# Intermediate Algebra and Intermediate Algebra with Review Sample Final

```Intermediate Algebra and Intermediate Algebra with Review Sample Final
The final exam will contain 25 questions. Twenty-two of the questions will be multiple choice and 3
will be open-ended. This will be an in-class, closed book exam. A formula sheet will be provided.
This sample final contains a variety of multiple choice and open-ended questions.
Simplify.
1)
2p - 2 10p - 10
÷
p
8p2
A)
20p2 + 40p + 20
8p3
B)
16p3 - 16p2
10p2 - 10p
C)
5
8p
D)
8p
5
Perform the indicated operation and simplify.
2
5
+
2)
y2 - 3y + 2 y2 - 1
Solve.
3)
A)
8y - 7
(y - 1)(y + 1)(y - 2)
B)
20y - 8
(y - 1)(y + 1)(y - 2)
C)
7y - 8
(y - 1)(y - 2)
D)
7y - 8
(y - 1)(y + 1)(y - 2)
5
8
2
=
m - 2 m + 2 m2 - 4
A) {8, -8}
B) {8}
C) {-8}
D)
B) x2 y3(3y + 6)
C) 3x2 y3(y + 6)
D) 3x3 y2(y + 6)
Factor out the greatest common factor.
4) 3x2 y4 + 18x2 y3
A) y + 6
Solve the problem.
5) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 252 mi in the same time that Dana
travels 216 mi. If Chuck's rate of travel is 6 mph more than Dana's, and they travel the same length of time, at
what speed does Chuck travel?
A) 42 mph
B) 47 mph
C) 36 mph
D) 37 mph
B) (r2 + 3)(r + 1)
C) (r2 + 3)(r + 3)
D) (r2 + 1)(r + 3)
C) -3
D) 21
Factor by grouping.
6) r3 + r2 + 3r + 3
A) (r2 + 3)(r - 3)
Solve the problem.
7) Find f(3) when f(x) = x2 + 5x + 3.
A) -9
B) 27
1
Perform the indicated operations. Write the result in standard form.
8) (9 + 6i)(2 - 5i)
A) 48 + 33i
B) -30i2 - 33i + 18
C) -12 + 57i
D) 48 - 33i
C) 12
D) 1
C) 3x
D) 3x
Simplify the complex fraction.
2
4 +
x
9)
x
1
+
3
6
A)
12
x
B)
x
12
Divide and, if possible, simplify.
3 81x4
10)
3x
A) x
3
27
B) 3x
3
x
3
3
Rationalize the denominator.
49
11)
2
A)
7
2
2
B) 11
C)
49
2
2
D) 7
2
12)
2x + 8 32x + 4 72x
A) 57 2x
B) 12 106x
C) 56 2x
D) 13 106x
Find the slope of the line.
13)
A) -
2
3
B) -
3
2
C)
2
3
2
D)
2
3
Rewrite without rational exponents. Assume that even roots are of nonnegative quantities. Simplify if possible.
14) (4h 10k12)3/2
A) 8h 15k15
B) 8k15h 18
C) 8h 15k18
D) 4h 15k18
Solve the inequality and graph the solution set.
15) 7x - 8
-50 and 7x - 8
-22
A) [-6, -2]
B) [-6, -2)
C) (-6, -2]
D) (-6, -2)
Solve the absolute-value inequality.
16) 4x + 2 < 5
A) - , -
C) -
7
4
3
,
4
B) - , -
7 3
,
4 4
7
4
D) (- , 4)
Solve.
17) 2n 2 = -10n - 1
-5 + 3 -5 - 3
,
A)
2
2
C)
-5 + 23 -5 - 23
,
4
4
B)
-10 + 23 -10 - 23
,
2
2
D)
-5 + 23 -5 - 23
,
2
2
Express in terms of i.
18)
-200
A) -10i 2
B) 10i 2
C) -10 2
D) 10 2
B) -1
C) -i
D) i
Find the power of i.
19) i17
A) 1
3
Factor completely.
20) 2x7 - 32x6 + 126x 5
A) x5 (2x - 14)(x - 9)
B) x5 (x - 7)(2x - 18)
C) 2x5 (x - 7)(x - 9)
D) 25 (x2 - 16x + 63)
B) {2}
C) {8}
D) {4}
Solve.
21)
2k + 1 = 3
A) {-4}
Solve the equation.
22)
8m + 2 = 7
5 9
A) - ,
8 8
B)
5
9
,8
8
C)
5
9
,2
2
D)
C)
k2 + 7k
k- 7
D)
Multiply and simplify.
k2 + 5k + 6
k2 + 7k
·
23)
2
2
k + 9k + 14 k - 4k - 21
A)
k
k-7
B)
k
k2 + 9k + 14
1
k-7
Factor completely.
24) 64x2 - 9
A) (8x + 3)2
B) (8x - 3)2
Solve the equation.
