Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
Find the area of the trapezoid. The measures of the dimensions are given below the figure. 1)
b1 = 7 ft; b2 = 4 ft; h = 8 ft
A)
2)
3)
27 ft2
B) 56
ft2
C)
88 ft2
Fill in the blank with the appropriate symbol (<, >, =).
3 + (-8) | _____ | 3 | + | -8 |
A) >
B) =
D)
44 ft2
2)
C)
<
3)
Express the set in interval notation.
-8
A)
(- , -8)
-3
B) (-8, )
C)
[-8, -3]
D)
(-8, -3]
4)
Write an expression in words that describes the set of numbers given by the interval.
(-2, 3)
A) All real numbers less than -2 and greater than 3.
B) All real numbers less than or equal to -2 and greater than or equal to 3.
C) All real numbers greater than -2 and less than 3.
D) All real numbers greater than or equal to -2 and less than or equal to 3.
4)
5)
Evaluate the expression: (-10)2
A) -20
B) -100
5)
6)
Evaluate the expression, if possible:
A) 7
C) 49
C)
-8
D)
100
6)
-49
B) -7
D)
1
Not a real number
7)
7)
Indicate all the sets to which the number belongs.
Real
Irrational Rational Integers Whole
Natural
Numbers Numbers Numbers
Numbers Numbers
0.3
A)
Real
Irrational Rational Integers Whole
Natural
Numbers Numbers Numbers
Numbers Numbers
0.3
×
B)
Real
Irrational Rational Integers Whole
Natural
Numbers Numbers Numbers
Numbers Numbers
0.3
×
×
×
C)
Real
Irrational Rational Integers Whole
Natural
Numbers Numbers Numbers
Numbers Numbers
0.3
×
×
D)
Real
Irrational Rational Integers Whole
Natural
Numbers Numbers Numbers
Numbers Numbers
0.3
×
×
8)
9)
Solve the inequality. Write the answer in interval notation.
-8 < x + 8 0
A) [-8, -16)
B) (-16,-8]
C) (-16, )
11)
D)
(-16, 0]
9)
Solve the inequality.
7
1
7
4
- > -4 - y or
> 2y +
5
2
6
3
A)
10)
8)
(- , )
B)
-
26
1
, 5
12
C)
{}
Express the equation in the form y = mx + b by solving for y.
-4x - y = -9
A) y = 4x - 9
B) y = -4x - 9
C) y = 4x + 9
D)
- , -
1
12
10)
D)
y = -4x + 9
Let X = {x|x 10} and Y = {x|x < 7}. Determine the given intersection. Express the
answer in interval notation.
A)
B) [7,
10)
D) (- , 7] (10, )
{}
C) (7, 10]
2
11)
12)
Solve the equation:
A)
y=
68
201
5
1 1
y - = (3y - 1).
4
3 2
B)
12)
C)
y=0
y = -10
D)
y=
2
3
13)
Solve the inequality. Write the answer in interval notation.
0.5w + 4 < 2.5w - 4 or 0.4w -0.2w - 2.4
A) (- , )
B) (-4, ]
C) (- , -4] (4, )
D) { }
13)
14)
Graph the linear equation.
2
y= x-2
3
14)
A)
B)
3
C)
15)
D)
Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
16x - 3y = 6
4
1
x- y=5
3
4
A)
parallel
B) neither
C)
15)
perpendicular
16)
Write an equation of the line satisfying the given conditions. Write the answer in
slope-intercept form.
The line passes through (4, 8) and (1, 8).
3
5
3
5
xx+
A) y = B) y = C) y = 8
D) x = 8
16
2
16
2
16)
17)
Two points are given from each of two lines L1 and L2 . Without graphing the points,
17)
determine if the lines are perpendicular, parallel, or neither.
L1 : (-3, -12) and (7, 8)
L2 : (-6, 0) and (-8, 1)
A)
Neither
B) Perpendicular
4
C)
Parallel
18)
The graph shows the enrollment at Riverside Community College for selected years. Use
the coordinates of the given points to find the slope of the line. Interpret the meaning of
the slope in the context of this problem
18)
A)
m = -350; Enrollment decreases by approximately 350 students per year.
