Download Intermediate Algebra Review Questions for Department Assessment

Intermediate Algebra Review Questions for Computer Enhanced Exam
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the relation defines a function.
1)
(6,7), (6,9), (1,4), (4,4), (8,1)
A) Not a function
B) Function
Find the domain and range.
2)
(4,4), (1,1), (2,8), (2,3)}
A) domain = {-4,8,1,3}; range = {-4,-2,-1}
C) domain = {-4,-2,-1}; range = {4,8,1,3}
Given the function, find the indicated value.
3)
Find f(-2) when f(x) = 2x2+4x+4.
A) 20
B) 0
B) domain = {-4,-2,-1,2}; range = {-4,8,1,3}
D) domain = {-4,-2,-1,-12}; range = {-4,8,1,3}
C) -4
D) 4
Solve the system by graphing.
4)
y – 4x = 2
5y = 20x + 10
6
y
4
2
x
-6
-4
-2
2
4
6
-2
-4
-6
The x-value of the solution is:
A) -1.5
B) 1
Solve the system.
5)
2x + 3y = -5
3x – 5y = 21
The y-value of the solution is:
A) 2
B) 7
C) Infinite # of solutions
D) No solution
C) -3
D) No solution
C) 16 p12
D) 16 p7
Simplify the expression.
6)
4 p  4 p 
3
A)
p7
16
4
B) 16 p12
Simplify the expression. Write the answer with positive exponents.
7)
4 x11 y12 z 7
2 x 3 y 9 z10
x8 y 3
2z 3
A)
B) 2 x 8 y 3
C) x 8 y 3z 3
D)
2 x 8 y 3
z3
Simplify. Use positive exponents to write the answer.
8)
x 
x 
x
7
5 4
 2 8
A) x 4
B)
1
x 11
C)
1
x 43
D) x 43
Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or
none of these.
9)
10x 4  3w3  7w  5y 5  4
A) degree 5; trinomial
B) degree 5; none
Perform the indicated operations.
10)
9x
2
 
 9 x 4  4  6 x 3  5  2 x 3 5x 4 3x 2
C) degree 13; trinomial D) degree 14; binomial

A) 4 x 4  8x 3  12 x 2  9
B) 14 x 4  8x 3  12 x 2  9
C) 4 x 4  4 x 3  6x 2  1
D) 14 x 4  8x 3  12 x 2  1
Multiply.
11)
(-5x + 3y) (2x – 12y + 1)
12)
A) 10 x 2  60 xy  5x  36 y 2
B) 10 x 2  66 xy  66 y 2
C) 10 x 2  66xy  5x  36 y 2  3 y
D) 10x 2  6xy  5x  36 y 2  3 y
(-6 + x) (4x – 8)
A) x 2  32 x  32
13)
C) 4 x 2  33x  48
D) 4 x 2  32 x  48
B) 4 x 2  24 xy  9 y 2
C) 16 x 2  24 xy  9 y 2
D) 4 x 2  9 y 2
(4 x  3 y ) 2
A) 16 x 2  9 y 2
14)
B) 4 x 2  48x  32
4 
4

 x   x  
6 
6

4
4
2
A) x  x 
3
9
2
B) x 
4
9
2
C) x 
4
4
x
3
9
D) x 2 
4
9
Factor the trinomial.
15)
12 x 2 y 2  11xy 2  15y 2
A)
3x  5 y4x  3 y
B) y
2
x  512 x  3
C)
4x  5 y3x  3 y
D) y 3 x  54 x  3
2
Factor the polynomial.
16)
3x 6 y 2  81y 2
2


A) 3 y x 2 3 x 4 3x 2 9

2
D) 3 y
C) prime polynomial
17)

9
2
2
4
3x 2
49 x 2  16
A)
18)
 
x 3x
B) 3 y x 2 3 x 4 3x  9
7 x  42
B)
7 x  47 x  4
C) prime polynomial
B)
2x  y2x  5
C)
 3 2
, 
 5 3
C)  , 
9
20 p
C)
D)
7 x  42
4 x 2  2 xy  10 x  5 y
A)
2x  y2x  5
2x  5 y2x 1
D) prime polynomial
3 3 
5 2 
D) 
20 p
9
D)
45 p2  90 p  45
4 p3
D)
ts
ts
Solve the equation by factoring.
19)
9b2  21b  1  9
5 2 
A)  , 
3 3 
B) 
 5 2
, 
 3 3
Divide. Simplify the answer.
20)
5p  5 9 p  9

p
4 p2
A)
20 p 3  20 p 2
9 p2  9 p
B)
Perform the indicated operations. Simplify the answer.
21)
15s2  8st  t 2 2 s2  7 st  3t 2 10s2  3st  t 2

