Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
What must be done to the dividend before beginning the “long division” process for
(4y3+ 3y4+ 9y2+ 2y+ 1) ÷ (6y + 1)?
1)
2)
Explain how (–7)6 and –76 are different.
2)
3)
Does the product rule apply to 142·106? Explain why or why not.
3)
4)
Is it correct to simplify 24·42 as 88?
4)
5)
Explain how (–2x)6 and –2x6 are different.
5)
6)
What must be done to the dividend before beginning the “long division” process for
(9y5+ 3y3+ 2y2+ 2y+ 9) ÷ (6y + 5)?
6)
7)
x and y are natural numbers such that x is less than y. What is the degree of the quotient
when a polynomial of degree y is divided by a polynomial of degree x?
7)
8)
What is always the last step when dividing a polynomial by a polynomial?
8)
9)
For the exponential expression pn= 1, the variable p may equal ? .
9)
10)
Explain how (p+ q)3 differs from p3+ q3 by expanding (p+ q)3.
10)
11)
Explain how (a – b)3 differs from a3– b3 by expanding (a – b)3.
11)
12)
The polynomial 18m9+ 2m2+ 16 is called a ? .
12)
13)
Find and explain the mistake(s); then work the problem correctly.
(4x –9y)(4x –9y) =16x2+81y2
13)
14)
What is the degree of term 10s18?
14)
15)
Is (5x7y2)3 equivalent to 15x21y6?
15)
16)
Explain how (m+ n)2 differs from m2+ n2 by expanding (m+ n)2.
16)
17)
Why is scientific notation used?
17)
18)
In scientific notation, what is the largest integer which can be multiplied by a power of 10?
18)
19)
Give an example of a like term for 9a13b16.
19)
20)
What is the degree of term 14c2d18?
20)
21)
Is the product of a monomial and a binomial always a binomial? Why or why not?
21)
22)
In scientific notation, what is the smallest positive integer which can be multiplied by a
power of 10?
22)
1
23)
Does scientific notation allow a negative number to be multiplied by a power of 10?
23)
24)
Explain why the difference of two polynomials in x, both of degree 10, can be of degree 9.
24)
25)
The polynomial 18a5– 13a3 is called a ? .
25)
26)
The polynomial –16x4 is called a ? .
26)
27)
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.
(–9x3)·(4x5)= (–9x3·4)x5_____________
= (–9·4·x3)x5_____________
= (–9·4)(x3·x5) _____________
= – 9·4·x8
27)
28)
Explain how (p– q)2 differs from p2– q2 by expanding (p– q)2.
28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
29)
12x
29)
A)
Monomial, degree 0
B)
Monomial, degree 1
C)
Monomial, degree 12
D)
Binomial, degree 0
Identify the base and the exponent for the exponential expression.
30)
–45
30)
A)
Base: 5, exponent: –4
B)
Base: 5, exponent: 4
C)
Base: –4, exponent: 5
D)
Base: 4, exponent: 5
Simplify the expression.
31)
(–4p3q3r3)4
31)
A)
(–4)12p12q12r12
B)
(–4)4p12q12r12
C)
(–4)4p7q7r7
D)
–16p7q7r7
Find the product.
32)
(x + 2 y)3
32)
A)
x3+ 6 x2y + 12 xy2+ 8 y3
B)
3(x + 2 y)
C)
x3+ 8 y3
D)
x3+ 2 x2y + 4 xy + 4 xy2+ 8 y2+ 8 y3
4
Evaluate the expression.
33)
4–2
33)
A)
16
B)
1
8
C)
1
16
D)
–16
Perform the division.
34)
x3+ 125
x + 5
34)
A)
x2– 10x + 25
B)
x2– 5x + 25
C)
x2– 5x – 25
D)
x2+ 5x + 25
Find the value of the polynomial.
35)
4x2+ 2x – 5 when x =2
35)
A)
11
B)
7
C)
5
D)
15
Determine whether the expression represents a number that is positive, negative, or zero.
36)
1–5
36)
A)
Negative
B)
Zero
C)
Positive
Evaluate the expression.
37)
130+ 80
37)
A)
2
B)
1
C)
21
D)
0
5
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
38)
t–4
t–6
38)
A)
t–2
B)
t–10
C)
t10
D)
t2
Solve the problem.