B) m = -175; Enrollment decreases by approximately 175 students per year.
C) m = -350; Enrollment decreases by an approximate factor of 350 students per year.
D) m = -175; Enrollment decreases by an approximate factor of 175 students per year.
19)
Two points are given from each of two lines L1 and L2 . Without graphing the points,
19)
determine if the lines are perpendicular, parallel, or neither.
L1 : (8, 0) and (-3, -11)
L2 : (5, 14) and (-3, 6)
A)
20)
Perpendicular
B) Neither
C)
List the domain and range.
x y
-4 8
-8 10
2 2
-6 1
-8 7
2 1
A) Domain {-4, -8, 2, -6); range {8, 10, 2, 1, 7, 1}
B) Domain {-4, -8, 2, -6, -8, 2}; range {8, 10, 2, 1, 7, 1}
C) Domain {-4, -8, 2, -6}; range {8, 10, 2, 1, 7}
D) None of the above
5
Parallel
20)
21)
f (x) = 2x, g(x) = |x - 4|,
A)
22)
f
2
(-1) = g
5
m(x) = x2 , r(x) =
A)
9
4
f
(-1) = ?
g
B)
21)
f
2
(-1) =
g
5
C)
f
5
(-1) = g
2
D)
f
5
(-1) =
g
2
6
, (m r)(4) = ?
x-4
22)
B) 6
C)
D)
0
Undefined
23)
Determine if the function is constant, linear, quadratic, or none of these.
z(x) = 3 + 2x2 + 3x
A) Quadratic
B) Linear
C) Constant
D) None of these
23)
24)
f (x) = x2 - 3x, g(x) = 3x + 3, (f
A) ( f g)(2) = 54
C) ( f g)(2) = 21
24)
25)
27)
B) ( f
D)
(f
g)(2) = -18
g)(2) = -3
25)
Solve by using the substitution method.
x - 3y = 9
3x + 1y = -23
A) (-7, -2)
B) (3, -2)
C) (-6, -5)
D)
26)
g)(2) = ?
Infinitely many solutions; (x, y) y =
1
x - 3 ; dependent system
3
26)
Solve the system by the addition method.
-5.9x + 4.1y = 5.4
0.1x - 8.7y = 25.8
A) (1.1, 2.9)
B) (5.7, -2.9)
C)
(-7.1, -8.9)
D)
(-3, -3)
Solve the system by using the substitution method.
x = 0.1y - 6.9
y = -1.9x - 2.4
A) (-7.1, -2)
B) (-6, 9)
C) (0, -2.4)
D) No solution; { }; inconsistent system
6
27)
28)
28)
Write a system of linear equations represented by the augmented matrix.
1 0 0 -11
0 1 0 10
0 0 1 -10
A)
B) x =
x + y + z = -11
x + y + z = 10
x + y + z = -10
C) x = -11
y = 10
z = -10
11
y = -10
z = 10
D) (x - 1) + y + z = -11
x + (y - 1) + z = 10
x + y + (z - 1) = -10
29)
Solve the system by using the Gauss-Jordan method.
-3x + y = 8
-9x + 3y = 3
A) (1, 11)
B) (0, 8)
C) No solution; inconsistent system
D) Infinitely many solutions; {(x, y) | y = 3x + 8}; dependent system
29)
30)
Perform the indicated operation, and write your answer in scientific notation. Round the
final answer to one decimal place.
(1.9 × 10-5) ÷ (3.4 × 10-11)
30)
A)
31)
B) 5.6
× 100-16
C)
0.6 × 10-16
D)
5.6 × 105
Factor out the greatest common factor if necessary. Then determine if the polynomial is a
perfect square trinomial. If it is, factor it.
