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Test Bank for Precalculus , 10th Edition

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    T EST I TEM F ILE (D OWNLOAD O NLY ) PRECALCULUS TENTH EDITION M ICHAEL S ULLIVAN Chicago State University

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    Ch. 1 Graphs 1.1 The Distance and Midpoint Formulas 1 Rectangular Coordinates MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Name the quadrant in which the point is located. 1) (19, 6) A) I B) II C) III D) IV 2) ( - 8, 9) A) I B) II C) III D) IV 3) ( - 14, - 7) A) I B) II C) III D) IV 4) (2, - 18) A) I B) II C) III D) IV Identify the points in the graph for the ordered pairs. x -5 5 y 5 -5 A B C D E F G H I J K L x -5 5 y 5 -5 A B C D E F G H I J K L 5) (0, 2), (4, 3) A) C and E B) F and E C) B and C D) C and K 6) ( - 5, - 4), (0, - 3) A) I and J B) A and G C) G and I D) A and J 7) ( - 3, 4), (2, 0), (4, - 5) A) B, F, and L B) B, C, and L C) F, K, and L D) A, B, and F 8) (3, 5), ( - 3, 0) A) D and G B) D and J C) I and G D) L and J Page 1

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    Give the coordinates of the points shown on the graph. 9) x -5 5 y 5 -5 A B x -5 5 y 5 -5 A B A) A = (3, 4), B = ( - 5, 7) B) A = (4, 22), B = (7, - 5) C) A = (3, 7), B = (4, 7) D) A = (3, 4), B = (7, - 5) 10) x -5 5 y 5 -5 C D x -5 5 y 5 -5 C D A) C = ( - 4, 2), D = (3, - 5) B) C = (2, - 4), D = ( - 5, 3) C) C = ( - 4, - 5), D = (2, - 5) D) C = ( - 4, 2), D = ( - 5, 3) 11) x -5 5 y 5 -5 E F x -5 5 y 5 -5 E F A) E = ( - 3, 5), F = ( - 6, - 2) B) E = (5, - 3), F = ( - 2, - 6) C) E = ( - 3, - 2), F = (5, - 2) D) E = ( - 6, - 2) , F = ( - 3, 5) Page 2

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    12) x -5 5 y 5 -5 G H x -5 5 y 5 -5 G H A) G = (7, - 6), H = ( - 6, 3) B) G = ( - 6, 7), H = (3, - 6) C) G = (7, 3), H = ( - 6, 3) D) G = (7, - 6), H = (3, - 6) Plot the point in the xy - plane. Tell in which quadrant or on what axis the point lies. 13) (4, 2) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I Page 3

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV 14) ( - 2, 6) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV Page 4

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III 15) (1, - 5) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II Page 5

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I 16) ( - 5, - 4) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III Page 6

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II 17) (0, - 4) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis B) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis Page 7

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis 18) ( - 6, 0) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis B) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis Page 8

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    C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis 2 Use the Distance Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(P1, P2) between the points P1 and P2. 1) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) 2 5 B) 2 C) 3 D) 1 2) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 130 B) 4 2 C) 63 D) 2 Page 9

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    3) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 2 5 B) 12 3 C) 12 D) 2 4) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 3 13 B) 45 5 C) 45 D) 3 5) P1 = (5, 5); P2 = (5, - 1) A) 6 B) 6 C) 7 D) 5 6) P1 = (1, - 3); P2 = ( - 7, 3) A) 10 B) 100 C) 11 D) 20 7) P1 = (0, 10); P2 = ( - 3, 10) A) 3 B) 10 C) 109 D) 9 8) P1 = (0, 0); P2 = (9, 3) A) 3 10 B) 90 C) 12 D) 3 3 9) P1 = (6, 2); P2 = ( - 2, - 1) A) 73 B) 55 C) 24 D) 5 10) P1 = (6, - 4); P2 = (2, - 2) A) 2 5 B) 12 3 C) 12 D) 6 Page 10