39)
Find a polynomial that represents the area of the shaded region.
4x +8
6x +2
x
39)
A)
4x2+ 10x + 16
B)
4x2+ 16 –3x
C)
4x2+ 13x + 16
D)
4x2+13x –16
Determine whether the expression represents a number that is positive, negative, or zero.
40)
–110
40)
A)
Zero
B)
Positive
C)
Negative
Provide an appropriate response.
41)
Determine if the expression ( –5 )–8 is positive or negative.
41)
A)
Positive
B)
Negative
Add.
42)
6x8– 8x7– 6x6– 2
9x8– 2x7– 9x6+ 8
42)
A)
–4x8– 4x7+ 14x6+ 1
B)
–10x42 + 6
C)
15x8– 10x7– 15x6+ 6
D)
15x16 – 10x14 – 15x12 + 6
Determine the number of terms and name the coefficients of the terms.
43)
–8m + 3y
43)
A)
2; –8 and –3
B)
2; 8 and –3
C)
2; 8 and 3
D)
2; –8 and 3
Add like terms, if possible, and write the result in descending powers of the variable.
44)
7x5+ 6x5– 4x5
44)
A)
–168x5
B)
9x5
C)
9x15
D)
Cannot be simplified
Find the value of the polynomial.
45)
–7x +6 when x =3
45)
A)
–1
B)
–42
C)
–15
D)
–27
Provide an appropriate response.
46)
Decide whether the expression is positive, negative, or zero. 1
24
–68
46)
A)
Positive
B)
Negative
C)
Zero
Perform the indicated operation. Write the answer in scientific notation.
47)
(5.26 × 10–4)(5.35 × 10–2)
47)
A)
2.81 × 108
B)
2.8 × 108
C)
2.81 × 10–5
D)
2.8 × 10–5
Evaluate.
48)
34
48)
A)
81
B)
34
C)
3
D)
12
49)
(–5)2
49)
A)
25
B)
10
C)
–10
D)
–25
Perform the division.
50)
x6– 1
x3– 1
50)
A)
x3+ 1
B)
x3
C)
x3– 1
D)
x3+9x – 1
Find the value of the polynomial.
51)
2x5– 3x4+ 4x3–x2 when x =2
51)
A)
39
B)
44
C)
40
D)
73
8
Perform the indicated operation. Write the answer without exponents.
52)
(5.8 ×102) × (8.5 ×10–5)
52)
A)
49.3 ×10–3
B)
49.3 ×10–10
C)
0.0493
D)
0.00493
Determine whether the expression represents a number that is positive, negative, or zero.
53)
70
53)
A)
Negative
B)
Zero
C)
Positive
Write the expression using exponents.
54)
4
3
4
3
4
3
4
3
4
3
4
3
54)
A)
4
3
5
B)
4
3
6
C)
6
4
3
D)
64
3
Provide an appropriate response.
55)
Is it always true that a–b
c–d=cd
ab?
55)
A)
Yes
B)
No
Find the product.
56)
(5y – 6)(25y2+ 30y + 36)
56)
A)
125y3– 216
B)
125y3+ 180y2– 216
C)
25y3+ 216
D)
125y3+ 216
9
Add or subtract as indicated.
57)
(2x2y – 4xy) – (5x2y + 4xy2) – (6xy + 3xy2)
57)
A)
–3x2y + 7xy2– 10xy
B)
–3x2y – 7xy2– 10xy
C)
–3x2y + 7xy2+ 2xy
D)
–6x2y – 4xy2– 10xy
Perform the indicated operation.
58)
–(3x3+ x –8) + (8x3+2x2) – (6x2–7x –1)
58)
A)
11x3–8x2+6x –9
B)
4x3–2x2–6x +9
C)
5x3–4x2+6x +9
D)
5x3+4x2+8x –9
C
Solve the problem.
59)
Find an expression that represents the area of the figure.
2x2
7x5
59)
A)
14x10
B)
14x7
C)
9x10
D)
9x7
B
Write the expression using exponents.
60)
(–4x)(–4x)(–4x)(–4x)
60)
A)
(–4x)4
B)
–16x
C)
–4x4
D)
–(4x)4
A
B
Solve the problem. Express the answer in scientific notation to two decimals.
61)
The earth is approximately 92,900,000 miles from the sun. If 1 mile = 1.61 × 103 m, what is the
distance to the sun in meters?
61)
A)
5.7 × 1010 m
B)
1.50 × 1011 m
C)
5.7 × 10–10 m
D)
1.50 × 1010 m
Perform the division.
62)
(x2– 4) ÷ (x – 2)
62)
A)
x2– 2
B)
x – 4
C)
x + 2
D)
x + 4
Find the product.
63)
6x(–5x + 10)
63)
A)
–30x2+ 60x
B)
–30x2+ 10x
C)
30x2
D)
–5x2+ 60x
64)
(3x –5)(5x5–2x3+3x2– x +1)
64)
A)
15x6–6x4+9x3–3x2+3x –5
B)
15x5–25x4–6x3+19x2+8x –5
C)
15x6–25x5–6x4+19x3–18x2+8x –5
D)
15x6–25x5–6x4+ – 1x3–18x2+ – 2x +5
11
Perform the division. Write the answer with positive exponents.
65)
24x11 – 32x10 – 12x9+ 24x7+ 5x5
4x9
65)
A)
24x11 – 8x2– 3 +6
x2+5
4x3
B)
6x3– 32x10 – 12x9+ 24x7+ 5x5
C)
6x3– 8x2– 3
D)
6x2– 8x – 3 +6
x2+5
4x4
66)
–40x6– 48x5– 24x4
–8x5
66)
A)
5x + 6
B)
8x + 6
C)
5x + 6 +3
x
D)
5x – 48x5+3
x
Write the number without exponents.
67)
8.0929 × 10–7
67)
A)
0.00000080929
B)
0.000000080929
C)
0.0000080929
D)
–809,920,000
Add.
68)
(4a4– 9a3) + (6a4+ 3a3)
68)
A)
4a7
B)
10a8– 6a6
C)
10a4– 6a3
D)
4a14
12
Perform the indicated operation.
69)
Add (6a5+ 2a4) and (3a5+ 5a4).
69)
A)
16a18
B)
16a9
C)
9a10 + 7a8
D)
9a5+ 7a4
Provide an appropriate response.
70)
2x 3
2x
3
Find the total area.
70)
A)
4x2+6x +9
B)
2x2+6x +9
C)
2x2+12x +9
D)
4x2+12x +9
Find the product.
71)
(–5m2z4)(2m3z2)
71)
A)
–10mz6
B)
–10mz5
C)
–10m6z5
D)
–10m5z6
Perform the division.
72)
y2+ 8 y + 16
y + 4
72)
A)
y – 4
B)
y + 4
C)
y +4
y + 4
D)
y2+ 4
Perform the indicated operation.
73)
(3 a + 10c)( 3a – 10 c)
73)
A)
9 a2– 60 ac – 100 c2
B)
9 a2+ 60 ac – 100 c2
C)
9 a2– 100 c2
D)
3 a2– 10 c2
C
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
74)
19a2
74)
A)
Monomial, degree 19
B)
Binomial, degree 19
C)
Monomial, degree 2
D)
Binomial, degree 2
C
Solve the problem.
75)
Determine a polynomial that represents the area of the figure. Leave in the answer.
6x +3
75)
A)
36x2+36x +9
B)
36x2+36x +9
C)
36x2+9
D)
36x2+9
B
B
If the number in the statement is written in scientific notation, write it without exponents. If it is written without
exponents, write it in scientific notation.
76)
The life span of the average male human being is approximately 37,843,200 minutes.
76)
A)
37.8432 ×106 min
B)
3.78432 ×107 min
C)
3.78432 ×105 min
D)
3.78432 ×106 min
Solve the problem.
77)
The area of a rectangle is 20 m2– 18 m – 18 . Find the length if the width is 4m – 6 .
77)
A)
5m – 3
B)
5m + 3
C)
20 m – 3
D)
20 m + 3
Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.
78)
tz–4
t–2z
–4
78)
A)
z16
t8
B)
z20
t12
C)
t20
z12
D)
t16
z8
Perform the division. Write the answer with positive exponents.
79)
–6x11 + 20x7
–2x3
79)
A)
3x8+ 20x7
B)
–7x15
C)
–6x11 – 10x4
D)
3x8– 10x4
Provide an appropriate response.
