Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Special products can be illustrated by using areas of rectangles. Use the figure to justify the special product
(a +
b)2=a2+
2ab +b2.
1)
What is the sum of the monomials of the black, white, and gray rectangles?
1)
A)
2a + 2ab +b2
B)
a2+ 2ab +b2
C)
a2+ 2b2
D)
2a2+b2
2)
Give the monomial that represents the area of the black square.
2)
A)
2a
B)
ab
C)
b2
D)
a2
3)
Express the area of the large square as the square of a binomial.
3)
A)
2a + 2b
B)
ab
C)
(a + b)2
D)
a2+b2
4)
Give the monomial that represents the area of the white square.
4)
A)
ab
B)
a2
C)
b2
D)
2ab
5)
Give the monomial that represents the sum of the areas of the gray rectangles.
5)
A)
b2
B)
ab
C)
a2
D)
2ab
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
6)
If the quotient of a certain binomial and 36x2 is 27x4–18x2+5
x2, is the polynomial
972x6–648x4+180?
6)
7)
Give an example of a like term for –17c17d4.
7)
8)
The polynomial –12s4– 10s3– 17 is called a ? .
8)
9)
If k represents any positive integer, what is true about the answer you get
when multiplying (x + k)(x – k)?
9)
10)
If 24x2+ 15x + 3 represents the area of a rectangle and 3x represents the width, does
8x + 5 +1
x represent the length?
10)
Answer the question or write an explanation.
11)
Explain how (–5x)6 and –5x6 are different.
11)
Provide an appropriate response.
12)
Why is scientific notation used?
12)
13)
What must be done to the dividend before beginning the “long division” process for
(6b2+ 5b4+ 7b3+ 3b+ 6) ÷ (2b + 7)?
13)
14)
If k represents any positive integer, what is true about the answer you get
when multiplying (4x2+ 9x + k)(4x2+ 9x + k)?
14)
15)
Why is 2
11 x the same as 2x
11 ?
15)
16)
If k represents any positive integer, what is true about the answer you get
when multiplying (5x + k)(5x + k)?
16)
Answer the question or write an explanation.
17)
Explain how (–7)4 and –74 are different.
17)
18)
Does the product rule apply to 76·148? Explain why or why not.
18)
Provide an appropriate response.
19)
For the exponential expression y0= 1, the variable y may equal ? .
19)
Answer the question or write an explanation.
20)
Is it correct to simplify 25·52 as 1010?
20)
21)
Is (5x8y6)5 equivalent to 25x40y30?
21)
Provide an appropriate response.
22)
If –12x2– 21x + 3 represents the area of a rectangle and 3x represents the width, does
–4x – 7 + 1 represent the length?
22)
23)
Why isn’t 5
9x the same as 5
9x ?
23)
24)
What must be done to the dividend before beginning the “long division” process for
(5a5+ 9a4+ 4a2+ 8a+ 2) ÷ (4a + 5)?
24)
25)
The polynomial 11z7+ 11z3 is called a ? .
25)
26)
What is the degree of term 2a12b6?
26)
27)
What is always the last step when dividing a polynomial by a polynomial?
27)
28)
The polynomial –11t6 is called a ? .
28)
29)
p and q are natural numbers such that p is less than q. What is the degree of the quotient
when a polynomial of degree q is divided by a polynomial of degree p?
29)
30)
What is the degree of term 2d7?
30)
7
31)
Explain why the difference of two polynomials in x, both of degree 4, can be of degree 3.
31)
32)
In multiplying two monomials, you use (but do not always show) the commutative and
associative properties. In each line below, name the property that has been used.
(–10x3)·(–10x5)= (–10x3· – 10)x5_____________
= (–10 · – 10 ·x3)x5_____________
= (–10 · – 10)(x3·x5) _____________
= – 10 · – 10 ·x8
32)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate.
33)
(–4)0–40
33)
A)
1
B)
0
C)
–1
D)
4
Identify the base and the exponent for the exponential expression.
34)
1513
34)
A)
Base: 15, exponent: 13
B)
Base: 13, exponent: 195
C)
Base: 13, exponent: 15
D)
Base: 195, exponent: 13
Find the product.
35)
(8 y2– 6 )( 8 y2+ 6 )
35)
A)
8 y2– 36
B)
64 y4– 96 y2+ 96
C)
64 y4– 36
D)
64 y2+ 36
5
Identify the base and the exponent for the exponential expression.
36)
y7
36)
A)
Base: 7y, exponent: 7
B)
Base: 7, exponent: y
C)
Base: 7, exponent: 7y
D)
Base: y, exponent: 7
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
37)
1
x4
4
37)
A)
x16
B)
1
x8
C)
1
x16
D)
x8
Perform the indicated operation.
