Intermediate Algebra problems you can use for practice. Remember, you may not use a calculator
when you take the assessment test. Use these problems to help you get up to speed.
_________________________________________________________________________________________
Solve the equation.
x + 4 3x - 12
=1
1)
4
10
Solve.
A) 24
B) 6
C) - 24
D) -48
Solve the problem.
2) The difference of a number and 8 is the same
as 34 less the number. Find the number.
A) 21
B) -13
C) -21
D) 13
3) The population of a town is currently 22,000.
This represents an increase of 80% from the
population 5 years ago. Find the population of
the town 5 years ago. Round to the nearest
whole number if necessary.
A) 12,222
B) 4400
C) 17,600
D) 27,500
4) P = 2L + 2W for L
P - 2W
A) L =
2
C) L =
P-W
2
B) L = P - 2W
6) The average price (in dollars) to rent a studio
in a certain city can be approximated by the
equation p = 34.0t + 646 where t is the number
of years since 1990. Solve this equation for t
and use the new equation to determine
approximately what year it will be when the
average price of a studio in this city reaches
$1326.00.
A) 2012
B) 2013
C) 2010
D) 2011
Solve the linear inequality. Express the solution using
set-builder notation and interval notation. Graph the
solution set. NOTE: A square bracket, i.e. [, is the same as
a filled in circle. A round bracket, i.e. (, is the same as an
open circle.
7) 3x - 9 < 4(x - 3)
A) {x|x < -3}; (- , -3)
B) {x|x > -21}; (-21, )
D) L = P - W
C) {x|x > 3}; (3, )
nE
for n
5) I =
nr + R
A) n = IR(Ir - E)
C) n =
IR
Ir + E
B) n =
-IR
Ir - E
D) n =
-R
Ir - E
D) {x|x < 21}; (- , 21)
Solve the inequality. Graph the solution set, and state the
solution set in interval notation.
8) |x - 4| + 2
9
11) f(x) = x2 + 3
A) {x|x > -3}
B) {x|- < x < }
C) {x|x -3}
D) {x|x -3}
Find the slope of the line that goes through the given
points.
A) [-3, 9]
12) (-2, -1), (9, -1)
2
A) 11
B) [-3, 11]
C) 0
C) (-3, 11)
B) -
2
7
D) Undefined
Find an equation of the line with the given slope and
containing the given point. Express your answer in
slope-intercept form.
13) m = -3, (-6, 5)
D)
A) y = -3x + 13
B) y = -3x - 13
C) y - 5 = x + 6
D) y - 5 = mx + 6
14) m = -
List the intercepts of the graph.
9)
2
, (5, 5)
3
A) y = -
3
25
x2
2
B) y =
2
25
x3
3
C) y = -
2
25
x+
3
3
D) y = -
2
25
x3
3
15) m is undefined, (5, -1)
A) y = 5
B) x = 5
C) x = -1
D) y = -1
Use the given conditions to write an equation for the line
in slope-intercept form.
16) Passing through the point (2, 1) and
perpendicular to y = 3x - 3
5
5
A) y = 3x +
B) y = -3x +
3
3
A) (0, -2), (0, 8), (4, 0)
B) (0, -2), (8, 0), (0, 4)
C) (-2, 0), (0, 8), (4, 0)
C) y =
D) (-2, 0), (0, 8), (0, 4)
Find the domain of the function.
2x - 3
10) f(x) =
x+6
B) {x|x
C) {x|x -6}
D) {x|x -6,
D) y = -
1
5
x+
3
3
Determine whether the ordered pair is a solution of the
system of linear equations.
17) 4x = 18 - y ; (5, -2)
3x = 7 - 4y
3
}
2
A) {x|x 6}
1
5
x+
3
3
3
}
2
A) Yes
B) No
Solve the system of equations using elimination.
18) 3x - 6y = -7
8x - 5y = -5
41 5
5
41
,
,A)
B)
33 33
33
33
5 41
,
C)
33 33
41
5
,D) 33
33
Simplify the expression. All exponents should be positive
integers.
-6a13b-3
19)
3a 7b-9
A)
-2b6
a6
-2
C)
a 6 b6
B)
-2a6
b6
D) -2a 6b6
Simplify the expression.
20) (-5)2 · 100
A) -25
C) -
1
25
B)
1
25
D) 25
A) a(b2 + 11ab)(b2 - 11ab)
B) ab2 (b + 11a)(b - 11a)
C) ab2 (b - 11a)2
D) Prime
Find the product.
25) -5x6(11x7 + 6x4 + 12)
A) -55x7 - 30x4 - 60
B) -55x13 - 30x10
C) -55x13 + 6x4 + 12
D) -55x13 - 30x10 - 60x6
Solve the system of equations using substitution.
x - 6y = -42
26)
-5x - 5y = -35
A) (0, 7)
B) (-7, 0)
C) (1, 6)
D) no solution
Factor the sum or difference of two cubes completely.
27) x3 + 27
Perform the indicated operation. Express the solution in
scientific notation.
21) (8 × 10-5) · (6.1 × 10-3 )
22)
24) ab4 - 121a 3 b2
A) (x + 3)(x2 + 9)
B) (x - 3)(x2 + 3x + 9)
C) (x - 27)(x + 1)(x - 1)
A) 4.88 × 10-7
B) 4.88 × 1015
C) 488 × 10-8
D) 48.8 × 10-7
D) (x + 3)(x2 - 3x + 9)
28) 64y3 - 1
12.74 × 107
A) (64y - 1)(y2 + 4y + 1)
4.9 × 108
A) 2.6 × 10-1
B) 2.6 × 1015
C) 5.2 × 1015
D) 5.2 × 10-1
Factor the difference of two squares completely.
23) 25 - 16x2
A) (5 + 4x)(5 - 4x)
B) (5 + 4x)2
C) (5 - 4x)2
D) Prime
B) (4y - 1)(16y2 + 1)
C) (4y - 1)(16y2 + 4y + 1)
D) (4y + 1)(16y2 - 4y + 1)
Factor completely, or state that the polynomial is prime.
29) 40x2 + 2x - 24
A) (5x + 4)(8x - 6)
B) 2(5x + 4)(4x - 3)
C) (2x + 8)(4x - 3)
D) 2(5x - 4)(4x + 3)
Find the intercepts of the graph of the function.
30) 2x3 + 2000
36) g(t) = t2 + 6t - 16
A) 2(x + 10)3
A) (8, 0), (2, 0), (0, - 16)
B) 2(x3 + 1000)
B) (-8, 0), (2, 0), (0, - 16)
C) 2(x + 10)(x 2 - 10x + 100)
C) (-8, 0), (1, 0), (0, - 16)
D) Prime
D) (8, 0), (-2, 0)
Find the special product.
Factor the polynomial completely.
31) (7x + 12)2
37) x4 - 8x 2 + 7
A) 7x2 + 168x + 144
B) 49x2 + 144
C) 49x2 + 168x + 144
D) 7x2 + 144
A) (x2 - 1)(x2 - 7)
B) (x2 + 1)(x2 + 1)
C) (x2 + 1)(x2 - 7)
D) Prime
Find the values of x such that the given function has the
stated value.
32) (6x - y)2
38) f(x) = x2 + 8x; f(x) = 48
A) 36x2 - 12xy - 2y2
A) x = 12 or x = 4
B) x = -12 or x = 4
B) 36x2 + y2
C) x = 12 or x = -4
D) x = -12 or x = 1
C) 36x2 - 12xy + y2
D) 36x2 - 6xy + y2
Factor the polynomial completely. If the polynomial
cannot be factored, say it is prime.
Multiply the rational expression. Express the product as a
rational expression in lowest terms.
80x
10x - 50
·
39)
x2 - 25
8x2
33) x2 - 5xy - 24y2
A) (x - 3y)(x + y)
B) (x + 3y)(x - 8y)
C) (x - 3y)(x + 8y)
D) Prime
34) 10x2 + 7x - 12
40)
A) (2x - 3)(5x + 4)
B) (10x + 3)(x - 4)
C) (2x + 3)(5x - 4)
D) Prime
Factor completely, or state that the polynomial is prime.
