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Florida State
College at
Jacksonville
Assessment
and
Certification
Centers
FSCJ
7cm
22cm 6cm
MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question. Evaluate.
- 29 16 13 A. 455 B. 585 C. 58 D. 237
- 96 5 2 3 A. 546 B. 86 C. 546 D. 66
9 2 4 3 A. 7 B. 3 C. 9 D. 1
A. 47 B. 48
C. 49 D. 14
Find the area of the shaded area.
A. 196 square centimeters B. 924 square centimeters C. 35 square centimeters D. 174 square centimeters
Find the average.
- 11, 16, 15, 22 A. 64 B. 15 C. 17 D. 16
Solve.
- For five mathematics tests your scores were 81, 86, 81, 76, 71. What was your average score?
A. 383 B. 78
C. 79 D. 75
Choose a strategy and solve.
- Your car gets about 30 miles per gallon. You are planning to drive to see your friends who live about 930 miles away. How many gallons of gas will you need to purchase to make the trip to see your friends and to return home? State your answer to the nearest gallon?
A. about 30 gallons B. about 45 gallons C. about 62 gallons D. about 51 gallons
- In 1998 your house cost $82,400. In 2000 your house was valued at $102,650. How much did the value of your home increase? A. $19, B. $20, C. No increase, it was a decrease D. $21, 250
- While shopping you note the average price for a CD is $8 including tax. You have $112 in your pocket. About how many CDs can you buy? A. 21 B. 14 C. 17 D. 19
Solve the problem below. Write your answer in simplest form.
- Of a family’s $750 weekly income, $ usually goes toward groceries. What fraction of the family’s weekly income is usually spent on groceries? A. 35 750
B.
7 150 C. 150 7
D.
750 35
- You need a piece of fabric 125 yard long.
Which of these is the smallest piece of fabric that would work? A.^1 2
yard B.^5 16
yard
C. 2 3
yard
Add and simplify.
1 4
2 4 A. 3 8
B.
3 4 C. 1 2
D.
3 16
5 27
4 27
12 27 A. 20 27
B.
7 9 C. 21 27
D.
21 81
1 3
1 2 A. 1 6
B.
2 3 C. 5 6
D.
3 4
27.^2
3
1 12 A.^3 4
B.^9
12
C.^1
4
D.^7
12
- (^2 )
A. 3 68 B. 4 21 C. 3 1 8
D. 4
A. 22 152 B. 23 152
C. 22 158 D. 23 158
A. 7 2340 B. 5
C. 6 12 D. 6
Subtract and simplify.
31.^5
6
1 6 A.^2 3
B.^1
3 C.^4 12
D.
1 2
32.^26
11
51 11 A. 2 113 B. 1 119 C. 3 111 D. (^2 )
33.^8
9
1 2 A. 1 187 B. 7 18 C. 1 3
D.^1
11 15
1 3 A. 2 9
B.
2 3
C.
5 6
D.
2 5
A. 8 45 B. 9 15 C. 9 45 D. 10
A. 12 12 B. 12 151 C. 11 151 D. 12
A. 6 24 B. 6 34 C. 25 34 D. 24
A. 15 3135 B. 16 3135 C. 16 D. 16
Solve the problem below and write your answer in simplest form.
- A carpenter had a board 27 14 ” long. He
cut off 2 58 ”. How long was the remaining board?
A. 24 58 ” B. 26 58 ”
C. 25 85 ” D. 25 43
- Brian was training to run a marathon. During the three-day period before the race he decided that he would train for a total of 11 hours. If he trained for (^2 ) hours on the first day and 2 109 hours on the second day, how many hours would he need to train on the third day?
A. 5 45 B. 5 12 C. 5 35 D. 6
Multiply and reduce to lowest terms.
5 12
1 5 A. 1 10
B.
6 17
C.
5 60
D.
1 12
3 A.^3 14
B. 3 2
3
C. 10 1
2
D. 4 2
3
- (^3 ) A. 1 12 B. 2 109 C. 1 23 D. 2 103
A. 30 12 B. 33 C. 15 D. 30
Divide and reduce answers to lowest terms.
2 3
3 5 A. 2 5
B.
2 3
C. 1 19 D. 1
46.^1
2
8
A.^1 16
B. 4
C.^1
10
D. None of these
A.^1
5
B. 5
C. 10 D. 4
Solve the problem.
