TEST I TEM F ILE
(DOWNLOAD O NLY)
PRECALCULUS
TENTH EDITION
M ICHAEL SULLIVAN
Chicago State University

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
FG
H
I
J K
L
x-5 5
y
5
-5
A B
C
D
E
FG
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
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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)
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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
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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
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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 schoolʹs 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
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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)
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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 = x2 - x
Point: (-1, 0)
A) No B) Yes
2) Equation: x2 + y2 = 4
Point: (2, 2)
A) No B) Yes
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