5w2 - 30w - 25
A) 5(w + 5)(w - 1)
B) 5(w - 5)(w + 1)
C) 5(w + 5)(w + 1)
D)
32)
0.6 × 106
31)
5(w 2 - 6w - 5); Not a perfect square trinomial
32)
Simplify the expression. Write your answer with positive exponents only.
2
(t3 z)
z7t
A)
9
-2
(3t -2z4 )
B)
t10
C)
9z6
7
9z10
t
D)
1
81t4 z20
33)
34)
Solve the equation.
t(10t - 19) = -7
1 7
,A)
2 5
B)
0,
19
10
C)
-
1 7
,2 5
1 7
,
2 5
D)
34)
Add or subtract as indicated and simplify if possible.
-20x
7
+
-4x + 3 -4x + 3
A)
35)
33)
-20x + 7
-8x + 6
B)
-20x + 7
-4x + 3
C)
-140x
-4x + 3
D)
-13x
-4x + 3
35)
Simplify the complex fraction.
19 5
2+
3
2
7
+6
2
A)
36)
57
11
B) -
8
11
C)
11
8
D)
-
11
57
36)
4x9
3y6
B)
3y6
C)
4x9
3x11
D)
256y10
256y10
3x11
37)
Write the domain of the rational function in set-builder notation.
7
f (x) =
x - 11
A)
B) {x
{x x -11}
C) {x x = 11}
38)
-
Divide the rational expressions.
8y8 32y2
÷
3x
x10
A)
37)
-
x
D) {x x
11}
11, x
-7}
Write the expression by using rational exponents rather than radical notation.
5
8 x3
A)
(8x)3/5
B)
8
C)
x3/5
8
8x3/5
D)
8x5/3
38)
39)
40)
Add or subtract the radical expressions as indicated. Assume that all variables represent
positive real numbers.
5 2 9
3
x y 252x7 + x5 y8 175xy2 - 28x11y18
6
5
A)
8x5 y9 7x - x5 y9 28x
B) 8x5 y9
C)
6x5 y9 7x
D)
39)
7x - 28x11y18
Cannot be simplified further
Evaluate the root without using a calculator or note that root is not a real number.
40)
4
0.0081
A) 81
C) 3
41)
B) 0.3
D)
Not a real number
41)
Graph the function.
h(x) = -4x2
A)
B)
C)
D)
9
42)
42)
Find the x- and y-intercepts of the function.
f (x) =
8x2
– 80
A)
x-intercept: (0, 10); y-intercept: (-80, 0)
B) x-intercept: ( 10, 0); y-intercept: none
C) x-intercepts: (0, 10) and (0, - 10); y-intercept: (-80, 0)
D) x-intercepts: ( 10, 0) and (- 10, 0); y-intercept: (0, -80)
43)
43)
Find the x-intercepts of the function.
4x2
h(x) =
– 16x + 16
1
1
, 0 and - , 0
A)
2
2
C)
44)
B) (2,
D)
(2, 0) and (–2, 0)
0)
None.
44)
Write the inverse function for f = {(9, -2), (3, 9), (-2, -8), (8, 7)}.
A) f -1
B) f -1
= {(2, -9), (-9, -3), (8, 2), (-7, -8)}
= {(-9, 2), (-3, -9), (2, 8), (-8, -7)}
1 1 1 1
1 1 1 1
,- , , ,- ,- , ,
C) f -1 =
9 2 3 9
2 8 8 7
D)
45)
f -1 = {(-2, 9), (9, 3), (-8, -2), (7, 8)}
Expand into sums and/or differences of logarithms. Assume all variables represent
positive real numbers.
6
log
A)
C)
46)
ab
c2
1
1
log a + log b - 2 log c
6
6
6
45)
B) 6
D)
log a + log b + 2 log c
log a + log b - 2 log c
1
log a + log b - 2 log c
6
46)
Write the equation in exponential form.
log4 4096 = 6
A) 46
= 4096
B) 40966
C) 64
=4
10
= 4096
D) 64096
=4
47)
47)
Graph the solution set.
y -x2
A)
B)
C)
D)
11
48)
Use the equation of the parabola in standard form x = a(y - k)2 + h to determine the
coordinates of the vertex and the equation of the axis of symmetry (complete the square
if necessary). Then graph the parabola.