 2
5s2  14 st  3t 2 t 2  2 st  3s2
5s  6st  t 2
A)
t  5s 2 2s  t 2
4s  t 2 t 2 s 2 
B)
t  5s 
t  s t  s 
C) 1
Perform the indicated operations. Simplify the answer.
22)
3
7
 2
y  3y  2 y  1
2
A)
10 y  11
B)
 y  1 y  1 y  2
10 y  11
 y  1 y  2
C)
 4 y  17
D)
 y  1 y  1 y  2
11 y  10
 y  1 y  1 y  2
Simplify the complex fraction.
2
x
x 1

3 6
12
A)
x
4
23)
B) 12
C)
x
12
D) 1
Solve the equation.
24)
1
3
3

 2
x  7 x  4 x  11x  28
A) 
B) 0
C) -7
D) 4
Find the cube root. Round to the nearest thousandth, if necessary.
25)
3
x 12
64 y 6
4 y2
A)
x4
x4
B)
4 y2
x3
C)
4 y3
x4
D)
16 y 2
Use radical notation to write the expression. Simplify if possible.
26)
7x
2
5
7 x5
A)
B)
5
49 x 2
5
C) 7 x 2
D)
5
7x2
Write with positive exponents. Simplify if possible.
27)
 32
25
A) -125
28)
32
A)
1
125
B) 125
C)
B) 16
C) 
D) 
1
125
4 5
1
16
1
16
D) not a real number
Use the properties of exponents to simplify the expression. Write with positive exponents.
29)
x
4 5
x
A)
x
6
5
3
7
1
1
x 105
B) x
1
105
C)
1
181
x 105
D) x
181
105
Use the product rule to multiply. Assume all variables represent positive real numbers.
13x 2  13x 5
30)
169 x 8
A)
B)
13x 4
C) x 4 26
D) 13x 3 x
Simplify the expression. Assume all variables represent positive real numbers.
3
31)
54 x 7
3
2x
A) 3 x 2
B) x 2 3 3
C) x 2 3 2
D) 3x 2 3 x
Add or subtract. Assume all variables represent positive real numbers.
3x 3  3x 27 x 2  7 27 x 4
32)
B)  x 3x  12 x 2 3
A) 13x 2 3
C) x 3x  12 x 2 3
D) x 3x  12 x 2 3
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
33)
4

5 7 5 5 4

A) 28  20 52  16 5 B) 48 5  16
C) 65 5
D) 128  51 5
Rationalize the denominator. Assume all variables represent positive real numbers.
34)
2
4
a3
24 a 3
B)
a
24 a
A)
a
24 a 2
C)
a
D) 24 a
2
5 8
35)
A)
10  8 2
59
B)
10  8 2
59
C)
3 10  5 2
40
D)
10  8 2
13
Solve.
36)
4
s 1  8  0
A) 8
37)
B) 4096
C) -4096
D) 
C) 20 km
D) 24 km
Find the length of the unknown side of the triangle.
15 km
A) 18 km
25 km
B) 25 km
Perform the indicated operation. Write the result in the form a + bi.
38)
10  3i 2
A) 109  60i
B) 100  9i
C) 91  60i
D) 100  9i
Simplify.
39)
2  3i
2i
3
i
A)
2
B)
3
i
2
C) 
3
i
2
D) 
3
i
2
Use the square root property to solve the equation. Round to the nearest tenth, if necessary.
40)
 p  22  6
A)
2 i 6
B) 2  i 6 , 2  i 6
C) 2  i 6
Use the quadratic formula to solve the equation.
41)
7 x 2  6  5x
A)
5  143 5  143
,
14
14
B)
5  i 143 5  i 143
,
14
14
C)
5  i 143 5  i 143
,
14
14
D)
5  143 5  143
,
14
14
D) 2  i 6 ,  2  i 6
Intermediate Algebra Review Questions for Computer Enhanced Exam
Answer Key
1.
A
22.
C
2.
C
23.
A
3.
D
24.
A
4.
C
25.
B
5.
C
26.
C
6.
D
27.
C
7.
D
28.
C
8.
C
29.
B
9.
B
30.
D
10.
C
31.
A
11.
C
32.
D
12.
D
33.
D
13.
C
34.
A
14.
B
35.
A
15.
D
36.
D
16.
D
37.
C
17.
C
38.
C
18.
A
39.
A
19.
D
40.
D
20.
C
41.
B
21.
D
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