35) x3 - 4x 2 - 36x + 144
A) (x + 4)(x + 6)(x - 6)
B) (x - 4)(x + 6)(x - 6)
C) (x - 4)(x - 6)2
D) Prime
A)
100x
x+5
B)
10
x(x + 5)
C)
100
x(x + 5)
D)
64
x(x + 5)
6w - 36
w2 + 8w + 7
·
2
w + 1w w2 - 13w + 42
A)
6(w - 7)
w(w + 7)
B)
6(w + 7)
w-7
C)
6(w + 7)
w(w - 7)
D)
6
w
Determine the domain of the rational function.
2
41) R(x) =
x-7
A) {x|x 7}
B) {x|x -7}
C) {x|x
D) {x|x
0}
0, x
7}
Perform the indicated operation and simplify the result.
4x2 - 17x + 5 3x2 - 9x - 7
42)
x2 - 15x + 54 x2 - 15x + 54
43)
A)
x-2
x+9
B)
x2 - 8x + 12
x2 - 15x + 54
C)
x-2
x-9
D)
x+2
x-9
2x + 7
x-5
B)
27b - 16a2
30a 3b2
B)
27b + 16a2
D)
30a 3b2
B)
-11(y + 9)
(y + 2)(y - 9)
D) 0
10)
A) 10 + 2 5
B) 20
C) 100 + 2 5
D) 10 + 4 5
Use the product rule to simplify the expression. Assume
that the variables can be any real number.
405k7 q8
A) 9q4
C) 9k3 q4
5
D) 5x4
3k
B) 5k3 q4
3
D) 5k7 q8
3k
Simplify the radical.
3
50) (-6)3
27b - 8a 2
30a3 b2
Multiply, and then simplify if possible. Assume all
variables represent positive real numbers.
47)
3
51)
5
A) -18
B) -6
C) 18
D) 6
(x - 1)5
A) -x + 1
B) |x - 1|
C) -|x - 1|
D) x - 1
Evaluate the expression, if possible.
11(y + 9)
(y + 2)(y - 9)
2( 50 +
3k7
C) 5k3 q4
y+9 y+9
y+2 y-9
-7(y + 9)
C)
(y + 2)(y - 9)
46)
B) x4
75k7q8
A) 5q4
2x - 7
D)
x-5
27b - 16a2
C)
30a 2b3
A)
x
A) 5x4
3
C) x4 2
-5x
x-5
Add or subtract, as indicated, and simplify the result.
9
8
44)
10a 3b 15ab2
45)
3 250x 13
2x
49)
2x - 7
C)
5-x
A)
48)
Simplify the radical expression. Assume that all variables
represent positive real numbers.
2x
7
+
x-5 5-x
A)
Divide and simplify.
5k7
B) 9k3 q4
5k
5
D) 9k7 q8
5k
52) 64-4/3
A) 256
1
B)
256
C) -
1
256
D) not a real number
Multiply, and then simplify if possible. Assume all
variables represent positive real numbers.
53) ( 2 + 5)2
A) 10 + 2 10
B) -3 + 2 10
C) 7 + 2 10
D) 7 - 2 10
Add or subtract. Assume all variables represent positive
real numbers.
54) 2 125 - 3 20 - 4 45
A) -8 5
B) 7 5
C) -7 5
D) 2 5
Rationalize the denominator and simplify. Assume that all
variables represent positive real numbers.
5
55)
7-9
5 7 - 45
A)
74
C) -
5 7 + 45
B) 74
5 7 - 45
74
D)
5 7 + 45
74
B)
C) 4
D)
1
60) 4-x =
64
A) x =
1
16
C) x = -3
B) x = 3
D) x =
1
3
Simplify the radical expression. Assume that all variables
represent positive real numbers.
3
3
61) 6 · -36
Simplify the complex rational expression.
4
+1
a
56)
4
-1
a
A) 4 - a2
Solve for x.
a2
A) -6
B) -216
C) 6
D) 6 6
Complete the square for the binomial. Then factor the
resulting perfect square trinomial.
4 - a2
4+a
4-a
62) x2 - 14x
A) x2 - 14x - 49 = (x - 7)2
B) x2 - 14x + 196 = (x - 14)2
Solve for x.
