Intermediate Algebra
Make-up Online Lab 1
1. Find the indicated value for the given rational expression. Match your result to the
correct answer below.
8x  5
R( x) 
, R(2)
x 3
21
11
11

A) 5 B) 5 C) 5 D) 21
2. Reduce the given expression to lowest terms.
12
66
12
6
2
4
A) 66 B) 11 C) 11 D) 22
3. Reduce the given expression to lowest terms.
3y + 3
21
y 1
y 1
y+3
A) 3 B) 7 C) 7 D) y + 1
4. Reduce the given expression to lowest terms.
3x 2  7 x  2
4 x 2  16
3x 2  7 x  2
3x  1
3x  1
3x  1
A) 4( x  2) B) 4( x  2) C) 4( x  2) D) 4( x  2)( x  2)
5. Reduce the given expression to lowest terms and match your result to the correct answer
below.
15 x 4 y 2 z
35 x8 yz 3
3
3 x 4 yz 2
3 yz 2
3y
4
2
4 2
7 D) 7 x 4
A) 7 x z B) 7x yz C)
6. Reduce the expression to lowest terms and match your result to the correct answer
below.
3t  2
2
3t + 10t  8
3t  2
1
1
1
A) (t  4)(3t  2) B) t  4 C) 4  t D) t  4
7. Build the rational expression into an equivalent rational expression with the indicated
denominator. Match your result to the correct answer below.
p2
?
 2
p  3 p  p  12
p2  2 p  8
p2  6 p  8
p 2  p  12
p4
2
2
2
2
A) p  p  12 B) p  p  12 C) p  p  12 D) p  p  12
8. Perform the indicated operations and write your result in lowest terms. Match your
result to the correct answer below.
5y  3 2 y 1

y4
y4
3y  2
7y  4
7y  2
5y  2
A) y  4 B) y  4 C) y  4 D) y  4
9. Perform the indicated operations and write your result in lowest terms. Match your
result to the correct answer below.
14
7
7

 2
y y 1 y  y
7
7
7
2
A) y  1 B) y C) y  y D) 0
10. Solve the equation and match your result to the correct answer below. Watch for
extraneous solutions.
6
5
x –1
–

x–2 x+4 x+4
A) –2, 5 B) 4, –4 C) –4 D) No solution
Make-up Online Lab 2
1. Which of the following graphs correctly describes the system and its solution?
x  4 y  12
y  x
A)
B)
C)
D) None of these.
2. Which of the following systems of equations corresponds to the graph?
x y 2
x y 0
x  2 y  1
2x  3y  1
A) 3x  y  6 B) x  4 y  2 C) x  4 y  1 D) 3x  y  1
3. Solve the system of linear equations by the substitution method. Then, state whether the
system is independent, dependent, or inconsistent. Match your result to the correct answer
below.
4x + 10y = –28
6x + 7y = 6
A){(–2,–2)}, independent
C) {(8,–6)}, independent
B){(1,0)}, dependent
D) , inconsistent
4. Solve the system of linear equations by the substitution method. Then, state whether the
system is independent, dependent, or inconsistent. Match your result to the correct
answer below.
4x – 3y = 4
12x – 9y = 12
A) {(0, 0)}, independent B) {(4, 4)}, independent C) dependent D) , inconsistent
5. The length of a rectangular painting is 9 feet greater than the width. If the perimeter is
30 feet, then what are the length and the width?
A) Length 12 ft, width 3 ft B) Length 16 ft, width 7 ft
C) Length 10 ft, width 1 ft D) Length 20 ft, width 11 ft
Make-up Online Lab 3
1. Write as a single interval if possible: [–2, )(–,–7)
A) (–, ) B) [–2, ) C) (–7, –2) D) 
2. Graph the solution set of the compound inequality and match your result to the correct
answer below.
2  5x
0
6
3
18
2
A)

5
5
)
[
-4
-3
16

5
B)
-2
-1
0
]
-4
-3
1
2
3
4
1
2
3
4
2
5
(
-2
-1
0
16

5
C)
[
-4
D)
-3
-2
-1
0
1
[
-4
-3
2
3
1
2
4
2
5
16

5
)
-2
-1
0
3
4
3. Graph the solution to the compound inequality –4 < x – 2 < 1.
A)
B)
C)
D)
4. Solve: |3(x + 2) – 4| = 1
2 
 1
 1

