Mathematical Ideas 13th Edition By Miller – Test Bank

Mathematical Ideas 13th Edition By Miller – Test Bank

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Give the quadrant in which the point is located.
1) (19, 7)
A) Quadrant III B) Quadrant IV C) Quadrant I D) Quadrant II
Answer: C
2) (-7, 15)
A) Quadrant IV B) Quadrant III C) Quadrant II D) Quadrant I
Answer: C
3) (-13, -17)
A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV
Answer: C
4) (18, -13)
A) Quadrant IV B) Quadrant I C) Quadrant III D) Quadrant II
Answer: A
5) (-16, 0)
A) Quadrant II B) Quadrant III C) None D) Quadrant IV
Answer: C
6) (0, -10)
A) Quadrant III B) None C) Quadrant IV D) Quadrant II
Answer: B
Locate the point on the rectangular coordinate system.
7) (0, 2)
A) B B) F C) C D) K
Answer: C
8) (-5,-4)
A) I B) A C) L D) G
Answer: A
9) (-3, 4)
A) A B) F C) B D) K
Answer: C
1
10) (-3, 0)
A) G B) C C) F D) J
Answer: A
11) (3, 5)
A) D B) L C) I D) K
Answer: A
12) (4, 3)
A) E B) C C) K D) D
Answer: A
13) (0,-3)
A) G B) I C) C D) J
Answer: D
14) (2, 0)
A) C B) K C) F D) B
Answer: C
15) (4, -5)
A) K B) F C) A D) L
Answer: D
Use the distance formula to find the distance between the pair of points.
16) (1, 2) and (-2, -3)
A) 34 B) 15 C) -2 D) 16
Answer: A
17) (4, -5) and (6, -1)
A) 12 B) 2 5 C) 2 D) 12 3
Answer: B
18) (-6, -3) and (1, -4)
A) 48 B) 8 C) 5 2 D) 48 3
Answer: C
19) (-1, 5) and (6, 4)
A) 48 B) 8 C) 5 2 D) 48 3
Answer: C
Find the midpoint of the line segment joining the two points.
20) (2, 6) and (4, 4)
A) (6, 10) B) 3, 5 C) – 1, 1 D) (-2, 2)
Answer: B
2
21) (0, -4) and (0, 1)
A) (0, -3) B) 0, – 3
2 C) 0, – 5
2 D) (0, -5)
Answer: B
22) (-3, -8) and (4, 9)
A) 1
2 ,
1
2 B) (-7, -17) C) – 7
2 , – 17
2 D) (1, 1)
Answer: A
23) (9, 8) and (-4, 2)
A) (5, 10) B) (13, 6) C) 5
2
, 5 D) 13
2 , 3
Answer: C
Choose the equation that matches the graph.
24)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A) (x – 1)2 + (y – 1)2 = 25 B) (x – 1)2 – (y – 1)2 = 25
C) (x – 1)2 + (y – 1)2 = 2.236 D) (x – 1)2 + (y – 1)2 = 5
Answer: A
25)
-20 -10 10 20 x
y
20
10
-10
-20
-20 -10 10 20 x
y
20
10
-10
-20
A) (x + 2)2 + (y – 10)2 = 9 B) (x – 2)2 + (y + 10)2 = 9
C) (x – 2)2 + (y – 10)2 = 9 D) (x + 2)2 + (y + 10)2 = 9
Answer: C
3
Write the equation of a circle with the given center and radius.