- Mary needs to save $540 for a computer. It was used and the sales man told her he would sell it to her for 13 off the marked price. What is the price of the computer be after the mark down? A. $180 B. $ C. None of these D. $
Write the ratio as a fraction in simplest form.
- 12 to 16
A.^6 8
B.^8
6
C.^3
4
D.^4
3
In each of the problems below change the percent to an equivalent fraction or mixed number.
- 25%
A. 4 B. 1 4
C.
3 4
D.
4 100
- 125%
A. 1 14 B. 12 14 C.^1 8
D.^125
1000
66.^1
10
%
A.^1 10
B.^1
100 C.^1 1000
D.^1
10000
Solve each percent problem below.
- Find 40% of 700. A. 2.8 B. 28 C. 280 D. 2800
- Find .25% of 200. A. .5 B. 5 C. 50 D. 500
- Find 150% of $2500. A. $375 B. $ C. $37500 D. $
- Find 3 12 % of $36,000.
A. $126 B. $ C. $1260 D. $
Find the percent of increase or decrease in the problem below.
- A surfer purchased a new surf board for $264. The board was originally $330. What was the percent of change? A. 55% B. 20% C. 25% D. 30%
- A crafter wants to make 20% profit on the items he makes. If the cost of materials is $1.20, what should the items sell for to make a 20% profit? A. $1.44 B. $1. C. $1.24 D. $2.
Find the mean of the set of numbers.
- Your test scores are 78, 89, 76, 50, 82, and 69. Round your answer to the nearest whole number if necessary. A. 74 B. 76 C. 69 D. 72
Use the tables to solve the following problems.
Dog Weight (pounds) Husky 95 St. Bernard 145 Cocker Spaniel
Yorkie 3.
About how many times heavier is the largest dog when compared with the smallest dog? A. 3 B. 41 C. 2 D. 27
Change the given quantity to the indicated unit.
- 360 min = _____ hours A. 21600 B. 36 C. 6 D. 2
- 180 in = ___ft A. 60 B. 1.25 C. 540 D. 15
Find the square root of each of the problems below.
A. 16 B. 9 C. 32 D. 8
A. 121 B. 60.5 C. 11 D. 12
- The following table is used to determine the minimum payment on a credit card bill.
What is the minimum payment if you owe $300?
A. $300 B. $45 C. $25 D. $
Find the perimeter of the figure below.
3 ft
5 ft 5ft
3ft
A. 16 ft B. 8 ft C. 9 ft D. 25 ft
Solutions:
- D 2. D 3. D 4. B 5. A 6. D 7. C
- C 9. B 10. B 11. A 12. A 13.D 14. B
- A 16. B 17.A 18. D 19. C 20. B 21. A
- B 23. A 24. B 25. B 26. C 27. A 28. D
- C 30. D 31. A 32.A 33. B 34. D 35. A
- B 37. B 38. A 39. A 40. B 41. D 42. D
- B 44. B 45. C 46. A 47. B 48. B 49. C
- A 51. A 52. B 53. C 54. B 55. C 56. A
- B 58. B 59. B 60. D 61. A 62. C 63. C
- B 65. A 66. C 67. C 68. A 69. B 70. C
- B 72. A 73 A 74.B 75.C 76. D 77.D
- D 79. C 80. A
Balance $0- 25 $25.01- 250
$250.01- 1000
$1000. up Min. Payment
Full Balance
$25 10% of balance
$100 + 5% of balance greater than $
- Solve for x: 125 x 25 0
A. x = 12512 B. x = 60 C. x = – 60 D.^12512
- Solve for x: – x + 3 = 7x + 8
A. x = 5 8 B. x = 6 5 C. x = 1 3 D. x = 6 11
- Solve for x: 5(3 – 4x) = 7 – ( 4 – x)
A. x = 3 B. x = 18 5 C. x =
4 7 D. x = 19 8
- Solve for y:^34 y^53
A. y =
20 9 B. y = – 2
C. y =
11 12 D. y =
29 12
- Solve for z:^65 z^47
A. z =
22 35 B. z =
62 35
C. z =
24 35 D. z =
10 21
- Solve for z: 5.6 = 0.02z + 7. A. z = 0.2596 B. z = 649 C. z = 0.0356 D. z = – 89
- Solve for x: x 0 08
58 .
. A. x = 5.72 B. x = 5. C. x = 72.5 D. x = 0.
