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MAC 1105
College Algebra
Review # 1
Prof. Nicoli-Suco
----------------------Name___________________________________
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) (-5, 4)
1)
A) I
B) II
C) III
D) IV
B
Identify the points in the graph for the ordered pairs.
2) (0, 2), (4, 3)
2)
A) C and E
B) C and K
C) B and C
D) F and E
A
3) (-3, 4), (2, 0), (4, -5)
3)
A) A, B, and F
B) F, K, and L
C) B, C, and L
D) B, F, and L
D
1
Find the distance d(P1 , P2 ) between the points P1 and P2 .
4) P1 = (-7, -4); P2 = (1, -6)
4)
A) 10
B) 2 17
C) 60
D) 60 15
B
5) P1 = (-1, -5); P2 = (7, -3)
5)
A) 60
B) 6
C) 2 17
D) 60 15
C
6) P1 = (0, 0); P2 = (5, -7)
6)
A) 2
B)
74
C) 74
D)
7
B
7) P1 = (5, 5); P2 = (5, -1)
7)
A) 5
B) 6
C) 7
D)
6
B
Find the midpoint of the line segment joining the points P1 and P2.
8) P1 = (2, 3); P2 = (9, 6)
8)
A) -7, -3
11 9
,
B)
2 2
C) 11, 9
7
3
D) - , 2
2
B
2
9) P1 = (-0.5, 0.5); P2 = (2, -2.2)
9)
A) (-0.85, 0.75)
B) (1.25, -1.35)
C) (0.75, -0.85)
D) (-1.35, 1.25)
C
10) P1 = (6, 9); P2 = (7, 2)
10)
A) (13, 11)
11 13
B) ( , )
2 2
C) (-1, 7)
13 11
D) ( , )
2 2
D
List the intercepts of the graph.
11)
11)
A) 0, B) -
2
C) 0, D) -
2
2
, (-5, 0), 0,
, 0 , (0, -5),
2
2
, (0, -5), 0,
, 0 , (-5, 0),
2
2
,0
2
,0
B
3
12)
12)
A) (0, -1), (1, 0)
B) (-1, 0), (0, 1)
C) (0, -1), (0, 1)
D) (-1, 0), (1, 0)
D
13)
13)
A) (3, 0), (0, -3), (0, 1), (0, 5)
B) (3, 0), (0, 3), (0, 1), (0, -5)
C) (3, 0), (1, 0), (-5, 0), (0, 3)
D) (-3, 0), (1, 0) (5, 0), (0, 3)
D
4
List the intercepts for the graph of the equation.
14) 9x2 + 16y2 = 144
14)
A) (-9, 0), (-16, 0), (16, 0), (9, 0)
B) (-3, 0), (-4, 0), (4, 0), (3, 0)
C) (-4, 0), (0, -3), (0, 3), (4, 0)
D) (-16, 0), (0, -9), (0, 9), (16, 0)
C
15) y2 = x + 16
15)
A) (0, -4), (16, 0), (0, 4)
B) (-4, 0), (0, -16), (4, 0)
C) (4, 0), (0, 16), (0, -16)
D) (0, -4), (-16, 0), (0, 4)
D
16) y = x - 6
16)
A) (6, 0), (0, -6)
B) (-6, 0), (0, -6)
C) (6, 0), (0, 6)
D) (-6, 0), (0, 6)
A
17) x2 + y - 36 = 0
17)
A) (-6, 0), (0, 36), (6, 0)
B) (-6, 0), (0, -36), (6, 0)
C) (6, 0), (0, 36), (0, -36)
D) (0, -6), (36, 0), (0, 6)
A
5
List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of
these.
18)
18)
A) intercepts: (0, -1) and (0, 1)
symmetric with respect to x-axis, y-axis, and origin
B) intercepts: (-1, 0) and (1, 0)
symmetric with respect to origin
C) intercepts: (-1, 0) and (1, 0)
symmetric with respect to x-axis, y-axis, and origin
D) intercepts: (0, -1) and (0, 1)
symmetric with respect to y-axis
C
List the intercepts and type(s) of symmetry, if any.
