Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) Subtract the expressions with unlike denominators.
3 - x2
x
x+4
A)
-
1)
x2 - 16
x3 + 4x - 3
(x - 4)(x + 4)2
B)
-4x - 3
(x - 4)(x + 4)
C)
x2 + x - 3
(x + 4)(5 - x)
D)
2x2 - 4x - 3
(x - 4)(x + 4)
2) Write a variation model.
2)
the height (h) of a cone varies directly as the volume (V) and inversely as the square
of the radius (r)
k
kV
k
kV
A) h =
B) h =
C) h =
D) h =
V r
r
Vr2
r2
3) Simplify the expression to lowest terms.
y2 + 4y - 45
3)
y2 - 25
A)
y+9
y-5
B) cannot
C)
y+9
y+5
D)
simplify
4y - 45
25
4) Simplify the expression to lowest terms.
4)
-20(9x - 4)(x + 7)
4(x + 7)2
A)
-5(9x - 4)
x+7
B)
5(9x - 4)
x+7
C)
1
-5(9x - 4)
D)
-20(9x - 4)
4
5) Find the least common denominator, then convert each expression into an equivalent
5)
expression with denominator equal to the least common denominator.
-15
11
,
2
49z 42z3
A)
C)
-15
294z3
11
,
B)
294z3
-630z3
2058z5
,
539z2
D)
2058z5
-90z3
294z5
-90z
294z3
,
,
77z2
294z5
77
294z3
6) Simplify the complex fraction.
11-
A)
6)
36
t2
16 60
+
t
t2
t+6
t - 10
B)
t + 36
t + 10
C)
t-6
t - 10
D)
t - 36
t + 10
7) Divide.
25t2 - 1 5t2 + 26t + 5
÷
t2 - 9t
t2 - 4t - 45
A)
7)
(5t - 1)(5t + 1)
B)
t(t - 9)2
5t - 1
C)
t
D)
5t + 1
t(t + 5)
(5t - 1)(5t + 1)2
t(t - 9)2
8) Translate the following English phrase into an algebraic expression.
The quotient of 4 and the sum of a number y and 3.
4
3
1
A) 4y +
B) 3y +
C) 4y +
y
3y
y+4
8)
D)
4
y+3
9) The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you
want to make as much cake batter as you can using all of the flour you have, which is 27
cups. How many cups of sugar would you need? Round to one decimal place.
A) 7.7 cups
B) 11.6 cups
C) 19.3 cups
D) 63.0 cups
2
9)
10) Add or subtract the expressions with like denominators as indicated.
x2
18x + 80
x+8
A) x2
+
10)
x+8
B) x +
+ 14
C)
8
x + 10
D) x2
+ 28
11) Simplify the complex fraction.
11)
5 2
2 3
4
3
8A)
11
40
B)
110
9
C) -
1
4
D) -
3
16
12) Add or subtract the expressions with like denominators as indicated.
12)
6x
7
+
5x + 9 5x + 9
A)
13x
5x + 9
B)
42
5x + 9
C)
6x + 7
2(5x + 9)
D)
6x + 7
5x + 9
13) Simplify the expression to lowest terms.
13)
(k + 4)(k - 2)
(k + 9)(k + 4)
A)
(k + 9)
(k - 2)
B) -
(k - 2)
(k + 9)
C)
(k - 2)
(k + 9)
14) Add and subtract the expressions with unlike denominators.
4y
y2
A)
- 3y - 10
+
y + 1 2y - 7
y-5 y+2
3y + 8
B) -
(y - 5)2 (y + 2)2
C) -
y2 - 10y + 37
(y + 2)(y - 5)
D)
3
y2 - 24y + 33
(y + 2)(y - 5)
3y + 8
y2 - 4y - 13
D) -
2
9
14)
15) Add the expressions with unlike denominators.
2x
x2
A)
C)
+
- 18x + 80
x
x2
- 2x - 80
x(3x + 8)
(x -
10)2(x -
15)
B)
8)(x + 8)
3x
(x - 10)(x - 8)(x + 8)
D)
x(3x + 8)
(x - 10)(x - 8)(x + 8)
3x
(x -
10)2(x -
8)(x + 8)
16) Identify the least common denominator.
16)
7x
-5
,
x + 7 x2 - 49
A)
(x + 7)(x2 - 49)
C)
x+7
B) x – 7
D) x2 - 49
17) Solve for d2.
17)
1
1
1
=
+
f d1 d2
A) d2 =
d1f - d2f
d1
B) d2
fd1
C) d2 =
d1 - f
= f - d1
1
D) d2 =
f - d1
18) The two triangles pictured below are similar triangles. If side a is 9 inches, side b is 7
18)
inches, and side c is 11.25 inches, find the length of side d.
A)
9.8 inches
B) 8.75
C)
inches
9.25 inches
19) Add the expressions with unlike denominators.
(x - 2)(x + 26)
2(3x - 13)(x + 12)
x2 + 12x + 2
C)
7x - 38
4
5.6 inches
19)
x
2
+
6x - 26 x + 12
A)
D)
B)
x+2
7x - 38
D)
x+2
2(3x - 13)(x + 12)
20) Write a variation model. Use k as the constant of variation.
20)
the number of hours (t) it takes to paint a house is inversely proportional to the
number of people (n) painting
k
t
n
=k
A) t =
B)
C) t =
D) t = kn
n
n
k
21) The two triangles pictured below are similar triangles. Find the missing length.
A)
B) 17.5
19 feet
C)
feet
D)
10 feet
21)
20 feet
22) Solve for b1.
22)
h
A
=
2 b1 + b2
2
-b
A) b1 = A
h 2
C) b1 =
B) b1 =
2A - hb2
D) b1 =
h
h
-b
2 2
A
2A - b2
2h
23) Simplify the complex fraction.
56y3
23)
3x
21y
x5
A)
35y2
2x4
B)
8y4 x6
9
C)
5
8x4 y2
9
D)
392y4
x6
24) Find an expression that represents the perimeter of the rectangle (assume that x > 0)
24)
8
x+3
9
x+2
A)
72
(x + 2)(x + 3)
B)
2(17x + 43)
(x + 2)(x + 3)
C)
17x + 43
(x + 2)(x + 3)
D)
144
(x + 2)(x + 3)
25) Solve the equation.
25)
3m
3
1+
=
6m - 12 3m - 6
A)
m = -2
B) m
C)
= -2, m = 6
D)
no solution
m=2
26) Simplify the expression to lowest terms.
-n2 + 5n - 6
26)
n2 - 2n
A)
5n - 6
-2n
B)
-(n - 3)
n
C)
-(n - 3)
n-2
D)
cannot simplify
27) Find the least common denominator, then convert each expression into an equivalent
27)
expression with denominator equal to the least common denominator.
2t t + 4
,
t - 2 2t + 5
A)
4t + 5
2t - 2
,
3(t + 1) 3(t + 1)
B)
2t
t+4
,
(t - 2)(2t + 5) (t - 2)(2t + 5)
C)
4t2 + 10t
t2 + 2t - 8
,
(t - 2)(2t + 5) (t - 2)(2t + 5)
D)
2t2 - 4t
2t2 + 13t + 20
,
(t - 2)(2t + 5) (t - 2)(2t + 5)
28) Determine whether x and y vary directly, inversely, or jointly in the following equation.
y=
A)
16
x
jointly
B) inversely
C)
6
directly
28)
29) The current in a wire varies directly as the voltage and inversely as the resistance. If the
29)
current is 8 A (amperes) when the voltage is 40 V (volts) and the resistance is 5
(ohms), find the current when the voltage is 55 V and the resistance is 5 .
A) 11 A
B) 44 A
C) 4 A
D) 22 A
30) Simplify the expression to lowest terms.
30z9
30)
75z12
A)
2
5z3
B)
30
C)
75z3
2z21
5
D)
2z3
5
31) Add the expressions, if possible. Assume the variable represents a positive real number.
29 y + 39 y
A) 68 2y
B) 68 y
C) 136 2y
D)
68y
32) Multiply the expressions. Assume the variable represents a positive real number.
6x (2 + 15x)
A) 12 x + 3x 10
C) 2 6x + 3x 10
31)
32)
B) (2 + x) x + 90
D) 2 6x + x 15
33) Simplify the expression. Assume the variables represent positive real numbers.
2
33)
(8 3pq)
A)
34)
24p2q2
B) 192pq
C)
B) 5
D)
5 and 13
5 6 and 5 13
B) not
-3125
C) -
72p2q2
6 and - 3 6
35) Convert the expression to radical form and simplify, if possible.
-255/2
A)
D)
34)
Identify the pair of like radicals.
5
A) -13 5 and
5
C)
576pq
125
2
D)
7
a real number
3125
35)
36) Use the multiplication property of radicals to simplify the expression. Assume the
36)
variables represent positive real numbers.
18zt9
A)
3t4 2zt
B) 3zt4
C) 3t 2zt7
6t
D)
9t4 2zt
37) Simplify the expression using the properties of rational exponents. Assume the variable
37)
represents a positive real number.
t22
1/2
t-8
A) t7
B) t15
C) t3
D) t19
38) Write the expression using rational exponents rather than radical notation. Assume the
38)
variables represent positive real numbers.
3
A)
(-3ab)5
-3ab5/3
B) -3ab3/5
C)
(-3ab)3/5
D)
(-3ab)5/3
39) Subtract the expressions, if possible.
39)
2 10 - 5 10
A)
7 10
B) -3
C)
10
2 10 - 5 10
D)
-6 10
40) Multiply the expressions.
7
A) 14
40)
14
B) 14 2
C) 7 2
D)
7
41) The total number of people, P, in one city that have fallen for a telemarketing scam is
41)
approximated by the formula
P = 1,200 + 11,300x
where x is the number of days since a newspaper article exposed the scam. At the time
the article ran, 1,200 people had fallen for the scam. How long did it take for that
number to increase to 1,500? Round your answer to the nearest integer.
A) 2 weeks
B) 5 days
C) 3 weeks
D) 8 days
42) The total number of people, P, in one city that have fallen for a telemarketing scam is
approximated by the formula
P = 1,200 + 11,300x
where x is the number of days since a newspaper article exposed the scam. How many
additional people fell for the scam the first day after the article? Round your answer to
the nearest integer.
A) 1,306
B) 1,200
C) 106
D) 241
8
42)
43) Use the multiplication property of radicals to simplify the expression. Assume the variable 43)
represents a positive real number.
26a
A)
B) -2
26a
C)
13a
D)
2 13a
26a
44) Convert the expression to radical notation. Assume the variable represents a positive real
44)
number.
x1/3
A) 3 x
1
B)
C)
x3
x
3
D)
3
x
45) Use the division property of radicals, if necessary, to simplify the expression. Assume the 45)
variable represents a positive real number.
c3
100
A)
c3
10
B)
c2 c
100
C)
c2 c
10
D)
46) Multiply and divide as indicated.
y2 + 5y y2 - 25 y - 5
y-1
÷
3y - 3
46)
y
A)
3
B)
C)
(y + 5)(3y - 3)
y(y - 5)
D)
1
3(y2
- 25)
(y + 5)2 (y - 5)
3(y - 1)
47) Identify the restricted values.
47)
x+3
(5x - 11)(x - 8)
A) x = C)
c c
10
11
; x = -8
5
B) x = -3; x =
D) x =
x=0
9
11
;x=8
5
11
;x=8
5
48) Add the expressions with unlike denominators.
48)
3
-12
+
x - 2 x2 - 4
A)
-9
x2 + x - 6
B)
3
x+2
C)
3x + 18
D)
x2 - 4
15x2 - 60
(x - 2)(x2 - 4)
49) Find an expression that represents the perimeter of the rectangle. (assume that x > 0 and
49)
y > 0).
11x
y + 12
2x
y + 12
A)
26x2
units
y + 12
B)
C)
13x
units
y + 12
D)
26x
units
y + 12
22x2
( y + 12)2
units
50) Translate the following English phrase into an algebraic expression.
50)
The product of 6 and the reciprocal of the sum of a number t and 2.
1
1
1
1
+2
A) 6
B)
C) 6
D) 2 +
6(t + 2)
t
6t
t+2
51) Simplify the expression to lowest terms.
51)
9-m
-9 + m
A)
-1
B) 1
C)
cannot simplify
D)
81 - m 2
52) A manufacturer of miniture drones has a fixed cost of $380,000, plus a variable cost of
$380 per drone. The average cost per drone, y (in dollars), is given by the equation:
380,000 + 380x
y=
where x represent the number of drones produced.
x
Find the average cost per drone if the manufacturer produces 2000 drones.
A) $380.00
B) $190.00
C) $570.00
D) $1,140,000.00
10
52)
53) Write the expression in radical notation. Assume the variable represents a positive real
53)
number.
2x1/5
A)
5
B) 2
2x
5
1
C)
x
5
D)
2x
1
5
2 x
54) Use the order of operations, if necessary, to simplify the expression. Assume the variable
54)
represents a positive real number.
d19
d3
d17
A)
B) d8
d
C) d4
D)
d19/3
55) Simplify the expression using the properties of rational exponents. Assume the variable
55)
represents a positive real number.
x24/7
x10/7
A)
B) x10/7
x
C) x10
D) x2
56) Convert the expression to radical form and simplify.
1003/2
A)
56)
B) not
a real number
D) 1000
1010
C) 150
57) Determine whether x and y vary directly, inversely, or jointly in the following equation.
y = -20x
A) inversely
B) jointly
C)
directly
58) Find the least common denominator, then convert each expression into an equivalent
expression with denominator equal to the least common denominator.
30
2
,
19z2 z3
A)
30
19z5
,
2
19x5
B)
30z
19z3
,
38
C)
19z3
11
30z3
19z5
,
38z2
19z5
57)
D)
570z3
19z3
,
38z3
19z3
58)
59) Convert the expression to radical notation. Assume the variable represents a positive real
59)
number.
18z2/3
2
A) 18 z3
3
B) 18 z2
C)
3
18z2
D)
3
(18z)2
60) The amount of interest earned by an account based on simple interest varies jointly as the
principal amount and the number of years the investment has been held. If a principal of
$4000 invested for 8 years earns $1600 in interest, how much interest would be drawn by
$2000 invested for 13 years?
A)
$1605.00
B) $800.00
C)
12
$1500.00
D)
$1300.00
60)
Answer Key
Testname: TEST3EAPARCTICESUMMER
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D
D
C
A
D
A
C
D
B
C
A
D
C
B
B
D
C
B
A
A
B
C
C
B
C
B
C
B
A
A
B
C
B
A
A
A
B
D
B
C
D
C
D
D
D
A
D
B
B
A
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Answer Key
Testname: TEST3EAPARCTICESUMMER
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
A
C
B
B
D
D
C
B
B
D
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