48)
x = -y2 - 6y - 10
49)
50)
A)
B)
C)
D)
49)
Solve the system by the substitution method.
y = 6x2 – 12x
y = 6x
A) {(0, 0)}
C) {(3, 18)}
B) {(0,0),
D)
(3, 18)}
{}
50)
Clear parentheses and combine like terms.
2
1
2
(4n - 6m) - (15m - 12n - 2) +
2
3
3
A)
B) -8m
-8m + 11n - 2
C) -13m - 6n - 2
+ 5n + 2
D) -13m + 10n + 2
12
51)
Show that the number is a rational number by finding a ratio of two integers equal to the
number.
8
8
8
0
1
A)
B)
C)
D)
1
0
8
8
51)
52)
Solve the absolute value inequality. Write the solution in interval notation.
|x + 4| 12
52)
A)
B) [-
, -16] [8, ]
D) [-8, 16]
[-16, 8]
C) [-8, 8]
53)
Solve for x and then use its value to find the measure of each angle. Note: the measures of 53)
the indicated angles are equal.
(Figure is not necessarily drawn to scale.)
A) 33°
B) 37°
54)
55)
C)
38°
Which of the lines defined here have only one unique intercept?
a. x = -8
b. 2x - 3y = 6
c. -5y = -1
d. -6x + 3y = 0
A) b and d
B) b
C) a and c
Plot the point on the rectangular coordinate system.
(3.2, 2.7)
13
D)
35°
54)
D)
a, c, and d
55)
56)
A)
B)
C)
D)
56)
g(x) = 2x - 7, h(x) = 4 x - 8, (h g)(2) = ?
A)
4 11
B) Not
C)
16 3 - 7
D)
14
a real number
8 6-7
57)
57)
Match each equation with its graph.
g(x) = x2
f(x) = x
h(x) = |x|
I
II
III
A)
B)
f(x), III; g(x), I; h(x), II
C) f(x), II; g(x), III; h(x), I
58)
f(x), I; g(x), III; h(x), II
D) f(x), III; g(x), II; h(x), I
Solve the system by using the Gauss-Jordan method.
3x - 2y = -15
x + 3y = 17
295 36
79 66
,,
A) (-1, 6)
B)
C) 11
11
7 7
58)
D)
(-3, 3)
59)
Nail polish remover is essentially a mixture of water and a chemical called acetone. How
much pure acetone must be combined with a solution that is 40% acetone to make 30 oz
of a 58% solution?
A) 15 oz
B) 9 oz
C) 13 oz
D) 21 oz
59)
60)
Simplify the expression.
-2s(-5s + 3)(s - 1)
60)
A)
10s3 - 16s2 + 6
C)
10s3 - 16s2 + 6s
B) 10s3
D) 10s3
+ 8s2 - 3s
+ 6s
61)
On a certain map, Detroit and Cleveland are 3" apart. The actual distance from Detroit
to Cleveland is 170 miles. How far apart are two cities that are 11" apart on this map?
Round to the nearest tenth of a mile.
A) 482.3 miles
B) 717.3 miles
C) 0.2 miles
D) 623.3 miles
61)
62)
Multiply the radical expressions and simplify your answer.
62)
2 6x6 y3 2 10xy6
A)
8 15x7 y9
B) 8x3 y4
C)
15xy
15
16x3 y4 15xy
D)
16 x5 y7
63)
64)
65)
C)
{6, 13}
D)
{-6, -13}
64)
Solve the logarithmic equation.
11 – 7 log3(x – 5) = 4
11
A)
B) {–5}
3
C)
{}
Determine if the equation represents an ellipse or a hyperbola.
(x - 7)2 (y - 8)2
+
=1
25
49
A)
66)
63)
Solve the equation by using substitution.