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    11) P1 = ( - 7, - 2); P2 = (7, - 6) A) 2 53 B) 180 5 C) 180 D) 18 12) P1 = ( - 0.4, 0.5); P2 = ( - 2.2, 2.8) Round to three decimal places, if necessary. A) 2.921 B) 20.5 C) 9.236 D) 3.021 Decide whether or not the points are the vertices of a right triangle. 13) ( - 9, 6), ( - 1, 6), ( - 1, 9) A) Yes B) No 14) ( - 8, 7), ( - 6, 11), ( - 4, 10) A) Yes B) No 15) ( - 10, - 7), ( - 4, - 5), ( - 5, - 10) A) Yes B) No 16) ( - 6, - 7), (0, - 5), (6, - 12) A) Yes B) No Solve the problem. 17) Find all values of k so that the given points are 29 units apart. ( - 5, 5), (k, 0) A) - 3, - 7 B) - 7 C) 3, 7 D) 7 18) Find the area of the right triangle ABC with A = ( - 2, 7), B = (7, - 1), C = (3, 9). A) 29 square units B) 58 square units C) 58 2 square units D) 29 2 square units 19) Find all the points having an x - coordinate of 9 whose distance from the point (3, - 2) is 10. A) (9, 6), (9, - 10) B) (9, 2), (9, - 4) C) (9, - 12), (9, 8) D) (9, 13), (9, - 7) 20) A middle school ʹ s baseball playing field is a square, 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. A) 85 feet B) 86 feet C) 84 feet D) 92 feet 21) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find an expression for their distance apart in miles at the end of t hours. A) 52t miles B) t 68 miles C) 52 t miles D) 2t 13 miles 22) A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To the nearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75 yards. A) 346 yards B) 146 yards C) 345 yards D) 145 yards Page 11

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    23) Find the length of each side of the triangle determined by the three points P1, P2, and P3. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. P1 = ( - 5, - 4), P2 = ( - 3, 4), P3 = (0, - 1) A) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 both B) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 isosceles triangle C) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 right triangle D) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 neither 3 Use the Midpoint Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the midpoint of the line segment joining the points P1 and P2. 1) P1 = (4, 9); P2 = (8, 1) A) (6, 5) B) (12, 10) C) ( - 4, 8) D) (5, 6) 2) P1 = ( - 2, 3); P2 = ( - 4, - 3) A) - 3, 0 B) 1, 3 C) 2, 6 D) - 6, 0 3) P1 = (7, 1); P2 = ( - 16, - 16) A) - 9 2 , - 15 2 B) 23 2 , 17 2 C) - 9, - 15 D) 9, 15 4) P1 = ( - 0.2, - 0.3); P2 = ( - 2.1, - 1.6) A) ( - 1.15, - 0.95) B) ( - 0.95, - 1.15) C) ( - 0.95, - 0.65) D) ( - 0.65, - 0.95) 5) P1 = (a, 2); P2 = (0, 1) A) a 2 , 3 2 B) a, 3 C) - a 2 , 1 D) a, 3 2 6) P1 = (3a, 4); P2 = (4a, 9) A) 7a 2 , 13 2 B) 7a, 13 C) a, 5 D) 13a 2 , 7 2 Solve the problem. 7) If ( - 1, - 5) is the endpoint of a line segment, and (2, - 1) is its midpoint, find the other endpoint. A) (5, 3) B) (5, - 9) C) ( - 7, - 13) D) (7, 1) 8) If ( - 1, 2) is the endpoint of a line segment, and ( - 3, - 2) is its midpoint, find the other endpoint. A) ( - 5, - 6) B) ( - 5, 6) C) (3, 10) D) ( - 9, - 2) 9) If ( - 2, - 3) is the endpoint of a line segment, and (2, - 4) is its midpoint, find the other endpoint. A) (6, - 5) B) (6, - 2) C) ( - 10, - 1) D) ( - 4, 5) 10) If (4, - 7) is the endpoint of a line segment, and ( - 1, - 5) is its midpoint, find the other endpoint. A) ( - 6, - 3) B) ( - 6, - 9) C) (14, - 11) D) (8, - 17) Page 12

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    11) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two - thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0). A) 2 17 3 B) 17 3 C) 2 D) 8 3 1.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 1 Graph Equations by Plotting Points MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given point is on the graph of the equation. 1) Equation: y = x 2 - x Point: ( - 1, 0) A) No B) Yes 2) Equation: x 2 + y 2 = 4 Point: (2, 2) A) No B) Yes Page 13

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    Graph the equation by plotting points. 3) y = x - 1 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 14

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