 ,1
 
 , 1
 D) 1
A)  3  B)  3  C)  3
5. Solve the inequality and write the solution set in interval notation. Match your result to
the correct answer below.
3 < |x| – 5
A) (–8, 8) B) (–, –8)(8, ) C) (8, ) D) (–, –8)(8, )
6. Graph the solution to the absolute value inequality and match your result with the
correct answer below.
1
x 7 1
2
A)
3
4
5
6
7
8
9
10 11
3
4
5
6
7
8
9
10 11
3
4
5
6
7
8
9
10 11
B)
C)
D)
3 4 5 6 7 8 9 10 11
7. Which graph below correctly indicates the solution set of the linear inequality
2x  5 y  3 ?
A)
B)
C)
D)
8. Which graph below correctly indicates the solution set of the linear inequality
y  3x  2 ?
A)
B)
C)
D)
9. Which of the following graphs correctly represents the solution set of the compound
inequality y  2 x  2 or y   x  3 ?
A)
B)
C)
D)
10. Which of the following graphs correctly represents the solution set of the inequality
3x  y  1
?
A)
B)
C)
D)
Make-up Online Lab 4
1.
3
Find the root: 64
A) 4 B) –16 C) 16 D) –4
2.
4 20
Find the root: t
4
5
9
19
A) t B) t C) t D) t
3.
12
Simplify: 81
2 3
A) 9 4 B) 2 3 C) 9 D) –4
4. Find the domain9of the radical function.
f ( x)  4  x
A) [–4, 4] B) [–4, ∞) C) (–∞, 4] D) (–∞, ∞)
5. Evaluate: (125)–4/3
1
1
1
A) 25 B) 625 C) 125 D) 5
6. Simplify.
5 5 5
A) 6 5 B)
7.

5  5 5 C) 4 5 D) 5
8 2 7
7 + 10 2


Simplify:
A) 18 14 – 153 B) 153 C) –2 14 + 153 D) 18 14 + 153
8.
4
Simplify: 2  12
12
2 D) 1  2 3
A) 1  3 B) 1  3 C)
2
Find all real solutions: x = 81
A) {9} B) {–9} C) {–9, 9} D) 
Find all real solutions: z2 – 20 = 0
2 5
2 5, 2 5
2 5
A)
B)
C)
D) 
3  3i    5  6i 
Find the sum:
A) 2  3i B) 3 C) 2  3i D) 2  3i
Find the product: (–6 + 4i)(–6 + 4i)
A) 20 B) – 48i C) –10 – 48i D) 20 – 48i
–5  i
Find the quotient: 10 – 8i
29 15
21 25
29 15
–
– i
– + i
–
+ i
A) 82 82 B) 82 82 C) 82 82 D) –58 – 30i
2
Find the complex solutions: 5 x  12  0

9.
10.
11.
12.
13.
14.
  
 

A)
2
3i, 2 3i

B)
2
15i, 2 15i

C)  15
15 
i,
i

5 
 5
D)  2 15 2 15 
i,
i

5
5 

15. Solve: 3 z  2  4
 34 
 31 
 34 
 
 
 
A)  9  B)  9  C)  3  D) 
Make-up Online Lab 5
1. Solve by factoring: x2 + x – 72 = 0
A) {–9, –8} B) {8, 9} C) {–8, 9} D) {–9, 8}
2. Solve: (x – 3)2 = 36
A) {–3, 3} B) {–3, 9} C) {9, 9} D) {3, 9}
3. Solve by completing the square and match your result to the correct answer below.
3x2 + 5x – 1 = 0
A)  –5  37 –5  37 
C)  –5  37 
,




6
6
6




B)  5  37 
D)  5  37 5  37 
,




6 
 6 
 6
4.
Solve: – x + 5  x – 3
A) {1, 4} B) {–1, –4} C) {4} D) 
5. Find the imaginary solutions: x2 – 18x + 130 = 0
A) {–9 + 7i, 9 – 7i} B) {9 – 7i, –9 – 7i} C) {9 – 7i} D) {9 – 7i, 9 + 7i}
6. Solve the given equation using the quadratic formula. Show your work.
y2 + 15y = –54
A){–9, –6} B) {9, 6} C) {9} D) 
7. Find b2 – 4ac and the number of real solutions for the given equation.
x 2  24 x  144  0
A) 0, 1 B) 0, 2 C) 1152, 2 D) 0, 0
8. Determine whether the graph of the quadratic function opens upward or downward.
f(x) = x2 + x – 9
A) Upward B) Downward
9. Which of the following is the correct graph of the function f(x) = x2 - 1?
A)
C)
B)
D)
2
Find the vertex and intercepts of the function f ( x)  x  x  2 . Match your result to the
correct answer below.
A)
 0, 2 ; Intercepts:  2,0 , 1,0 ,  0, 2
Vertex:
B)
 1 9
 , 
 2,0 , 1,0 ,  0, 2
Vertex:  2 4  ; Intercepts:
C)
 1 9
 , 
 2,0 , 1,0 ,  0, 2
Vertex:  2 4  ; Intercepts:
D)
 1, 18 ; Intercepts:  2,0 , 1,0 ,  0, 2
Vertex:
10.