-x5
19) y =
x2 - 8
19)
A) intercepts: (2 2, 0), (-2 2, 0), (0, 0)
symmetric with respect to origin
B) intercept: (0, 0)
symmetric with respect to y-axis
C) intercept: (0, 0)
symmetric with respect to origin
D) intercept: (0, 0)
symmetric with respect to x-axis
C
Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.
20) y2 - x - 49 = 0
20)
A) y-axis
B) origin
C) x-axis
D) x-axis, y-axis, origin
E) none
C
6
21) 4x2 + 9y2 = 36
21)
A) x-axis
B) origin
C) y-axis
D) x-axis, y-axis, origin
E) none
D
22) y =
4x
2
x + 16
22)
A) y-axis
B) origin
C) x-axis
D) x-axis, y-axis, origin
E) none
B
Find the slope of the line containing the two points.
23) (-2, -7); (4, -2)
5
A)
6
B) C)
23)
6
5
6
5
D) -
5
6
A
24) (4, -8); (-4, 3)
8
A)
11
B) C)
24)
8
11
11
8
D) -
11
8
D
Find an equation for the line with the given properties.
25) Slope undefined; containing the point (6, -9)
25)
A) x = 6
B) y = -9
C) x = -9
D) y = 6
A
7
26) Vertical line; containing the point (8, 2)
26)
A) y = 8
B) x = 8
C) x = 2
D) y = 2
B
27) Slope undefined; containing the point A) x = B) x = 1
C) y = -
3
,1
4
27)
3
4
3
4
D) y = 1
A
Find the slope-intercept form of the equation of the line with the given properties.
28) Horizontal; containing the point (4, 5)
28)
A) x = 5
B) x = 4
C) y = 4
D) y = 5
D
29) Slope = 0; containing the point (5, 1)
29)
A) y = 5
B) y = 1
C) x = 5
D) x = 1
B
30) Horizontal; containing the point -
3
,9
4
30)
A) y = 0
B) y = 9
C) y = -
3
4
D) y = -9
B
8
Find an equation for the line, in the indicated form, with the given properties.
31) Containing the points (8, -7) and (-9, 2); general form
31)
A) -9x + 17y = -47
B) 9x + 17y = -47
C) -15x + 11y = 113
D) 15x - 11y = 113
B
32) Containing the points (1, -3) and (8, 6); slope-intercept form
9
30
A) y = - x 7
7
B) y = mx C) y =
32)
30
7
9
30
x7
7
D) y + 3 =
9
(x - 1)
7
C
33) Containing the points (7, -8) and (-3, 1); general form
33)
A) -15x + 4y = 41
B) -9x + 10y = -17
C) 15x - 4y = 41
D) 9x + 10y = -17
D
Find the slope-intercept form of the equation of the line with the given properties.
34) Slope = 6; containing the point (-2, -6)
34)
A) y = 6x - 6
B) y = 6x + 6
C) y = -6x + 6
D) y = -6x - 6
B
35) Slope = 0; containing the point (1, -7)
35)
A) x = 1
B) y = -7
C) x = -7
D) y = 1
B
9
Find the slope and y-intercept of the line.
36) 5x + 7y = 3
A) slope =
36)
15
3
; y-intercept =
7
7
B) slope = 5; y-intercept = 15
7
3
C) slope = ; y-intercept = 5
5
D) slope =
5
3
; y-intercept =
7
7
D
Find an equation for the line with the given properties.