C) x2 - 14x - 196 = (x - 14)2
57) 11x = 1
A) x = 1
B) x =
C) x = 0
D)
D) x2 - 14x + 49 = (x - 7)2
1
11
Add or subtract, as indicated, and simplify the result.
3
5
+
63)
2
2
y - 3y + 2 y - 1
Solve the equation by completing the square.
58) x2 + 10x + 15 = 0
A) {5 -
15, 5 +
B) {5 +
10}
C) {-5 D) {-10 +
15}
10, -5 +
10}
15}
Solve the rational inequality.
60
< 16
59) x +
x
A) (0, 6)
C) (- , 0)
(10, )
(10, )
A)
8y - 7
(y - 1)(y + 1)(y - 2)
B)
30y - 7
(y - 1)(y + 1)(y - 2)
C)
8y - 7
(y - 1)(y - 2)
D)
7y - 8
(y - 1)(y + 1)(y - 2)
Solve the equation.
64) log3 (2x + 2) = log3 (30)
B) (- , 0)
D) (0, 6)
(6, 10)
(6, 10)
A) x = 56
B) x = 14
C) x = 16
D) x = 64
65) log2 (x + 4) - log2 (x + 3) = 1
A) x = 2
B) x = - 2
C) x = 1
D) no solution
66) log2 (x + 1) + log2 (x - 5) = 4
A) x = 8
B) x = 7
C) x = -3
D) x = 7, x = -3
Evaluate the expression, if possible.
27 -1/3
72)
8
A) -
Solve the equation. Give an exact solution.
67) e4x = 6
A) 4 ln 6
C)
ln 4
6
B)
3
e
2
D)
ln 6
4
C)
3
2
73)
D)
A) {2, 8}
74)
4
}
3
D) {-4}
10x - 9 - 9 = 0
C) {
Rationalize the denominator. Assume that all variables
represent positive real numbers.
4
69)
7
A)
4 7
7
B) 53
C)
16 7
7
D) 4 7
Solve the equation.
B) {9}
36
}
5
D) no real solution
Solve the rational inequality.
x-1
>0
75)
x+3
A) (-3, 1)
B) (- , -3)
C) (1, )
D) (- , -3)
Solve the equation.
1 42
76) 1 + =
y y2
A) y = -7 or y = 6
70) x4 - 20x2 + 64 = 0
B) y = 7 or y = -6
A) {2, 4}
B) {4, 16}
C) {-2i, 2i, -4i, 4i}
D) {-2, 2, -4, 4}
C) y = 7 or y = 6
1
1
D) y = - or y =
7
6
Simplify the complex rational expression.
71)
77) m -
x 1
9 x
3
=2
m
A) m = -3 or m = 1
1
B) m = - or m = 1
3
3
1+
x
2
3
B) {8}
A) {81}
log 2
+7
log 3
3
2
2x + 1 = x - 3
C) {-4,
B) log 3 - log 2 - log 7
log 2
+ log 7
C)
log 3
B) -
Solve the equation.
68) 2x + 7 = 3
log 3
-7
A)
log 2
D)
2
3
1
3
A)
9
x+3
B)
x-3
9
C) m = -1 or m =
C)
9
x-3
D)
x+3
9
D) m = -1 or m = 3
(1, )
78)
6
9
3
=
x + 4 x - 4 x2 - 16
A) x = 67
B) x = 63
C) x = -21
D) x = 21
Solve.
79) A ladder that is 26 feet long is 10 feet from the
base of a wall. How far up the wall does the
ladder reach?
A) 24 ft
B) 4 ft
C) 576 ft
D) 2 194 ft
Use the quadratic formula to solve the equation.
80) 8x2 + 24x = - 17
-6 - 70 -6 + 70
,
A)
4
4
2 -24 +
,
4
B)
-24 4
C)
-6 - 2 -6 + 2
,
16
16
D)
-6 - 2 -6 + 2
,
4
4
2
81) 8x2 + 1 = 3x
-3 - i 23 3 + i 23
,
A)
16
16
B)
3 - i 23 -3 + i 23
,
16
16
C)
3 - i 23 3 + i 23
,
16
16
D)
-3 - i 23 -3 + i 23
,
16
16