(t + 10)2 – (t + 10) – 12 = 0
A) {-14, -7}
B) {4, –3}
D)
{8}
65)
B) Hyperbola
Ellipse
Complete the table.
Number Opposite Reciprocal Absolute Value
1
24
A)
Number Opposite Reciprocal Absolute Value
1
-24
24
24
24
B)
Number Opposite Reciprocal Absolute Value
1
-24
24
-24
24
C)
Number Opposite Reciprocal Absolute Value
1
1
-24
24
24
24
D)
Number Opposite Reciprocal Absolute Value
1
24
-24
24
24
16
66)
67)
Solve the absolute value inequality. Write the solution in interval notation.
8 + 2x - 11 2
5
17
,
,
A)
B) (- , )
2
2
C)
68)
5 17
,
2 2
Determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular.
-4x + 9y = 7
3
1
x+ y=8
2
3
A)
69)
D)
{}
neither
B) parallel
C)
C)
B) [–40,
{–20, –10, 0, 10, 15}
{0, –20, –40, 20}
D)
17
20]
[–20, 15]
68)
perpendicular
Find the range of the relation. Use interval notation where appropriate.
A)
67)
69)
70)
71)
70)
Graph the solution set of the compound inequality.
y – 2x 4 and 3y 6x – 9
A)
B)
C)
D)
No solution
Divide the polynomials by using an appropriate method.
(40n3 - 78n2 + 20n + 16) ÷ (5n2 - 6n -3)
8n
8n - 2
A) 8n - 6 +
B) 8n - 6 +
5n2 - 6n -3
5n2 - 6n -3
C)
8n - 6 -
8n - 2
D)
5n2 - 6n -3
18
8n + 6
71)
72)
72)
Simplify the complex fraction.
-4
x2
17
3x
A)
73)
-
21
x2 - 3x
B) -
17x
12
C)
-
68
3x3
-
12
17x
73)
Convert the expression to radical form and simplify.
91/2
A)
81
B) 3
C)
9
2
D)
19
D)
Not a real number
74)
Graph the parabola. Use the graph to write the domain and range in interval notation.
f (x) = -3(x - 2)2
A) Domain: [- , 2); Range: (- , )
B) Domain: (- , ); Range: [0, )
C)
75)
76)
D)
Domain: (- , 0]; Range: (- , )
74)
Domain: (- , ); Range: (- , 0]
75)
Solve the logarithmic equation.
log1/3 (2z + 5) - log1/3 z = -3
11
1
A)
B)
3
5
C)
{}
Use the distance formula to find the distance between the two points.
(-13, 4) and (-7, -4)
A) 14
B) 10
C) 100
20
D)
{9}
76)
D)
14
77)
77)
Graph the set and express it in interval notation.
All real numbers between 7 and 12.
A) [7, )
B) [7, 12)
7
C)
D)
[7, 12]
7
7
12
7
12
(7, 12)
12
78)
Solve the absolute value inequality. Write the solution in interval notation.
15 23 + |y + 5|
A) [-13, 3]
B) (- , )
C) (- , -13]
D) { }
78)
79)
Write an equation of the line satisfying the given conditions. Write the answer in
slope-intercept form.
79)
The line contains the point (-4, -12) and is perpendicular to a line with a slope of A)
80)
y=
3
x-4
2
B) y =
-
3
x-6
2
C)
y=
D)
y=
3
x-6
2
80)
Is the graph below the graph of a function?
A)
3
x - 12
2
2
.
3
B) No
Yes
21
Answer Key
Testname: FINALREVIEW123
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
D
C
C
C
D
D
C
B
A
D
A
D
C
A
A
C
B
B
C
C
A
D
A
A
C
D
B
C
C
D
D
B
D
B
D
B
B
C
C
B
A
D
B
D
A
A
B
D
B
D
22
Answer Key
Testname: FINALREVIEW123
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
A
A
D
D
B
B
A
A
B
C
D
B
D
D
A
A
B
A
B
D
B
D
B
D
B
B
D
D
D
A
23