25) 49k2 - 9 = 0
A) {3, 0}
B)
C) (8x + 3)(8x - 3)
7
,0
3
C)
3
3
,7
7
D) Prime
D)
7
3
,3
7
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
3
26) Through (2, 4); m = 5
A) 3x + 5y = -26
B) 3x - 5y = 26
C) 3x + 5y = 26
D) 5x + 3y = -26
Solve the problem.
27) The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car
traveling at 40 miles per hour to stop, what distance is required for a speed of 46 miles per hour?
Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
28) Below is a diagram of a water slide. The slide is 19 ft long. The ladder leading to the slide is 15 ft long. How far
is it from the end of the slide to the foot of the ladder? Round approximations to the nearest tenth.
15 ft
19 ft
?
4
Solve the equation.
29) x2 + 4x - 32 = 0
Solve.
30)
4
4
+
=6
x- 4
2x - 8
Solve the problem.
31) A rectangle has a length of x + 2 and a width of x - 2, and has an area of 60 square units. Find the length and
width of the rectangle. (A = LW)
Simplify. Assume the variable represents a positive number.
3
32) 125k12
Find the slope of the line through the pair of points.
33) (7, -3) and (-2, 1)
Perform the indicated operation and simplify.
7 - 3y 3 - 3y
34)
12
9
Multiply. Assume that all variables represent nonnegative real numbers.
35)
15( 15 +
2)
3
3
36) 11 2 - 4 128
Solve the equation.
37) 8k2 - 39k - 5 = 0
Solve by completing the square.
38) x2 + 8x - 28 = 0
Rationalize the denominator.
3 6
39)
5
Rewrite without rational exponents. Assume that even roots are of nonnegative quantities. Simplify if possible.
40) 361/2
Find an equation of the line passing through the two points. Write the equation in standard form.
41) (9, -9) and (2, -5)
5
Solve the equation.
x+6 x+7
=
42)
7
8
Factor completely.
43) x2 + 7xy + 12y2
Solve the equation.
44) 18d2 + 39d + 15 = 0
Solve the problem. If necessary, round to the nearest tenth.
45) A painter leans a ladder against one wall of a house. The ladder is 26 ft long. The base of the ladder is 19 ft from
the house. How high is the wall? Round approximations to the nearest tenth.
?
26 ft
19 ft
Perform the indicated operations. Write the result in standard form.
46) 3i(9 - 2i)
Solve the equation.
47)
x = -3.8
Solve the absolute-value inequality.
48) r - 5 > 9
49) |7x - 9| + 4 < 1
50) 3 - x
3
Solve the equation.
51) 8r2 = 2r
Solve the problem.
52) The intensity of a radio signal from the radio station varies inversely as the square of the distance from the
station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of
6
Intermediate Algebra Sample Final Answer Key 1) D 2) D 3) B 4) C 5) A 6) B 7) B 8) D 9) A 10) C 11) A 12) A 13) B 14) C 15) A 16) C 17) D 18) B 19) D 20) C 21) D 22) B 23) A 24) C 25) C 26) C 27) 148.12 ft 28) 11.7 ft 29) {­8, 4} 30) { 5} 31) width = 6 units; length = 10 units 32) 33) 5 k 4 -
4
9 34) y + 3
12 35) 15 + 30 36) - 5 3 2 37) 38)
{- 4 ± 2 11 }
39) 40) 6 41) 4x + 7y = ­27 42) {1} 43) (x + 3y)(x + 4y) 44) 45) 17.7 ft 46) 6 + 27i 47)
∅
48) (­∞, ­4) ∪ ( 14, ∞) 49)
∅
50) (­∞, 0] ∪ [ 6, ∞) 51) 52) 222 units
Intermediate Algebra and Intermediate Algebra with Review Formulas
Properties of Exponents
(a
aman = am+n
p
a mp
 am 
 n  = np
b
b 
( b)
n
m
=
n
m
a
= a m− n
n
a
1
b− p = p
b
b n ) = a mp b np
p
(a )
m n
= a mn
m
n
b = b n, b > 0
anb=
m
n
m n
m
b=
mn
b
n
a
=
b
n
n
ab
Slope
y − y1
m= 2
x 2 − x1
Cube
V = s3
A = LW
Uniform Motion
d
r=
t
d = rt
Pythagorean Theorem
a2 + b2 = c2
a
,b≠ 0
b
Rectangle
P = 2L + 2W
− b ± b 2 − 4ac
x=
2a
t=
d
r
Equations of Lines
Point-Slope
Slope-Intercept Standard Form
y – y1 = m(x – x1)
y = mx + b
Ax + By = C
Factoring
Difference of Two Squares:
Difference of Two Cubes:
Sum of Two Cubes:
|x|<c
|x|>c
a2 – b2 = (a + b)(a – b)
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
Properties of Absolute Value Inequalities
(c ≥ 0)
if and only if
-c < x < c
(c ≥ 0)
if and only if
either x < -c or x > c
Direct: y = kx
Variation
Inverse: y=k/x
```