26) Center at (0, 0); Radius 7
A) x2 + y2 = 7 B) x2 – y2 = 7 C) x2 + y2 = 49 D) x2 – y2 = 7
Answer: C
27) Center at (10, -7); Radius 8
A) (x + 7)2 + (y – 10)2 = 8 B) (x – 10)2 + (y + 7)2 = 64
C) (x – 7)2 + (y + 10)2 = 8 D) (x + 10)2 + (y – 7)2 = 64
Answer: B
28) Center at (9, 0); Radius 5
A) (x + 9)2 + y2 = 25 B) x2 + (y – 9)2 = 5 C) x2 + (y + 9)2 = 5 D) (x – 9)2 + y2 = 25
Answer: D
29) Center at (0, 3); Radius 10
A) (x + 3)2 + y2 = 100 B) (x – 3)2 + y2 = 100 C) x2 + (y – 3)2 = 100 D) x2 + (y + 3)2 = 10
Answer: C
30) Center at (2, 3); Radius 11
A) (x – 3)2 + (y – 2)2 = 121 B) (x – 2)2 + (y – 3)2 = 11
C) (x + 2)2 + (y + 3)2 = 11 D) (x + 3)2 + (y + 2)2 = 121
Answer: B
31) Center at (0, 8); Radius 6
A) (x + 8)2 + y2 = 36 B) (x – 8)2 + y2 = 36 C) x2 + (y – 8)2 = 6 D) x2 + (y + 8)2 = 6
Answer: C
32) Center at (-2, 0); Radius 19
A) x2 + (y – 2)2 = 361 B) x2 + (y + 2)2 = 361 C) (x – 2)2 + y2 = 19 D) (x + 2)2 + y2 = 19
Answer: D
Find the center and radius of the circle.
33) x2 + y2 = 4
A) (0, 0), r = 4 B) (0, 2), r = 4 C) (0, 0), r = 2 D) (2, 2), r = 4
Answer: C
34) (x + 3)
2 + y2 = 49
A) (0, 3), r = 7 B) (-3, 0), r = 7 C) (3, 0), r = 49 D) (0, -3), r = 49
Answer: B
35) x2 + (y + 1)
2 = 100
A) (1, 0), r = 100 B) (-1, 0), r = 100 C) (0, 1), r = 10 D) (0, -1), r = 10
Answer: D
36) (x – 8)2 + (y + 8)2 = 4
A) (8, -8), r = 2 B) (-8, 8), r = 4 C) (8, -8), r = 4 D) (-8, 8), r = 2
Answer: A
4
37) x2 – 18x + 81 + y2 – 6y + 9 = 49
A) (-9, -3), r = 49 B) (-3, -9), r = 49 C) (9, 3), r = 7 D) (3, 9), r = 7
Answer: C
38) x2 + y2 – 14x – 8y + 65 = 9
A) (-7, -4), r = 9 B) (4, 7), r = 3 C) (7, 4), r = 3 D) (-4, -7), r = 9
Answer: C
39) x2 + y2 – 14x + 6y = -42
A) (-7, 3), r = 16 B) (-3, 7), r = 4 C) (7, -3), r = 4 D) (3, -7), r = 16
Answer: C
40) x2 + y2 – 2x – 4y = 20
A) (-2, -1), r = 25 B) (2, 1), r = 5 C) (-1, -2), r = 25 D) (1, 2), r = 5
Answer: D
41) 5×2 + 5y2 + 50x + 20y + 65 = 0
A) (-5, -2), r = 4 B) (-2, -5), r = 4 C) (2, 5), r = 16 D) (5, 2), r = 16
Answer: A
Graph the circle.
42) x2 + y2 = 64
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
5
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: D
43) (x – 4)2 + (y – 5)2 = 16
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
6
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: A
44) x2 + (y – 2)2 = 16
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
7
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: D
45) (x + 3)
2 + y2 = 16
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
8
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: D
46) x2 + y2 – 8x – 2y – 8 = 0
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
9
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: B
47) x2 + y2 + 4x + 10y + 20 = 0
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
10
C)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: D
Solve the problem.
48) The enrollment at State University for 2004 was 14 thousand students. The projected enrollment for
2010 is 32 thousand students. Use the midpoint formula to estimate the enrollment for
2007.
A) 46 thousand students B) 28 thousand students
C) 18 thousand students D) 23 thousand students
Answer: D
49) If the coordinates of one endpoint of a line segment are (4, 2) and the coordinates of the midpoint of the segment
are (6, 4), what are the coordinates of the other endpoint?
A) (8, 2) B) (2, 6) C) (8, 6) D) (2, 2)
Answer: C
50) Three receiving stations at (8, 11), (4, 6), and (12, 9) record distances to an earthquake of 2 units, 5 units, and 4
units, respectively.Find the coordinates of the epicenter.
A) (8, 9) B) (9, 8) C) (1, 2) D) (-6, -5)
Answer: A
Decide whether the statement is true or false.
51) If a point lies on the x-axis, its x-coordinate is zero.
