TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

Transcription

1 MATH COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #1 - FALL DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Mark the statement as true or false. 1) Ever rational number is an integer. 2) Some rational numbers are irrational. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. 3) (7n 7 + 7n 4 + 4) + (7n 7-9n 4 - ) A) 11n 7-2n B) 14-2n 7-1n 4 C) 14n 7-2n 4-1 D) 11n 11 4) (7n n 4 + 2) - (-9n 4 + 4n ) A) 3n n B) 3n n 4-11 C) 3n n D) 20n 11 ) ( ) + ( ) A) B) C) D) Find the product. 6) ( + 6)(- + 9) A) B) C) D) ) ( + )( + ) A) B) C) D) ) (3-7)(3 + 7) A) B) C) D) ) (2p - 1)(4p2 + 2p + 1) Solve the problem. A) 4p 3-1 B) 8p 3-1 C) 8p D) 8p 3 + 6p 2-1 ) The polnomial gives the approimate total earnings of a compan, in millions of dollars, where = 0 corresponds to 1996, = 1 corresponds to 1997, and so on. This model is valid for the ears from 1996 to Determine the earnings for A) $2.16 million B) $2.03 million C) $2.19 million D) $2.33 million 11) The polnomial gives the predicted sales volume of a compan, in millions of items, where is the number of ears from now. Determine the predicted sales 11 ears from now. A) 4.96 million B) 7.63 million C) million D) 2.89 million Factor out the greatest common factor. 12) 12m 7-21m - 18m 2 A) 3m 2 (4m - 7m 3-6) B) m 2 (12m - 21m 3-18) C) No common factor D) 3(4m 7-7m - 6m 2 )

2 13) A) ( ) B) No common factor C) 18( ) D) 18 2 ( ) 14) m 2-17r 3 Factor completel. A) 3(3m 2 - r 3 ) B) No common factor C) 2(m 2 + 8r 3 ) D) m 2 ( - 17m) 1) A) ( + 7)( - 6) B) ( + 1)( - 42) C) ( + 6)( - 7) D) Cannot be factored factored 16) A) ( - )( + 7) B) ( - 3)( + 1) C) ( + )( - 7) D) Cannot be factored 17) A) 4( - 2)( + 3) B) (4 + 8)( - 3) C) 4( + 2)( - 3) D) Cannot be factored 18) A) (7 + 3)2 B) (7 + 3)(7-3) C) (7-3)2 D) Cannot be factored 19) A) ( + 8)2 B) ( + 8)( - 8) C) ( - 8)2 D) Cannot be factored 20) 3-8 A) ( - 2)(2 + 4) B) ( + 8)(2-1) C) ( + 2)( ) D) ( - 2)( ) 21) 12a3-8b3 A) (a - 2b)(2a2 + 4b2) B) (a + 2b2)(2a2 - ab + 4b2) C) (a - 2b)(2a2 + ab + 4b2) D) (12a - 2b)(a2 + ab + 4b2) Use factoring to solve the equation. 22) ( + 6)( - 18) = 0 A) 6, -18 B) -6, 18 C) 18, 6 D) -18, 6 23) = 4 A) 11 B) 2, -2 C), -9 D) 9, 24) r r + 36 = 14 A) , 6-14 B) , C) 8 D) 14, 14 2) = 0 A), 2, 3 B) 0, 2, 3 C) -2, -3 D) 2, 3

3 Solve b the square-root propert. 26) ( - 3) 2 = 49 A) 2 B), -4 C) -4, - D) 7, -7 27) (r + 3)2 = 17 A) , 3-17 B) , C) 17, 17 D) 14 Use the quadratic formula to solve the equation. 28) 2m2 + 8m + 3 = 0-8 ± A) 2 B) -4 ± 2 C) -4 ± 4 D) -4 ± ) = ± 31 A) 3 B) - ± 19 3 C) - ± 19 3 D) - ± ) 2 - = -6 A) -7, -8 B) 1, 6 C) 7, 8 D) No real number solutions Use the discriminant to determine the number of real solutions of the equation. 31) s2 + 7s - 8 = 0 A) 1 B) 2 C) No real solutions 32) t 2-12t + 36 = 0 A) No real solutions B) 2 C) 1 33) w 2 + 2w + 7 = 0 A) 2 B) No real solutions C) 1 Solve the problem. 34) Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 1 mi, the distance between the cars was mi more than the distance traveled b the car heading east. How far had the eastbound car traveled? A) 30 mi B) 20 mi C) 1 mi D) 2 mi 3) A picture is to be mounted on a piece of matte board inches b 2 inches so that there is an even amount of matting all around the picture. How wide will the border be if the area of the mounted picture is 344 square inches? A) 6 in. B) 6. in. C) in. D) 4 in. Determine whether the given ordered pair is a solution of the given equation. 36) 3 + = 18; (, 3) A) No B) Yes 37) 2 - = 18; (4, 2) A) No B) Yes 38) = -21; (4, -1) A) Yes B) No 39) = 22; (1, -3) A) Yes B) No

4 Graph the linear equation. 40) -2 = - 8 A) B) C) D) ) - 2 = A) B) C) D)

5 42) 12 = 2-14 A) B) C) D) ) + 2 = 0 A) B) C) D)

6 44) = -3 A) B) C) D) Give the -intercepts and -intercepts of the graph. 4) A) -intercept: -6; -intercept: -1 B) -intercept: -1; -intercept: -6 C) -intercept: 6; -intercept: 1 D) -intercept: 1; -intercept: 6 46) A) -intercept: 6; -intercept: -2 B) -intercept: -2; -intercept: 6 C) -intercept: 2; -intercept: -6 D) -intercept: -6; -intercept: 2 Find the -intercepts and -intercepts of the graph of the equation. 47) 2 + = -4 A) -intercept: -6; -intercept: 8 B) -intercept: -4; -intercept: -2 C) -intercept: 8; -intercept: -6 D) -intercept: -2; -intercept: -4

7 48) -2 + = -6 A) -intercept: -8; -intercept: -1 B) -intercept: -6; -intercept: 3 C) -intercept: -1; -intercept: -8 D) -intercept: 3; -intercept: -6 Solve the problem. 49) Craft Bill's Cool Car Sales opened as a used car sales lot in The graph shows the number of cars sold as a function of time. What is the approimate number of cars sold in 1993? A) 30 B) 400 C) 0 D) 00 0) Big "D" Sales Month Which month in 1989 had the lowest sales? A) Month 2 B) Month 6 C) Month 8 D) Month 3 1) The height h in feet of a projectile thrown upward from the roof of a building after time t seconds is shown in the graph below. How high will the projectile be after 3.3 s? 600 h t A) 600 ft B) 40 ft C) 0 ft D) 00 ft Find the slope of the line, if it is defined. 2) Through (9, -2) and (7, 4) A) 2 B) 6 C) -3 D) 3 3) Through (1, -3) and (6, ) A) Undefined B) 1 3 C) 2 D) 1 3

8 4) Through (-1, -3) and (-1, -9) A) 3 B) 2 C) Undefined D) -6 ) Through (9, 4) and (-7, 4) A) 3 B) 4 C) 12 D) 0 Write an equation in slope-intercept form of a line satisfing the given conditions. 6) m = ; b = 43 7 A) = B) = C) = D) = ) Slope - 17 ; -intercept 6 3 A) = B) = C) = D) = Find the slope and the -intercept of the line. 8) = 18 A) m = ; b = 4 B) m = 4 3 ; b = 9 2 C) m = 3 4 ; b = 18 D) m = ; b = 9 2 9) = A) m = 1; b = 0 B) m = 0; b = C) m = ; b = 0 D) m = 1 ; b = 60) + = 2 A) m = -1; b = 2 B) m = 2; b = 0 C) m = 1; b = -2 D) m = 0; b = -1 Identif whether the slope is positive, negative, zero, or undefined. 61) A) Undefined B) Positive C) Negative D) Zero 62) A) Undefined B) Zero C) Positive D) Negative

9 63) A) Undefined B) Positive C) Negative D) Zero 64) A) Zero B) Undefined C) Positive D) Negative Decide whether the pair of lines is parallel, perpendicular, or neither. 6) 3-6 = = 20 A) Parallel B) Neither C) Perpendicular 66) = = 18 A) Parallel B) Neither C) Perpendicular 67) The line through (-20, ) and (-4, 7) and the line through (-, ) and (7, 4) A) Neither B) Perpendicular C) Parallel Find an equation of the the line satisfing the given conditions. 68) Through (3, 3); m = - 9 A) + 9 = 42 B) + 9 = -42 C) 9 + = -42 D) - 9 = 42 69) Through (0, 2); m = 3 2 A) 3-2 = 4 B) = -4 C) 2-3 = -4 D) 3-2 = -4 70) Through (-6, -); m = 0 A) = 0 B) = - C) = -6 D) -6 - = 0 71) Through (4, ); undefined slope A) 4 + = 0 B) = C) + 4 = 0 D) = 4 Write an equation in standard form for a line passing through the pair of points. 72) (-4, ) and (0, -2) A) 7-4 = 8 B) 9-2 = -4 C) -7-4 = 8 D) = -4

10 Find an equation of the the line satisfing the given conditions. 73) Through the origin with slope 7 A) = -7 B) = 7 C) = 7 D) = 7 74) Through (-2, -9) and vertical A) = -2 B) = -2 C) = 9 D) = 2 7) Through (7, 2); perpendicular to = 46 A) 4-9 = B) = C) 9-4 = 1 D) 9-4 = 76) Through (7, 2); parallel to 2 + = -1 A) 2 - = 24 B) 7 + = -1 C) + 2 = 2 D) 2 + = 24 Solve the problem. 77) Let C() = be the cost to manufacture items. Find the average cost per item to produce 30 items. A) $2190 B) $33 C) $237 D) $ ) The cost of manufacturing a molded part is related to the quantit of part produced during a production run. When 0 parts are produced, the cost is $300. When 600 parts are produced, the cost is $3300. A) $6.00 per part B) $7.00 per part C) $0.17 per part D) $.00 per part 79) Suppose the sales of a particular brand of appliance satisf the relationship S() = , where S() represents the number of sales in ear, with = 0 corresponding to Find the number of sales in A) 9080 B) 8920 C) 4380 D) ) Assume that the sales of a certain appliance dealer are approimated b a linear function. Suppose that sales were $600 in 1982 and $64,00 in Let = 0 represent Find the equation giving earl sales S(). A) S() = 8, ,00 B) S() = 11, C) S() = 11, ,00 D) S() = 8, Solve and graph the inequalit and graph the solution. 81) - < 2 A) (7, ) B) (-, 7) C) [7, ) D) (-, 7]

11 82) 6-7 > - 16 A) (-, -9) B) (-, -23) C) (-23, ) D) (-9, ) ) A) (-, -8] B) (-, -) C) [-8, ) D) (-, ) Solve the problem. 84) The equation = can be used to determine the approimate profit, in dollars, of producing items. How man items must be produced so the profit will be at least $4246? A) 891,97.00 B) 849,140 C) 0 < 849,139 D) 849,260 8) The equation = can be used to determine the approimate cost, in dollars, of producing items. How man items must be produced so the cost will be no more than $348? A) 0 < 116,0 B) 0 < 11,900 C) 0 < 121,69.00 D) 0 < 11,901 86) Paul has grades of 7 and 66 on his first two tests. What must he score on his third test in order to have an average of at least 80? A) at least 71 B) at most 80 C) at least 99 D) at most 74 Solve the inequalit. 87) Compan A rents copiers for a monthl charge of $120 plus 8 cents per cop. Compan B rents copiers for a monthl charge of $240 plus 4 cents per cop. What is the number of copies above which Compan A's charges are the higher of the two? A) 30 copies B) 3000 copies C) 100 copies D) 6000 copies

12 Solve the inequalit and graph the solution. 88) ( - 7)( + ) > 0 A) (-, ) B) (-, -) or (7, ) C) (-, -7) or (, ) D) (-, 7) ) t 2-2t A) (-, -4] B) [6, ) -4 C) [-4, 6] D) (-, -4] or [6, ) -4 6

13 90) v2 - v A) (-, 4] or [6, ) B) [6, ) 4 6 C) (-, 4] 6 D) [4, 6] Determine whether the following rule defines as a function of. 91) = 3 A) Function B) Not a function 92) 2 = 7 A) Not a function B) Function 93) = 6-2 A) Function B) Not a function State the domain of the given function. 94) f() = 3 + A) (-, ) B) all real numbers ecept 0 C) (-, 0] D) [0, ) 9) = 4 - A) [4, ) B) (-, ) C) (-, 4) D) (-, 4] 96) = - 8 A) (-, ) B) all real numbers ecept 8 C) (8, ) D) 8 97) f() = A) - 3 2, B) all real number ecept C) [0, ) D) (-, ) For the given function, find 98) 3-2 f( + h) -f(). h A) 1 B) 3 C) h - 4 h D) 3h - 4 h

14 99) A) 2 + h + 14 B) 2 + h C) 1 D) h + 14 h 0) 2-8 A) 2h + h 2-8h - 16 h B) h C) 2 + h D) h

15 Answer Ke Testname: MATH PRACTICE EXAM #1 1) FALSE 2) FALSE 3) C 4) B ) A 6) A 7) D 8) B 9) B ) A 11) B 12) A 13) A 14) B 1) C 16) D 17) C 18) B 19) D 20) D 21) C 22) B 23) D 24) B 2) D 26) B 27) B 28) B 29) B 30) D 31) B 32) C 33) B 34) B 3) D 36) B 37) A 38) A 39) B 40) C 41) D 42) D 43) D 44) D 4) D 46) C 47) D 48) D 49) C 0) D 1) C 2) C 3) B 4) C ) D 6) D 7) A 8) D 9) C 60) A 61) B 62) D 63) D 64) B 6) C 66) A 67) A 68) A 69) D 70) B 71) D 72) C 73) D 74) B 7) D 76) D 77) B 78) A 79) D 80) B 81) B 82) D 83) A 84) B 8) B 86) C 87) B 88) B 89) C 90) A 91) A 92) A 93) A 94) A 9) D 96) B 97) D 98) B 99) B 0) D