37) Parallel to the line y = -4x; containing the point (6, 8)
37)
A) y = -4x + 32
B) y = -4x - 32
C) y = -4x
D) y - 8 = -4x - 6
A
38) Parallel to the line x + 3y = 3; containing the point (0, 0)
2
A) y =
3
B) y = -
1
x
3
C) y = -
1
x+3
3
D) y =
38)
1
x
3
B
39) Parallel to the line -2x - y = 6; containing the point (0, 0)
39)
A) y = -2x
1
B) y = x
2
C) y =
1
x+6
2
D) y = -
1
x
2
A
40) Parallel to the line 9x + 4y = 57; containing the point (5, -1)
A) 4x + 9y = -1
B) 9x - 4y = 41
C) 9x + 4y = 41
D) 5x + 4y = 57
C
10
40)
41) Perpendicular to the line y =
1
x + 6; containing the point (2, -2)
3
41)
A) y = - 3x - 4
B) y = - 3x + 4
1
4
C) y = - x 3
3
D) y = 3x - 4
B
1
)
2
42)
43) Perpendicular to the line x - 7y = 3; containing the point (5, 5)
43)
42) Perpendicular to the line 4x - y = 2; containing the point (0,
A) y =
1
1
x+
4
2
B) y =
1
4
C) y = -
1
1
x+
4
2
D) y = -
1
x+2
4
C
A) y = 7x - 40
1
40
B) y = - x 7
7
C) y = - 7x - 40
D) y = - 7x + 40
D
44) Perpendicular to the line y = -8; containing the point (9, 6)
44)
A) y = 6
B) x = 6
C) y = 9
D) x = 9
D
45) Perpendicular to the line 2x - 3y = -10; containing the point (7, -8)
A) 2x + 3 = 2
B) 3x - 2y = 5
C) 7x + 3y = -10
D) 3x + 2y = 5
D
11
45)
Write the standard form of the equation of the circle with radius r and center (h, k).
46) r =
6; (h, k) = (9, -3)
46)
A) (x + 3)2 + (y - 9)2 = 36
B) (x - 9)2 + (y + 3)2 = 6
C) (x + 9)2 + (y - 3)2 = 6
D) (x - 3)2 + (y + 9)2 = 36
B
47) r = 2; (h, k) = (0, 0)
47)
A) (x - 2)2 + (y - 2)2 = 2
B) x2 + y2 = 4
C) (x - 2)2 + (y - 2)2 = 4
D) x2 + y2 = 2
B
48) r = 11; (h, k) = (-2, 4)
48)
A) (x + 2)2 + (y - 4)2 = 121
B) (x - 2)2 + (y + 4)2 = 121
C) (x - 2)2 + (y + 4)2 = 11
D) (x + 2)2 + (y - 4)2 = 11
A
49) r = 12; (h, k) = (-3, 0)
49)
A) (x + 3)2 + y2 = 144
B) x2 + (y - 3)2 = 12
C) (x - 3)2 + y2 = 144
D) x2 + (y + 3)2 = 12
A
Solve the problem.
50) Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a
diameter.
A) (x + 1)2 + (y + 1)2 = 136
B) (x + 1)2 + (y + 1)2 = 34
C) (x - 1)2 + (y - 1)2 = 136
D) (x - 1)2 + (y - 1)2 = 34
D
12
50)
Graph the equation.
51) x2 + (y - 6)2 = 4
51)
A)
B)
13
C)
D)
D
Solve the problem.
52) Find the equation of a circle in standard form with center at the point (-3, 2) and tangent to the line
y = 4.
52)
A) (x - 3)2 + (y + 2)2 = 4
B) (x - 3)2 + (y + 2)2 = 16
C) (x + 3)2 + (y - 2)2 = 4
D) (x + 3)2 + (y - 2)2 = 16
C
Find the center (h, k) and radius r of the circle with the given equation.
53) x2 - 8x + 16 + (y - 7)2 = 36
53)
A) (h, k) = (-7, -4); r = 36
B) (h, k) = (7, 4); r = 6
C) (h, k) = (-4, -7); r = 36
D) (h, k) = (4, 7); r = 6
D
14
54) x2 - 14x + 49 + y2 + 14y + 49 = 49
54)
A) (h, k) = (7, -7); r = 7
B) (h, k) = (7, -7); r = 49
C) (h, k) = (-7, 7); r = 7
D) (h, k) = (-7, 7); r = 49
A
55) 4x2 + 4y2 - 12x + 16y - 5 = 0
3
3 5
A) (h, k) = ( , -2); r =
2
2
B) (h, k) = (-
55)
3
3 5
, 2); r=
2
2
3
30
C) (h, k) = ( , -2); r =
2
2
D) (h, k) = (-
3
, 2); r =
2
30
2
C
15