A) True B) False
Answer: B
52) If a point lies on the y-axis, its x-coordinate is zero.
A) True B) False
Answer: A
53) The graphs of x2 + y2 = r2 and x2 + y2 = s2 do not intersect if r is not equal to s.
A) True B) False
Answer: A
54) The distance between the points (p, q) and (a, b) is given by
d = (p – q)2 + (a – b)2
A) True B) False
Answer: B
11
55) If the coordinates of one endpoint of a line segment are (0, 0) and the coordinates of the midpoint of the segment
are (p, q), then the coordinates of the other endpoint are (-p, -q).
A) True B) False
Answer: B
56) If the coordinates of one endpoint of a line segment are (a, b) and the coordinates of the midpoint of the segment
are (p, q), then the coordinates of the other endpoint are (2p-a, 2q-b).
A) True B) False
Answer: A
57) The radius of a circle must be an integer number.
A) True B) False
Answer: B
58) The circle with equation (x – 5)2 + (y + 2)2 = 36 has center at (-5, 2).
A) True B) False
Answer: B
59) The equation of a circle centered at the origin with radius 3 is x2 + y2 = 3.
A) True B) False
Answer: B
60) The graph of (x – 5)2 + (y + 8)2 = 0 contains no points.
A) True B) False
Answer: B
Complete the ordered pairs. Then graph the equation.
61) x + y = -5
(0, ), ( , 0), (4, )
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
12
A) (0, 5), (-5, 0), (4, 9)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, -5), (-5, 0), (4, -9)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, 5), (5, 0), (4, 1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, -5), (5, 0), (4, -1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: B
62) y = x – 5
(0, ), ( , 0), (4, )
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
13
A) (0, 5), (5, 0), (4, 1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, 5), (-5, 0), (4, 9)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, -5), (5, 0), (4, -1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, -5), (-5, 0), (4, -9)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: C
63) y – 2 = x
(0, ), ( , 0), (3, )
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
14
A) (0, 2), (-2, 0), (3, 5)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, 2), (2, 0), (3, -1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, -2), (2, 0), (3, 1)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, -2), (-2, 0), (3, -5)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: A
64) y = 4x – 4
(0, ), ( , 0), (4, )
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
15
A) (0, -4), (1, 0), (4, 12)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, 4), (-1, 0), (4, 20)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, -4), (-16, 0), (4, -3)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, -4), (-1, 0), (4, -20)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: A
65) 3x – y = 6
(0, ), ( , 0), (3, )
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
16
A) (0, -6), (-18, 0), (3, -5)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, -6), (-2, 0), (3, -15)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, -6), (2, 0), (3, 3)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, 6), (-2, 0), (3, 15)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: C
66) 3x + 4y = 16
x y
0
0
-2
2
-10 -5 5 x
10 y
5
-5
-10
-10 -5 5 x
10 y
5
-5
-10
17
A) (0, 4), 16
3 , 0 , -2, 5
2 , 8, 2
-10 -5 5 x
10 y
5
-5
-10
-10 -5 5 x
10 y
5
-5
-10
B) (0, 4), 16
3 , 0 , -2, 11
2 , 8
3
, 2
-10 -5 5 x
10 y
5
-5
-10
-10 -5 5 x
10 y
5
-5
-10
C) (0, -4), 16
3 , 0 , -2, – 11
2 , 8, 2
-10 -5 5 x
10 y
5
-5
-10
-10 -5 5 x
10 y
5
-5
-10
D) 0, 16
3 , 4, 0 , -2, 8 , 5
2
, 2
-10 -5 5 x
10 y
5
-5
-10
-10 -5 5 x
10 y
5
-5
-10
Answer: B
Find the y- and x-intercepts for the equation. Then graph the equation.
18
67) y – 1
2
x = 5
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A) (0, 5), (-5, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, -10), (10, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, 5), (-10, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, 5), (10, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: C
19
68) x = -2 – y
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
A) (0, 2), (-2, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
B) (0, -2), (-2, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
C) (0, -2), (2, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
D) (0, 2), (2, 0)
-10 -5 5 10 x
y
10
5
-5
-10
-10 -5 5 10 x
y
10
5
-5
-10
Answer: