Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Which of the following sets: N, Z, Q and I, together compose the set of real numbers?
1)
A)
I and Z together
B)
Z and Q together
C)
I and Q together
D)
N and Z together
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
2)
Perform the indicated operation and reduce to lowest terms: 20x3y
4xy + 8y ·x2– 4
16x2– 32x
2)
3)
Solve by factoring: 4y2= 10y
3)
4)
Write 7.214 ×107 in standard notation.
4)
5)
Convert the repeating decimal 0.454 545 . . . into a reduced fraction.
5)
6)
Perform the indicated operation and reduce to lowest terms:
3x + 3y
x2– 5xy –14y2÷6x + 6y
x2+ 9xy +14y2
6)
7)
Factor the expression using integer coefficients: 24a2x3–3a2y3.
7)
8)
Change to simplest radical form: (2xy6z35)3/7
8)
9)
Simplify and express the answer using positive exponents only: (2x–5/8y3/4)8
9)
10)
The supply and demand equations for a certain product are s = 2,500p – 14,500 and
d =3,000
p, where p is the price in dollars. Find the price where supply equals demand.
10)
11)
Factor by grouping: 12x3–8x2+ 3x – 2
11)
12)
Indicate True (T) or False (F), and for each false statement find real number replacements
for a, b, and c that will provide a counterexample.
(A) a – b = b – a
(B) (a – b) – c = a – (b – c)
(C) a + b = b + a
(D) (a · b) · c = a · (b · c)
12)
13)
Write 3x3(x –2)3–2x2(x – 2)4
(x – 2)2 with positive exponents only, and as a single fraction
reduced to lowest terms.
13)
14)
Change to simplest radical form: 12m8n63m8n2
14)
15)
Simplify and express using positive exponents: 4x2/3
10x–1/4
15)
16)
Simplify and express using positive exponents: 5m–3
n4
16)
17)
Each ounce of food A contains 4 units of calcium, and each ounce of food B contains 7 units
of calcium. A 150 ounce diet mix is formed using foods A and B. If x is the number of
ounces of food A used, write an algebraic expression that represents the total number of
units of calcium in the diet mix. Simplify the expression.
17)
18)
Indicate True (T) or False (F) by each statement.
(A) Every real number is a natural number.
(B) An irrational number is not a real number.
(C) Every natural number is an integer.
(D) An integer is a rational number.
18)
19)
Convert the repeating decimal 2.626 262 . . . into a reduced fraction.
19)
20)
Factor, if possible, as the product of two first–degree polynomials with integer coefficients:
4x2– 131x + 435
20)
21)
According to the 2000 U.S. census, the population of the United States on April 1, 2000 was
approximately 281,422,000 (Source: www.census.gov). The population of the U.S. in 1900
was approximately 76,212,000. Write both population numbers in scientific notation and
use these expressions to calculate the ratio of the population in 2000 to that in 1900. Express
the ratio in standard decimal form to four decimal places.
21)
22)
Write 3x5–4x3+ 9x
3x2 in the form axp+bxq+cxr, where a, b, and c are real numbers and p,
q and r are integers.
22)
23)
Change to simplest radical form: 49x4y
7x
23)
24)
Simplify and express the answer using positive exponents: 5m–4
m–8
24)
Simplify the expression by combining like terms, if possible.
25)
Perform the indicated operation and simplify: 3t – [5 – 3{t – t(6 + t)}].
25)
Provide an appropriate response.
26)
Factor using integer coefficients: 4x3y2–20x3y +25x3
26)
27)
Write in simplest radical form: 5243x13y22
27)
28)
Combine into a single fraction and simplify: 1
49x4–7x + 1
5x3+5
245x
28)
29)
Combine into a single fraction and simplify: y – 5
y2– 4 –y + 5
y2– 4y + 4 –3
2 – y
29)
30)
Which polynomial can be factored using integer coefficients? Find its factored form.
I) 20x2– 3x – 35
II) 16m2+25n2
III) x2+ 7x – 5
30)
31)
Given the sets N, Z, Q, and R, indicate to which set(s) each of the following numbers
belong.
(A) 5
6
(B) e
(C) –2
(D) 8
31)
32)
Express as a simple fraction reduced to lowest terms:
a
b– 3 +2b
a
32)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
33)
3x + 2
15x2+ 16x + 4
33)
A)
3x + 2
15x2+ 16x + 4
B)
3x
5x + 2
C)
3x + 5
5x + 16
D)
1
5x + 2
Find the product.
34)
(6y + 11)(7y2– 2y –4)
34)
A)
119y2–34y –68
B)
42y3+89y2+46y +44
C)
42y3–12y2–24y + 11
D)
42y3+65y2–46y –44
5
35)
(7x – 2y)(4x + 10y)
35)
A)
28x2+ 62xy + 62y2
B)
28x2– 8xy – 20y2
C)
28x2+ 70xy – 20y2
D)
28x2+ 62xy – 20y2
Simplify. The exponents in the answer should be positive integers.
36)
–7ym2n
–3ym5n
36)
A)
1
4m3
B)
4
m3
C)
7
3m3
D)
4y2n2
m3
C
Rewrite the expression with a positive rational exponent. Simplify, if possible.
37)
27a3b-6
a-3b6
1/3
37)
A)
3a2
b4
B)
9b6
a
C)
3a2b6
D)
9a
b2
A
Use the square root property to solve the equation.
38)
(x + 2)2=44
38)
A)
{2 11 –2, 2 11 +2}
B)
{–2– 2 11, –2+ 2 11}
C)
{–211, 2 11}
D)
{–2– 2 22, –2+ 2 22}
B
6
D
Use the quadratic formula to solve the equation.
39)
x2+ 14x + 38 = 0
39)
A)
{–7–11, –7+11}
B)
{7 –38, 7+38}
C)
{–14 +38}
D)
{7 +11}
Simplify. The exponents in the answer should be positive integers.
40)
(9x–3y5)(9–1x6y–8)
40)
A)
x9
y13
B)
x3
y3
C)
1
x18y40
D)
–x3
9y3
Factor the GCF from the polynomial.
41)
15x8y8z –25x7y7
41)
A)
x7y7(15xyz –25)
B)
5x7y7(3xyz – 5)
C)
5xy(3x7y7z – 5x6y6)
D)
5x7y7z(3xy – 5)
Factor completely using grouping.
42)
8y2+ 36y – 20
42)
A)
4(2y + 1)(y – 5)
B)
(8y – 4)(y + 5)
C)
4(2y – 1)(y + 5)
D)
prime
Simplify the expression by combining like terms, if possible.
43)
–5(2r + 10) + 2(4r + 3)
43)
A)
-2r + 10
B)
–60r
C)
-3r + 5
D)
-2r – 44
7
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
44)
3
7+10
44)
A)
10 +7
B)
10 –7
C)
3
D)
7–10
8
Answer Key
Testname: C16
9
Answer Key
Testname: C16