38)
(19a5+ 15a3) – (3a5– 7a3)
38)
A)
16a5+ 8a3
B)
38a8
C)
22a5+ 8a3
D)
16a5+ 22a3
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
39)
p4
p–6
39)
A)
p–10
B)
1
p10
C)
p–2
D)
p10
Use a combination of rules for exponents to simplify. Write answers with only positive exponents. Assume that all
variables represent nonzero real numbers.
40)
6r 56r –4
40)
A)
6r
B)
1
6r
C)
36r
D)
36r9
Use the product rule for exponents to simplify the expression, if possible. Write the answer in exponential form.
41)
(–8)(–8)4(–8)(–8)(–8)2
41)
A)
–89
B)
(–8)9
C)
(–8)8
D)
(–8)6
Solve the problem.
42)
Find the sum of (–5+ 9n7– 8n4) and (2n7+ 3n4– 8).
42)
A)
11n7– 5n4– 13
B)
–3n7+ 12n4– 16
C)
11 – 5n7– 13n4
D)
–7n11
Perform the division.
43)
(x2– 16) ÷ (x + 4)
43)
A)
x + 16
B)
x – 16
C)
x – 4
D)
x2– 4
44)
x2– 2x – 48
x – 8
44)
A)
x + 6
B)
x2+ 6
C)
x – 6
D)
x + 6 +8
x – 8
Evaluate the expression.
45)
(–3)–2
45)
A)
9
B)
1
9
C)
–9
D)
–1
9
Perform the division. Write the answer with positive exponents.
46)
36x7+ 36x6+ 42x5
6x6
46)
A)
6x + 6 +7
x
B)
6x + 6
C)
6x + 36x6+7
x
D)
13x + 6
A
Explanation:
Provide an appropriate response.
47)
Is it true that the product of two binomials (–9x + 9)(–9x – 9) is equal to
the polynomial : –92x2+ 2 · – 9·9·x + 92?
47)
A)
True
B)
False
B
Explanation:
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
48)
–8y5– 7y4+ 4
48)
A)
Trinomial, degree 10
B)
Trinomial, degree 9
C)
Trinomial, degree 5
D)
Binomial, degree 5
C
Explanation:
49)
2
5r3+3
5r2
49)
A)
Binomial, degree 2
B)
Binomial, degree 3
C)
Binomial, degree 5
D)
Trinomial, degree 2
B
Explanation:
B
Explanation:
Perform the division.
50)
81x9y9– 81x6y5– 63x2y2
9x2y2
50)
A)
9x9y9– 9x6y5– 7x2y2
B)
9x7y9– 9x4y5– 7y2
C)
–9x7y7– 9x4y3+ 7
D)
9x7y7– 9x4y3– 7
Perform the indicated operation. Write the answer without exponents.
51)
(3 ×10–3) × (7×105) × (7×104)
51)
A)
147 ×106
B)
147,000,000
C)
14,700,000
D)
147 ×10–60
Find the product.
52)
(3p – 1)(9p2+ 3p + 1)
52)
A)
27p3+ 1
B)
27p3+ 12p2– 1
C)
27p3– 1
D)
9p3– 1
Determine whether or not the number is written in scientific notation.
53)
264,000
53)
A)
Yes
B)
No
Add or subtract as indicated.
54)
(x3y2+ 5x2y3+ 3xy – 2) + (x2y3+ 5x3y2– 5xy – 1)
54)
A)
2x3y2+ 10x2y3– 2xy – 3
B)
6x3y2+ 6x2y3+ 3xy – 3
C)
6x3y2+ 6x2y3– 2xy – 3
D)
4x3y2+ 6x2y3– 2xy – 3
9
Write the number in scientific notation.
55)
6,200,000
55)
A)
6.2 ×10–5
B)
6.2 ×106
C)
6.2 ×10–6
D)
6.2 ×105
Perform the division.
56)
m4n4+ mn3
mn
56)
A)
m3n3+ mn2
B)
m5n5+m2n4
C)
m3n3+n3
D)
m3n3+n2
Use the product rule for exponents to simplify the expression, if possible. Write the answer in exponential form.
57)
37·38·32
57)
A)
317
B)
27112
C)
3112
D)
2717
Determine whether or not the number is written in scientific notation.
58)
0.36 ×1011
58)
A)
Yes
B)
No
Provide an appropriate response.
59)
Decide whether the expression is positive, negative, or zero. 1
71
–74
59)
A)
Zero
B)
Negative
C)
Positive
Write the expression using exponents.
60)
(–5x)(–5x)(–5x)(–5x)
60)
A)
–5x4
B)
–20x
C)
–(5x)4
D)
(–5x)4
Determine the number of terms and identify the coefficient of each term of the expression.
