Exam 1 Review for College Algebra
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation by factoring.
1) x2 = x + 6
A) {1, 6}
2) 2 - 10x = (3x - 7)(x + 1)
1
A)
5
B) {2, 3}
C) {-2, 3}
D) {-2, -3}
2)
7
B) -1,
3
C) {-1, 3}
D) {-3, 1}
Solve the equation by the square root property.
3) 2x 2 = 26
A) {14}
4) 4(x - 2)2 = 20
A) {-2 ± 5}
1)
3)
B) {-13, 13}
C) {- 13,
B) {2 ±
C) {-7, 3}
13}
D) {13}
4)
5}
D) {-3, 7}
Solve the equation by completing the square.
5) x2 + 4x - 3 = 0
A) {2 + 7}
C) {-1 - 7 , -1 +
5)
B) {-2 - 2 7 , -2 + 2 7}
D) {-2 - 7 , -2 + 7}
7}
Solve the equation using the quadratic formula.
6) 5x 2 + x - 3 = 0
6)
A)
-1 - 61 -1 + 61
,
2
2
B)
C)
-1 - 61 -1 + 61
,
10
10
D)
1 - 61 1 + 61
,
10
10
Compute the discriminant. Then determine the number and type of solutions for the given equation.
7) x2 + 12x + 36 = 0
7)
Solve the equation by the method of your choice.
8) 2x 2 - 10 = 0
8)
A) -144; two complex imaginary solutions
B) 0; one real solution
C) 144; two unequal real solutions
A) { 5}
C) {-
10 ,
10}
1
B) { -
5,
D) -
10
,
2
5}
10
2
9) 4x 2 = -10x - 3
-10 - 13 -10 + 13
,
A)
4
4
C)
9)
-5 - 13 -5 + 13
,
8
8
Solve the linear inequality. Other than
a number line.
10) -8x 24
B)
-5 - 37 -5 + 37
,
4
4
D)
-5 - 13 -5 + 13
,
4
4
, use interval notation to express the solution set and graph the solution set on
10)
A) (- , 3]
B) [-3, )
C) [3, )
D) (- , -3]
11) 6x - 7
5x - 8
11)
A) [-1, )
B) (- , -1)
C) (-15, )
D) (- , -1]
2
Solve the compound inequality. Other than
set on a number line.
12) -5 < x - 4 4
, use interval notation to express the solution set and graph the solution
12)
A) [-9, 0)
B) (-9, 0]
C) (-1, 8]
D) [-1, 8)
13) -24
-5x + 1 < -9
13)
A) (-5, -2]
B) (2, 5]
C) [-5, -2)
D) [2, 5)
3
Graph the equation.
14) y = x 3 - 5
14)
A)
B)
C)
D)
4
Use the graph to determine the x- and y-intercepts.
15)
15)
A) x-intercepts: -3, 1; y-intercept: 3
C) x-intercept: 1; y-intercept: 3
B) x-intercept: 3; y-intercepts: -3, 1
D) x-intercept: -3; y-intercepts: 1, 3
Find the slope of the line that goes through the given points.
16) (-3, 1), (-9, 1)
1
1
A) Undefined
B) C) 6
3
16)
D) 0
1
1
17) ( , 4) and ( , -4)
3
3
A) -
7
8
17)
B) -
8
7
C) 0
D) Undefined
Use the given conditions to write an equation for the line in point-slope form.
18) Slope = 4, passing through (-3, 7)
A) y - 7 = 4(x + 3)
B) y = 4x + 19
C) y + 7 = 4(x - 3)
19) Passing through (-4, -3) and (-8, -6)
3
3
A) y + 3 = (x + 8) or y + 6 = (x + 4)
4
4
C) y + 3 =
D) x - 7 = 4(y + 3)
3
3
B) y + 3 = (x + 4) or y + 6 = (x + 8)
4
4
3
3
x - 4 or y + 6 = x + 3
4
4
D) y - 3 =
2
31
C) y = x +
5
5
Graph the equation in the rectangular coordinate system.
5
19)
3
3
(x - 4) or y - 6 = (x - 8)
4
4
Use the given conditions to write an equation for the line in slope-intercept form.
20) Slope = 4, passing through (-2, 6)
A) y - 6 = x + 2
B) y = 4x - 14
C) y = 4x + 14
21) Passing through (-3, 5) and (2, 7)
2
31
A) y - 5 = (x + 3)
B) y = mx +
5
5
18)
D) y - 6 = 4x + 2
2
31
D) y = - x +
5
5
20)
21)
22) 4y = -12
22)
A)
B)
C)
D)
Determine the slope and the y-intercept of the graph of the equation.
23) x + y - 7 = 0
A) m = -1; (0, 7)
B) m = 1; (0, 7)
C) m = -1; (0, -7)
6
D) m = 0; (0, 7)
23)
24) x + 14y -1 = 0
1
1
; 0,
A) m = 14
14
24)
B) m = -14; (0, 14)
D) m =
C) m = 1; (0, 1)
1
1
; 0,
14
14
Graph the linear function by plotting the x- and y-intercepts.
25) -3x - 6y - 18 = 0
25)
A) intercepts: (0, -3), (-6, 0)
B) intercepts: (0, 6), (3, 0)
C) intercepts: (0, -3), (6, 0)
D) intercepts: (0, -6), (-3, 0)
7
Use the given conditions to write an equation for the line in the indicated form.
26) Passing through (4, -1) and parallel to the line whose equation is y = -2x + 3 ;
point-slope form
A) y + 1 = -2(x - 4)
B) y = 2x
C) y + 1 = x - 4
D) y - 4 = -2(x + 1)
27) Passing through (4, 5) and perpendicular to the line whose equation is y =
26)
1
x + 8;
8
27)
slope-intercept form
A) y = - 8x - 37
B) y = - 8x + 37
28) Passing through (5, 2) and perpendicular to the line whose equation is y =
slope-intercept form
1
21
A) y = - x 8
4
D) y = -
C) y = 8x - 37
B) y = - 8x - 42
1
37
x8
8
1
x + 7;
8
C) y = - 8x + 42
28)
D) y = 8x - 42
29) Passing through (4, 3) and parallel to the line whose equation is 7x + y - 9 = 0;
slope-intercept form
A) y = 7x - 31
B) y = - 7x - 31
C) y = - 7x + 31
29)
D) y = -
Find the distance between the pair of points.
30) (7, 4) and (-2, -3)
A) 63
B)
1
31
x7
7
30)
C) 2
130
Write the standard form of the equation of the circle with the given center and radius.
31) (0, 5); 11
A) x2 + (y + 5)2 = 11
B) (x - 5)2 + y2 = 121
C) x2 + (y - 5)2 = 121
D)
32
31)
D) (x + 5)2 + y2 = 121
Complete the square and write the equation in standard form. Then give the center and radius of the circle.
32) x2 + y2 - 14x - 2y + 50 = 4
32)
2
2
2
2
A) (x - 7) + (y - 1) = 4
B) (x - 1) + (y - 7) = 4
(-7, -1), r = 4
C) (x - 7)2 + (y - 1)2 = 4
(7, 1), r = 2
(-1, -7), r = 4
D) (x - 1)2 + (y- 7)2 = 4
(1, 7), r = 2
8