, 4), (-8, 0) B) (0, 4), (8, 0) C) (0, 4), (-4, 0) D) (0, -8), (8, 0) Write the point-slope form of the line satisfying the conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation in function notation. 43) Slope = -8, passing through (3, 3) 43) A) f(x) = 8x - 27 B) f(x) = - 1 8 x - 27 8 C) f(x) = - 8x + 27 D) f(x) = - 8x - 27 12
44) Slope = 5, passing through (2, -2) 44) 9 A) f(x) = - 9 5 x - 28 5 C) f(x) = - 5 9 x - 28 9 B) f(x) = 5 9 x - 28 9 D) f(x) = - 5 9 x + 28 9 45) Slope = 2, passing through (0, 5) 45) 5 A) f(x) = 2 5 x - 5 B) f(x) = - 2 5 x - 5 C) f(x) = 5 2 x + 25 2 D) f(x) = 2 5 x + 5 46) Slope = -3, passing through (2, 4) 46) A) f(x) = - 3x + 10 B) f(x) = - 1 3 x - 10 3 C) f(x) = - 3x - 10 D) f(x) = 3x - 10 47) Passing through (-2, -22) and (8, 68) 47) A) f(x) = -9x - 40 B) f(x) = - 1 9 x - 200 9 C) f(x) = 9x - 4 D) f(x) = 1 9 x - 196 9 48) Passing through (8, -19) and (6, -13) 48) A) f(x) = 3x - 43 B) f(x) = - 1 3 x - 49 3 C) f(x) = -3x + 5 D) f(x) = 1 3 x - 65 3 49) Passing through (5, -25) and (-9, 17) 49) A) f(x) = 1 3 x - 80 B) f(x) = - 1 3 3 x - 70 3 C) f(x) = 3x - 40 D) f(x) = -3x - 10 Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 50) A B' 50) A) {t, v, x} B) {q, s, t, u, v, w, x, y} C) {u, w} D) {r, s, t, u, v, w, x, z} 51) C' A' 51) A) {q, s, u, v, w, x, y, z} B) {r, t} C) {q, r, s, t, u, v, x, z} D) {w, y} 13
52) (A C)' 52) A) {w, y} B) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z} D) {q, r, s, t, u, v, x, z} 53) (A B)' 53) A) {t, v, x} B) {r, t, v, x} C) {r, s, t, u, v, w, x, z} D) {s, u, w} 54) C' A' 54) A) {s, t} B) {q, s, u, v, w, x, y, z} C) {q, r, s, t, u, v, x, z} D) {w, y} 55) C 55) A) {q, s, y, z} B) {q, s, u, w, y} C) { } D) {v, w, x, y, z} 56) B U 56) A) {q, s, u, w, y} B) {v, w, x, y, z} C) {q, r, s, t, u, v, w, x, y, z} D) {q, s, y, z} 57) A B' 57) A) {q, s, t, u, v, w, x, y} B) {r, s, t, u, v, w, x, z} C) {t, v, x} D) {u, w} 58) (A B)' 58) A) {q, s, t, u, v, w, x, y} B) {t, v, x} C) {s, u, w} D) {r, t, u, v, w, x, z} 59) C' A' 59) A) {w, y} B) {s, t} C) {q, s, u, v, w, x, y, z} D) {q, r, s, t, u, v, x, z} 60) A' 60) A) {q, s, y, z} B) {q, r, s, t, u, v, w, x, y, z} C) {s, u, w, y} D) {r, t, v, x, z} 61) (A C)' 61) A) {q, r, s, t, u, v, x, z} B) {w, y} C) {q, s, y, z} D) {q, r, s, t, u, v, w, x, y, z} Use a Venn diagram to answer the question. 62) At East Zone University (EZU) there are 730 students taking College Algebra or Calculus. 427 are taking College Algebra, 366 are taking Calculus, and 63 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? A) 364 B) 667 C) 303 D) 301 63) At East Zone University (EZU) there are 565 students taking College Algebra or Calculus. 327 are taking College Algebra, 266 are taking Calculus, and 28 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra? A) 537 B) 299 C) 238 D) 271 62) 63) 14
64) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 400 responses with the following results: 120 were interested in an interview show and a documentary, but not reruns; 16 were interested in an interview show and reruns, but not a documentary; 56 were interested in reruns but not documentaries or interviews; 96 were interested in an interview show but not a documentary; 40 were interested in a documentary and reruns; 24 were interested in an interview show and reruns; 32 were interested in none of the three. How many are interested in exactly one kind of show? A) 172 B) 192 C) 182 D) 202 64) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 65) There are 777,859 physicians in the United States. 177,030 are women. 33,947 physicians have cardiology as their specialty. 6,817 women physicians specialize in cardiology. 65) Identify the Venn diagram in which U is the set of all physicians, W is the set of all women physicians, and C is the set of all U.S. physicians specializing in cardiology. Fill in each of the four regions of the Venn diagram with the number of physicians who belong to that region. Use your Venn diagram to answer the questions. How many physicians in the United States are there who are men specializing in cardiology? How many male physicians in the United States do not specialize in cardiology? 15
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Complete the truth table by filling in the required columns. 66) p ~ q 66) p q ~ q p ~ q T T T F F T F F A) p q ~ q p ~ q T T F F T F T T F T F F F F T F B) p q ~ q p ~ q T T F F T F T T F T T F F F T F C) p q ~ q p ~ q T T F F T F T T F T F F F F T T D) p q ~ q p ~ q T T F T T F T T F T F F F F T F 67) ~ p ~ q 67) p q ~ p ~ q ~ p ~ q T T T F F T F F A) p q ~ p ~ q ~ p ~ q T T F F F T F F F T F T F F T F T B) p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F F F F T T F C) p q ~ p ~ q ~ p ~ q T T F F F T F F T F F T T F F F F D) p q ~ p ~ q ~ p ~ q T T F F F T F F T T F T T F T F F 16
Construct a truth table for the statement. 68) (p t) (~p ~t) 68) A) p t (p t) (~p ~t) T F F F T F C) p t (p t) (~p ~t) T T F T F F F T T F F T B) p t (p t) (~p ~t) T F F F T F F F T D) p t (p t) (~p ~t) T F T F T T F F F 69) ~ p ~ q 69) A) B) p q ~ p ~ q ~ p ~ q p q ~ p ~ q ~ p ~ q T T F F T T T F F F T F F T T T F F T T F T T F F F T T F F F F F F C) p q ~ p ~ q ~ p ~ q T T F T T T F F F T F T F F T F F D) p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F F F F 70) ~(q ~ p) 70) A) B) p q ~ p q ~ p ~(q ~ p) p q ~ p q ~ p ~(q ~ p) T T F F T T T F F T T F F F T T F F T F F F F F F F T T F F F T T F C) p q ~ p q ~ p ~(q ~ p) T T F T F T F F F T F T T F T F F T F T D) p q ~ p q ~ p ~(q ~ p) T T F F T T F F T F F T F F T T F 17
71) ~t (~t p) 71) A) t p ~t (~t p) T F F F T T F F F C) t p ~t (~t p) T T F T F F F T T F F F B) t p ~t (~t p) T F T F T T F F F D) t p ~t (~t p) T F T F T T F F T 72) (q ~p) (q ~p) 72) A) q p (q ~p) (q ~p) T F T F T F F F F C) q p (q ~p) (q ~p) T T F T F T F T T F F T B) q p (q ~p) (q ~p) T T F T F F F F F F T T D) q p (q ~p) (q ~p) T F T F T F F F T 73) ~(p q) (p ~q) 73) A) p q ~(p q) (p ~q) T F F F T F F F T C) p q ~(p q) (p ~q) T F F F T T F F T B) p q ~(p q) (p ~q) T F T F T T F F T D) p q ~(p q) (p ~q) T F F F T F F F F 74) ~(p q) ~(p q) 74) A) p q ~(p q) ~(p q) T F F F T F F F T C) p q ~(p q) ~(p q) T T F T F T F T T F F T B) p q ~(p q) ~(p q) T T F T F F F T F F F T D) p q ~(p q) ~(p q) T F T F T T F F T 18
Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 75) 8, 5, 4, 11, 6, 12, 9, 4 75) A) 7.86 B) 6.88 C) 7.38 D) 8.43 76) 78, 78, 87, 71, 91, 78 76) A) 67.5 B) 80.5 C) 81 D) 96.6 77) 5, 8.1, 1.6, 6, 5, 4.1, 5, 3.1, 3.1, 3.6 77) A) 3.46 B) 4.15 C) 4.46 D) 4.96 Find the median for the group of data items. 78) 11, 8, 4, 0, 1, 1, 1, 0, 0 78) A) 1 B) 4 C) 5 D) 0 79) 97, 97, 91, 47, 72, 97 79) A) 94 B) 91 C) 47 D) 97 80) 1.2, 2.1, 1.6, 2.5, 1.2, 2.1, 1.2, 8.4, 8.4, 2 80) A) 2 B) 2.05 C) 2.1 D) 1.2 Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 81) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting 81) a 7. A) 1 B) 7 C) 7 6 D) 0 82) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card. 82) A) 1 13 B) 3 52 C) 3 26 D) 3 13 83) A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss. 83) A) 1 2 B) 3 4 C) 1 D) 1 4 84) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 9. 84) A) 9 6 B) 0 C) 9 D) 1 85) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 6. 85) A) 0 B) 1 C) 6 D) 1 6 19
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. In the following problem: a. Put the equation in slope-intercept form. b. Identify the slope and y-intercept. c. Graph the line. 86) 2y + x = 0 86) 87) 5y = 8x 87) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 88) 1 {1, 3, 5, 7, 9} 88) A) True B) False 89) 19 {2, 4, 6,..., 20} 89) A) True B) False Fill in the blank with either or to make the statement true. 90) Saskatchewan the set of states in the United States 90) A) B) 20
Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 91) p: Spartacus is a film. 91) q: Rambo is a film. Spartacus is a film and Rambo is a film. A) p ~ q B) p q C) p q D) p q 92) p: Tosca is an opera. q: Carmen is an opera. Tosca is an opera and Carmen is not an opera. A) p ~ q B) p q C) p ~ q D) p ~ q 93) p: They set the alarm. q: They get up on time. They set the alarm or they get up on time. A) p q B) p q C) p ~ q D) p q 92) 93) Simplify the algebraic expression. 94) -4(x + y) 94) A) -4x - 4y B) -4x + 4y C) -4x + y D) -4xy 95) (8y + 10) - (5y - 4) 95) A) 3y + 6 B) 13y + 14 C) 3y + 14 D) 3y - 14 96) 4(8x - 4) - 3(x - 1) 96) A) 29x - 5 B) 29x - 13 C) 29x - 19 D) 20x - 13 97) -6(2x + 10) + 5(7x + 10) 97) A) 23x + 10 B) -72x C) -4x + 4 D) 23x - 10 98) 5[3(7x + 5) - 3(5x + 6)] 98) A) 30x + 165 B) 30x - 5 C) 90x - 3 D) 30x - 15 Evaluate the algebraic expression for the given value(s) of the variable(s). 99) x 2-8x ; x = 9 99) A) x 2-72 B) 9 C) -54 D) 73 100) (x + 2y)2 ; x = 4, y = 2 100) A) 8 B) 36 C) 16 D) 64 21
Answer Key Testname: REVIEW FINAL EXAM PRESTAT 1) A 2) B 3) A 4) B 5) D 6) B 7) C 8) B 9) D 10) C 11) B 12) A 13) A 14) B 15) A 16) D 17) C 18) A 19) C 20) D 21) A 22) D 23) A 24) D 25) B 26) D 27) C 28) D 29) C 30) B 31) D 32) C 33) C 34) A 35) C 36) C 37) D 38) D 39) B 40) B 41) A 42) B 43) C 44) B 45) D 46) A 47) C 48) C 49) D 50) C 22
Answer Key Testname: REVIEW FINAL EXAM PRESTAT 51) B 52) D 53) B 54) C 55) D 56) C 57) D 58) D 59) D 60) D 61) A 62) A 63) C 64) B 65) 27,130 male physicians in the United States specialize in cardiology. 573,699 male physicians in the United States do not specialize in cardiology. 66) A 67) D 68) B 69) A 70) B 71) B 72) A 73) B 74) A 75) C 76) B 77) C 78) A 79) A 80) B 81) D 82) D 83) A 84) B 85) D 23
Answer Key Testname: REVIEW FINAL EXAM PRESTAT 86) a. y = - 1 2 x b. slope = - 1 2, y-intercept = 0 c. 87) a. y = 8 5 x b. slope = 8 5, y-intercept = 0 c. 88) A 89) B 90) B 91) B 92) D 93) B 94) A 95) C 96) B 97) D 98) D 99) B 24
Answer Key Testname: REVIEW FINAL EXAM PRESTAT 100) D 25