61)
–8h – 6s
61)
A)
2; 8 and 6
B)
2; 8 and –6
C)
2; –8 and –6
D)
2; –8 and 6
C
Find the square.
62)
(9 x – 10 y2)
62)
A)
81 x2– 180 xy + 100 y2
B)
9 x2+ 100 y2
C)
9 x2– 180 xy + 100 y2
D)
81 x2+ 100 y2
A
Determine whether or not the number is written in scientific notation.
63)
0.0003
63)
A)
Yes
B)
No
B
Solve the problem.
64)
Find the volume of the figure.
p +1
p + 2
p4
64)
A)
p6+ 3p5+ 2p
B)
p6+ 3p5+ 2
C)
p3+ 3p2+ 2p
D)
p6+ 3p5+ 2p4
D
D
Provide an appropriate response.
65)
Is it true that in order to multiply a number by a positive power of ten, you must move the decimal
point to the left as many places as indicated by the exponent on the ten?
65)
A)
True
B)
False
B)
Solve the problem.
66)
A patio has an area of 4 m3+ 24 m2+ 4 m – 56 . Find the length if the width is 4m + 8 .
66)
A)
m2+ 16 m – 7
B)
m3+ 4 m2– 7 m
C)
m2– 4 m + 7
D)
m2+ 4 m – 7
B)
D)
Find the product.
67)
(2m + 4)(4m3– 2m2+ 2m+ 4)
67)
A)
8m4+ 12m3+ 12m2+ 16m+ 16
B)
8m4– 12m3– 4m2+ 16m+ 16
C)
8m4+ 12m3– 4m2+ 8m+ 16
D)
8m4+ 12m3– 4m2+ 16m+ 16
B)
D)
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
68)
–r3s2–r2s45
68)
A)
–r–4s22
B)
–r41s1026
C)
r16s22
D)
–r16s22
B)
D)
Evaluate.
69)
140+ 30
69)
A)
2
B)
1
C)
17
D)
0
B)
D)
12
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
70)
(x +e)–5
(x +e)–6
70)
A)
(x +e)11
B)
1
(x +e)
C)
1
(x +e)11
D)
x+e
Evaluate the polynomial.
71)
–5x5– 3x4+ 6x3–x2for x = – 2
71)
A)
56
B)
55
C)
60
D)
89
C
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
72)
(–5p3q3r3)6
72)
A)
(–5)6p18q18r18
B)
(–5)18p18q18r18
C)
–30p9q9r9
D)
(–5)6p9q9r9
A
Add or subtract as indicated.
73)
(11x +6xy –8y) – (26x –5xy –25y)
73)
A)
13xy
B)
–15x +11xy + 17y
C)
–15x –11xy –33y
D)
5x + 15xy +33
B
13
D
Evaluate the expression.
74)
7–1+ 3–1
74)
A)
10
21
B)
1
4
C)
2
D)
21
10
Find the product.
75)
(x –9.9)(5x +0.3)
75)
A)
5x2+ 49.2x +2.97
B)
6x2– 49.2x + 9.6
C)
5x2– 49.2x –2.97
D)
6x2+ 49.2x – 9.6
Provide an appropriate response.
76)
Decide whether the expression is positive, negative, or zero. 100–750
76)
A)
Zero
B)
Negative
C)
Positive
Perform the indicated operation.
77)
(–5x3+ 4x5+ 6) + (–8x4+ 4) – (6x4+ 7x5+ 3x3)
77)
A)
11x5– 2x4– 2x3+ 10
B)
–3x5– 2x4– 2x3+ 2
C)
–3x5– 14x4– 8x3+ 10
D)
11x5– 2x4– 2x3+ 2
Perform the division.
78)
x2– 6x + 8
x – 2
78)
A)
x – 4
B)
x + 2
C)
4– x
D)
x + 4
14
Use the product rule for exponents to simplify the expression, if possible. Write the answer in exponential form.
79)
34·64
79)
A)
94
B)
The product rule does not apply.
C)
916
D)
1816
Combine like terms whenever possible. Write the result with descending powers.
80)
5x2+ 2x2– 4x2
80)
A)
3x2
B)
3x6
C)
Cannot be simplified
D)
–40x2
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
81)
8a–5b5
64a–13 b7
81)
A)
a8
8b2
B)
8a8
b2
C)
–a7
8b3
D)
b3
8a8
Provide an appropriate response.
82)
Approximately 8×103 employees of a certain company average $30,000 each year in salary. What
is the total amount earned by all the employees of this company per year? Write your answer in
scientific notation.
82)
A)
$24 ×108
B)
$24 ×109
C)
$2.4 ×109
D)
$2.4 ×108