- The formula for the perimeter of a rectangle is: P = 2L + 2W Solve for W when P = 23 and L = 7. A. W = 4.5 B. W = 2 C. W = 18.5 D. W = 18
- Best Buy is selling a television for $1250.00. Sales tax in Duval County is 6%. Using P as the amount I will have to pay for the television (including sales tax),write an algebraic equation that describes this transaction. A. P = (0.06)(1250) B. P = 1250 0. C. P = 1250 + (0.06)(1250) D. P = 1250(0.94)
- Jeremy put $1250 into his savings account, which pays 5% per year simple interest and left it there for 3 years. Using A as the total amount that will be in the bank at the end of the 3 years, write an algebraic equation that describes this transaction. A. A = 1230 + 1250(0.05)(3) B. A = 1250(0.05)(3) C. A = 1250 – 1250(0.05)(3) D. A = 1250 + (0.05)(3)
- Keisha is investing her money in an IRA. Initially she will be putting in $775. Using C as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year. A. 775 + C B. 775 – 12C C. 775C D. 775 + 12C
- Multiply and simplify where possible: 3x(7x – 4) A. 21x^2 – 4 B. 21x^2 – 12 C. 9x^2 D. 21x^2 – 12x
- Multiply and simplify where possible: 4x(2y + 3z – 12) A. 6xy + 12xz – 48 B. 8xy + 12xz – 48x C. 8x^2 y^2 + 12x^2 z^2 + 48 D. 8xy + 12xz – 12
- Multiply and simplify where possible: xy(6x^2 – 3y^3 z) A. 6x^3 y – 3xy^4 z B. 7x^3 y – 2xy^4 z C. 6x^2 y – xy^3 z D. 3x^3 y^4 z
- Multiply and simplify where possible: (5x – 2)(6x + 3) A. 30x^2 – 6 B. 30x^2 + 3x – 6 C. 11x^2 – 5 D. 30x^2 + 3x + 5
- Multiply and simplify where possible: ( z (^) 43 )( z^34 ) A. z^2 43 B. 2z C. z^2 23 D. z^2
- Multiply and simplify where possible: A. 16x^2 – 4z^2 B. 8x^2 + 4z^2 C. 16x^2 + 16xz – 4z^2 D. 8x^2 + 4z^2
- Simplify: (6x^2 – 3x – 7) + (3x^2 + 5) A. 3x^2 – 3x – 2 B. 9x^2 – 3x – 12 C. 9x^2 – 3x – 2 D. 9x^2 – 3x +
- Simplify: (z^2 – 3z + 1) – (7z^2 – 8z + 5) A. – 6z^2 – 11z + 6 B. – 6z^2 + 5z – 4 C. – 6z^2 – 11z – 4 D. – 7z^2 + 5z – 4
- Simplify:(z^2 + 3) +(4z – 7) – (5z^2 + z – 9) A. – 4z^2 + 5z + 5 B. – 4z^2 + 3z + 5 C. – 4z^2 + 5z – 13 D. – 6z^2 + 3z – 13
Solutions:
- C 2. B 3. B 4. D 5. D 6. C 7. D
- C 9. B 10. A 11.B 12. D 13. A 14. B
- B 16. A 17. C 18. C 19. D 20. D 21. D
- A 23. C 24.A 25. D 26.D 27. B 28. A
- B 30. D 31. A 32. C 33. B 34. B
Solutions Section 1 Sample Problems:
- D 2. B 3. D 4. C 5. A 6. A 7. A
- A 9. B 10. C 11. C 12. B 13. C
Sample Problems Using Radicals
Simplify each problem .
- (^) 12 x^2 2. (^) 20 a^5 2 a^25 a 3. (^) 3 6 6 4. 3 n 24 n
- 3 x 51 x^3 6. 45 a^720 a 7. 2 12 7 3 8.
- 4 5 2 45 10. 40 a b^3 4 11. 12 48 27 12.
2 11 2
- k 7 x^2 4 x 63 k^2 14. 3 7 2 15. 2 5 r 3 r 8 2 h
Solutions :
- 2 x 3 2. 20 a^5 3. 18 4. 6 n 2 5. 3 x^217
- 30 a^4 7. 3 3 8. 9 3 9. 2 5 10. 2 ab 2 10 a
- 3 3 12. 13 2 22 13. 13 kx 7 14. 21 6 15. 2 r 15 16 10 hr
Sample problems using factoring
If necessary find the greatest common factor and then factor completely.
