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Chapter R Review
1
3
+
8
4
7
1
A)
B)
8
2
1. Add.
9
8
C)
3
4
D)
1
2. Simplify.
A)
32
15
5
1
  3
9
32
2
B) 
C)
3
9
D) 
5
3
3. Which property of the real numbers is illustrated by the following statement?
6(8x) = (6 ∙ 8)x
A) Associative property of multiplication C) Associative property of addition
B) Distributive property
D) Commutative property of
multiplication
4. Which property of the real numbers is illustrated by the following statement?
3(c + ax) + 0 = 3(c + ax)
A) Associative property of multiplication C) Distributive property
B) Additive identity property
D) Associative property of addition
5. Given that ab  0, what may we conclude about the values of a and b?
A) both of the variables must equal 0
B) at least one of the variables has to equal 0
C) nothing can be concluded about the values of the variables
D) only one of the variables can equal 0
6. The number 7 belongs to which of the following sets of numbers? List all that apply.
I. natural numbers, II. integers, III. rational numbers, IV. irrational numbers
A) I and II B) II and III C) II D) I, II, and III
7. Evaluate.
–50
A) –1 B) 0 C) –5
D) 1
8. Write 27,700 in scientific notation.
A) 2.77  103 B) 27.7  103 C) 2.77  104 D) 27.7  104
9. Change to radical form. Do not simplify.
8y 4/3
A)
3
8y 4
B)
4
8y 3
C) 8 4 y 3
D) 8 3 y 4
Copyright 2011, McGraw Hill, Barnett
Page 1
Chapter R
10. Evaluate the expression if it is a real number.
512 2/3
1
1
A) 
B) Not a real number C)
D) 64
64
64
11. Simplify and express your answer using positive exponents only.
 m –4 m 4 
 7 –2 
m m 
A) m8
B)
3
1
m8
C)
1
m15
D) m15
12. Write the expression in simplified radical form.
3 21
A) 7 3
B) 3 7
C) 3 6
D) 2 6
13. Add 4c2 – 7c – 1 and 2c2 + 8c – 9.
A) 6c2 + 15c – 10 B) 6c2 + c – 10
C) 6c2 + 15c + 8
D) 6c2 + c + 8
14. Subtract w3 + 7w2 + 10w + 8 from w4 + 10w2 + 4w – 4.
A) w4 + w3 + 3w2 + 14w – 12
C) w4 – w3 + 3w2 + 14w + 4
4
3
2
B) w + w + 3w – 6w + 4
D) w4 – w3 + 3w2 – 6w – 12
15. Perform the indicated operations and simplify.
5x – 4x[8 – 3(x – 2)]
A) 12x2 + 5x – 6 B) 6x2 – 3x C) 12x2 – 51x D) 12x2 + 5x + 6
16. Perform the indicated operations and simplify.
(3x2 – 2x – 1)(x2 + x + 5)
A) 3x4 + x3 + 12x2 – 11x – 5
C) 3x4 + x3 + 14x2 – 11x – 5
4
3
2
B) 3x – x + 12x + 11x – 5
D) 3x4 – x3 + 14x2 + 11x – 5
17. Factor completely relative to the integers.
6b4 – 18b3 – 60b2
A) 6b2(b – 2)(b + 5)
B) 6(b2 + 2)(b2 – 5)
C) b2(2b + 5)(3b + 10)
D) 6b2(b + 2)(b – 5)
18. A vending machine contains dimes and quarters only. There are 11 less dimes than
quarters. If x represents the number of quarters, write an algebraic expression in terms of
x that represents the value of all the coins in the vending machine in cents. Simplify the
expression.
A) Value  35x  275
C) Value  35x  275
B) Value  35x 110
D) Value  35x 110
Copyright 2011, McGraw Hill, Barnett
Page 2
Chapter R
19. Reduce to lowest terms.
x 2 – 4 x – 12
x 2  36
1
x–2
x+2
A) –
B)
C)
3
x–6
x+6
D)
x +1
x +3
20. Perform the indicated operations and reduce to lowest terms.
b2  b a 
  
3a  a3 4b 
4ab 2
a3
b2
b2
A)
B)
C)
D)
3
12
12a3
12a
21. Perform the indicated operations and reduce to lowest terms.
–10
5
3


2
x  8 x  15 x  5 x  3
2x
8x
2
8
A) 
B)
C) 
D)
x3
x3
( x  3)( x  5)
( x  3)( x  5)
22. Perform the indicated operations and reduce to lowest terms.
x  5 x 2  10 x  25

x(5  x)
x 2  25
x5
1
x5
A)
B) 
C) 1 D) 
2
2
5x  x
x
5x  x
23. Perform the indicated operations and reduce to lowest terms.
x 2  16
x 2  10 x  24

5 x 2  35 x  60
x3  27
( x  3)2
x 2 – 3x  9
( x  4)2 ( x  6)
( x  4)2 ( x  6)
A)
B)
C)
D)
5( x  6)
5( x  6)
( x  3)2 ( x 2 – 3x  9)
( x  3)4
24. Perform the indicated operations and reduce to lowest form. Reduce any compound
fractions and simple fractions reduced to lowest terms.
3x  3h  4 3x  4

xh
x
h
–3
3
–4
4
A)
B)
C)
D)
x ( x  h)
x ( x  h)
x ( x  h)
x ( x  h)
Copyright 2011, McGraw Hill, Barnett
Page 3
Chapter R
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
A
A
A
B
B
D
A
C
D
C
C
B
B
D
C
A
D
B
C
A
D
D
C
C
Copyright 2011, McGraw Hill, Barnett
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