80)
Determine if the expression ( –7 )–5 is positive or negative.
80)
A)
Positive
B)
Negative
Determine whether or not the number is written in scientific notation.
81)
2.19 × 106
81)
A)
in scientific notation
B)
not in scientific notation
Perform the division.
82)
x4– 625
x2– 25
82)
A)
x2– 25x + 5
B)
x2+ 25
C)
x2+ 5x + 5
D)
x2– 25
Write the expression using exponents.
83)
x · x · x · x · x · x · x · x
83)
A)
8
B)
8(x)
C)
x8
D)
8x
Perform the division.
84)
6x5+ 9x4– 3x3+ 18x2– 3x + 9
3x2– 3x + 3
84)
A)
2x3+ 5x2– 2x + 3
B)
2x3+ 5x2+ 2x + 3
C)
2x3– 5x2+ 2x + 3
D)
2x3+ 5x2+ 2x – 3
Solve the problem.
85)
What polynomial, when divided by 4ax 6, yields –6ax 6– 4 x3+ 8 as a quotient?
85)
A)
–24 a2x12 – 16 ax 9+ 32ax 6
B)
–24 a2x12 – 16 ax 9
C)
–24 ax 6– 16 x3+ 32
D)
–24 a2x12 – 4 x3+ 8
16
86)
Find an expression that represents the area of the figure.(Leave in the answer.)
6t5
86)
A)
12t10
B)
36t5
C)
36t25
D)
36t10
Solve the problem. Express the answer in scientific notation to two decimals.
87)
The national debt of a small country is $6,670,000,000 and the population is 2,884,000. What is the
amount of debt per person?
87)
A)
$2.31
B)
$23.10
C)
$2.31 × 103
D)
$2.31 × 106
Perform the division.
88)
(35m9n –30m8n5+20m7n7) ÷ (5m6n)
88)
A)
29
B)
7m3–6m2n4+4mn6
C)
7m15 –6m14n6+4m13n8
D)
7m3–30m8n5+20m7n7
Add or subtract as indicated.
89)
(r + 5s – 3) + (–5r + s) + (s – 2)
89)
A)
–4r + 7s – 5
B)
–6r + 7s – 5
C)
–5r + 5s – 5
D)
–4r + 6s – 5
Graph the equation by completing the table of values.
17
90)
y =5x2
x y
–2
–1
0
1
2
90)
A)
x y
–220
–1 5
0 0
1 5
220
B)
x y
–2 4
–1 1
0 0
1 1
2 4
C)
x y
–225
–110
0 0
110
225
D)
x y
–20.8
–10.2
0 0
10.2
20.8
Find the product.
91)
(x + 8 )(x – 8 )
91)
A)
x2+ 16 x – 64
B)
x2– 64
C)
x2– 16 x – 64
D)
x2– 16
Perform the indicated operation.
92)
Add (–6x – 4 + 3x3) to the sum of (1+ x2– 5x) and (4x + 1 + x3).
92)
A)
4x3+ x2– 7x – 2
B)
5x3– 7x – 2
C)
4x3+ 5x2– 11x – 2
D)
4x3+ x2– 7x – 3
Simplify the expression.
93)
1
x3
4 (x
0)
93)
A)
x12
B)
x7
C)
1
x7
D)
1
x12
Predict the display a calculator would give for the expression shown in the screen.
94)
.0000062
94)
A)
62E6
B)
62E–6
C)
6.2 E–6
D)
6.2E6
Perform the division.
95)
( x2+ 3x – 54) ÷ ( x + 9)
95)
A)
x – 6
B)
x2– 6
C)
x2+ 4x – 45
D)
x + 6
Find the product. Use the FOIL method.
96)
(3x – 3)(3x – 3)
96)
A)
9x2+ 9x – 18
B)
3x2– 18x – 19
C)
9x2– 18x + 9
D)
3x2– 19x + 9
C
Solve the problem.
97)
Determine a polynomial that represents the area of the figure. Leave in the answer.
6x +5
97)
A)
36x2+25
B)
36x2+25
C)
36x2+60x +25
D)
36x2+60x +25
D
Find the product.
98)
(2a)(6a2)
98)
A)
12a3
B)
2a + 6a2
C)
8a3
D)
12a4
A
A