- 12 cd^3 8 c d 2^2 10 c d^5 3 2. y^2 5 y 4
- x^^2 6 x^9 4.^3^ m^2^^3 n^2
- 6^ c^2^^13 c^6 6.^2^ b^^^213 b^7
Solutions:
- 2 cd^2 ( 6 d 4 c 5 c d^4 ) 2. ( y 1 )( y 4 )
- ( x 3 )( x 3 ) 4. 3 ( m n )( m n )
- ( 2 c 3 )( 3 c 2 ) 6. ( 2 b 1 )( b 7 )
Sample problems simplifying rational expressions
Factor and reduce each expression to lowest terms.
30 12 2
bc b
5 5 (^21)
t t
y y y y
2 2
4 4 3 5 2
a a a a
2 2
2 1 2 3 1
Solutions:
5 2
c b
5 t 1
y y
2 3 1
a a
1 2 1
Sample problems multiplying and dividing rational expressions
3 4
6 3
2 2
xyz xz
x y
3 5
9 d 15 df
2 2
3 3 9 1
4 4 2
2 t
t t
t
5 10 75 4 24 28
2 10 28 7 10
2 2
2 2
x x x x
x x x x
a a a
(^2 2 15) a 2 3
4 2 Solutions:
3 2
x^2 y
- f 3.^2 3
2 1
5 3 x
x 5. 2 2
2 5 a a
a
Sample problems adding and subtracting rational expressions
6 8 ab a
m m^2 4 m
2 3 6
1 9 20
5 h^2 h h^2 10 h 25
y y
y y
y y y
1 1
2 2 2 3 2
d d d
d d
4 2 8
2 (^2 )
Solutions:
1.^6 8 b ab
3 2 2
5 4 m m
m 3. 4 52
4 15 h h
h
Sample problems that can be solved by factoring :
- x^2 4 x 21 0 2. x^2 4 x 32 3. x^2 6 x 55 0
Solutions:
- x = 7 or x =– 3 2. x = 8 or x = – 4 3. x = – 5 or x = 11
Sample problems that can be solved using the quadratic formula. Write your answers in set notation.
- x^2 15 x 54 0 2. x^2 4 x 2 3. 2 x^2 11 x 15 0
Solutions:
- {-9, -6} 2.{0.45, -4.45} 3. {6,5}
Practice for Intermediate Algebra
1.Solve for x: 2 3 x 5 4
A. 7 3
x 3 B. 1 x 2
C.^7 3
x 3 D. 3 7 3
x
- Solve the system of equations: 2 5 1
a b a b
A. ( 2 1 , ) B. ( , ) 2 1 C. ( , 2 1 ) D. ( 2 , 1 )
- Solve the system of equations: 3 5 3 8 4
x y x y
A. ( 4 3 , ) B. ( , 3 4 )
C. ( , ) 4 3 D. ( 3 , 4 )
- Solve the system of equations: 6 7 9 8 9 11
x y x y
A. ( , ) 2 3 B. ( 2 , 3 )
C. ( , 3 2 ) D. ( 2 3 , )
- Simplify: x x x x
2 2
9 8 3 4
A.
x x
1 4
B.
x x
8 1 C. x x
8 4
D.
x x
8 4
- Simplify: y y y
y y y
2 2
10 25 2 9
3 5
A.
y y y
( 5 ) 3
B.
y y y
( 5 ) 3
C. y y
5 3
D.
y y y
(^2 ) 3
- Add and simplify:^9 1
3 x x
A.^12
1
x x x ( )
B.^12
x x ( 1 )
C. 12 2 x 1
D.
15 x 1
- Simplify: x x x x
x x x
2 2
2 3 2 2
1 2 1
A.
x ( x 2 )( x 1 )
B.
x x x x
( ) ( )( )
1 2 1 C. (^ )(^ ) ( )
x x x x
2 1 1
D. x x x x
( ) ( )( )
1 2 1
- Simplify: x x^2 9 x 20 x^2 x
4 7 12
A.
( x )( x ) x
5 3 5
B. x x x
5 ( 5 )( 3 )
C. x x x
5 ( 5 )( 3 )
D.
x x x x
5 ( 3 )( 4 )( 5 )
