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)
N and Z together
D)
I and Q 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:
3x + 3y
x2– 5xy –14y2÷6x + 6y
x2+ 9xy +14y2
2)
3)
Combine into a single fraction and simplify: 1
49x4–7x + 1
5x3+5
245x
3)
4)
Change to simplest radical form: 49x4y
7x
4)
5)
Solve by factoring: 4y2= 10y
5)
6)
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.
6)
7)
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.
7)
8)
Change to simplest radical form: (2xy6z35)3/7
8)
9)
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
9)
Simplify the expression by combining like terms, if possible.
10)
Perform the indicated operation and simplify: 3t – [5 – 3{t – t(6 + t)}].
10)
Provide an appropriate response.
11)
Change to simplest radical form: 12m8n63m8n2
11)
12)
Simplify and express using positive exponents: 4x2/3
10x–1/4
–1
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)
Combine into a single fraction and simplify: y – 5
y2– 4 –y + 5
y2– 4y + 4 –3
2 – y
14)
15)
Write 7.214 ×107 in standard notation.
15)
16)
Express as a simple fraction reduced to lowest terms:
a
b– 3 +2b
a
16)
17)
Factor, if possible, as the product of two first–degree polynomials with integer coefficients:
4x2– 131x + 435
17)
18)
Simplify and express using positive exponents: 5m–3
n4
18)
19)
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)
19)
20)
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.
20)
21)
Factor by grouping: 12x3–8x2+ 3x – 2
21)
22)
Convert the repeating decimal 0.454 545 . . . into a reduced fraction.
22)
23)
Simplify and express the answer using positive exponents only: (2x–5/8y3/4)8
23)
24)
Write in simplest radical form: 5243x13y22
24)
25)
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.
25)
26)
Simplify and express the answer using positive exponents: 5m–4
m–8
26)
27)
Perform the indicated operation and reduce to lowest terms: 20x3y
4xy + 8y ·x2– 4
16x2– 32x
27)
4
28)
Convert the repeating decimal 2.626 262 . . . into a reduced fraction.
28)
29)
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.
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)
Factor using integer coefficients: 4x3y2–20x3y +25x3
31)
32)
Factor the expression using integer coefficients: 24a2x3–3a2y3.
32)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify. The exponents in the answer should be positive integers.
33)
(6x–3y5)(6–1x6y–8)
33)
A)
–x3
6y3
B)
1
x18y40
C)
x3
y3
D)
x9
y13
Find the product.
34)
(8y + 11)(4y2– 2y –9)
34)
A)
32y3+60y2+94y +99
B)
32y3–16y2–72y + 11
C)
32y3+28y2–94y –99
D)
76y2–38y –171
35)
(9x + 6y)(8x – 11y)
35)
A)
72x2+ 48xy – 66y2
B)
72x2– 99xy – 66y2
C)
72x2– 51xy – 51y2
D)
72x2– 51xy – 66y2
D
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
36)
2
5+7
36)
A)
2
B)
5–7
C)
7+5
D)
7–5
D
Factor completely using grouping.
37)
14y2+ 63y – 35
37)
A)
7(2y + 1)(y – 5)
B)
(14y – 7)(y + 5)
C)
7(2y – 1)(y + 5)
D)
prime
C
Use the square root property to solve the equation.
38)
(x + 3)2=44
38)
A)
{–211, 2 11}
B)
{–3– 2 11, –3+ 2 11}
C)
{–3– 2 22, –3+ 2 22}
D)
{2 11 –3, 2 11 +3}
B
6
C
Simplify. The exponents in the answer should be positive integers.
39)
–8ym2n
–5ym5n
39)
A)
8
5m3
B)
1
3m3
C)
3
m3
D)
3y2n2
m3
Simplify the expression.
40)
4x + 2
12x2+ 14x + 4
40)
A)
4x + 2
12x2+ 14x + 4
B)
1
3x + 2
C)
4x + 3
3x + 14
D)
4x
3x + 2
Rewrite the expression with a positive rational exponent. Simplify, if possible.
41)
4a2b-4
a-2b4
1/2
41)
A)
2a2b4
B)
4b4
a
C)
4a
b2
D)
2a2
b4
Use the quadratic formula to solve the equation.
42)
x2+ 10x + 10 = 0
42)
A)
{–5–15, –5+15}
B)
{–10 +10}
C)
{5 +15}
D)
{5 –10, 5+10}
7
Factor the GCF from the polynomial.
43)
6x7y6z –10x6y5
43)
A)
2x6y5z(3xy – 5)
B)
2xy(3x6y6z – 5x5y4)
C)
x6y5(6xyz –10)
D)
2x6y5(3xyz – 5)
Simplify the expression by combining like terms, if possible.
44)
–4(9r + 2) + 7(4r + 6)
44)
A)
-8r + 34
B)
-8r + 2
C)
–44r
D)
5r – 2
8
Answer Key
Testname: C9
9
Answer Key
Testname: C9