Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1)
Convert the repeating decimal 0.454 545 . . . into a reduced fraction.
Answer:
5
11
2)
Convert the repeating decimal 2.626 262 . . . into a reduced fraction.
Answer:
260
99
3)
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)
Answer:
(A) F, a = 1 and b = 2 provides a counterexample
(B) F, a = 3, b = 2, and c = 1 provides a counterexample
(C) T
(D) T
4)
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.
Answer:
(A) F; (B) F; (C) T; (D) T
5)
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
Answer:
(A) Q, R; (B) R; (C) Z, Q, R; (D) N, Z, Q, R
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
6)
Which of the following sets: N, Z, Q and I, together compose the set of real numbers?
A)
I and Z together
B)
Z and Q together
C)
N and Z together
D)
I and Q together
Answer:
D
1
Find the product.
7)
(5x + 3y)(9x + 12y)
A)
45x2+ 87xy + 87y2
B)
45x2+ 60xy + 36y2
C)
45x2+ 27xy + 36y2
D)
45x2+ 87xy + 36y2
Answer:
D
8)
(3y + 11)(2y2– 2y –4)
A)
28y2–28y –56
B)
6y3+16y2–34y –44
C)
6y3+28y2+34y +44
D)
6y3–6y2–12y + 11
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the expression by combining like terms, if possible.
9)
Perform the indicated operation and simplify: 3t – [5 – 3{t – t(6 + t)}].
Answer:
–5 – 12t +3t2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
10)
–3(5r + 6) + 3(4r + 7)
A)
–3r + 3
B)
–33r
C)
2r + 3
D)
–3r + 6
Answer:
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
11)
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.
Answer:
1050 –3x
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the GCF from the polynomial.
12)
21x7y5z –35x6y4
A)
7xy(3x6y6z – 5x5y3)
B)
x6y4(21xyz –35)
C)
7x6y4z(3xy – 5)
D)
7x6y4(3xyz – 5)
Answer:
D
Factor completely using grouping.
13)
14y2+ 63y – 35
A)
7(2y + 1)(y – 5)
B)
(14y – 7)(y + 5)
C)
7(2y – 1)(y + 5)
D)
prime
Answer:
C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
14)
Factor by grouping: 12x3–8x2+ 3x – 2
Answer:
(3x – 2)(4x2+ 1)
2
15)
Factor the expression using integer coefficients: 24a2x3–3a2y3.
Answer:
3a2(2x – y)(4x2+ 2xy +y2)
16)
Which polynomial can be factored using integer coefficients? Find its factored form.
I) 20x2– 3x – 35
II) 16m2+25n2
III) x2+ 7x – 5
Answer:
I; (4x + 5)(5x – 7)
17)
Factor using integer coefficients: 4x3y2–20x3y +25x3
Answer:
x3(2y – 5)2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
18)
3x + 3
12x2+ 21x + 9
A)
3x
4x + 3
B)
1
4x + 3
C)
3x + 4
4x + 21
D)
3x + 3
12x2+ 21x + 9
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
19)
Perform the indicated operation and reduce to lowest terms: 20x3y
4xy + 8y ·x2– 4
16x2– 32x
Answer:
5x2
16
20)
Perform the indicated operation and reduce to lowest terms: 3x + 3y
x2– 5xy –14y2÷6x + 6y
x2+ 9xy +14y2
Answer:
x + 7y
2(x – 7y)
21)
Combine into a single fraction and simplify: 1
49x4–7x + 1
5x3+5
245x
Answer:
5 – 49x –343x2+5x3
245x4
22)
Combine into a single fraction and simplify: y – 5
y2– 4 –y + 5
y2– 4y + 4 –3
2 – y
Answer:
3y2– 14y – 12
(y + 2)(y – 2)2
3
23)
Express as a simple fraction reduced to lowest terms:
a
b– 1 –2b
a
a
b– 3 +2b
a
Answer:
a + b
a – b
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.
24)
–3ym4n
–7ym7n
A)
3
7m3
B)
–4
m3
C)
–4y2n2
m3
D)
1
4m3
Answer:
A
25)
(9x–3y5)(9–1x6y–8)
A)
–x3
9y3
B)
x3
y3
C)
x9
y13
D)
1
x18y40
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
26)
Simplify and express using positive exponents: 5m–3
n4
–2
Answer:
m6n8
25
27)
Simplify and express the answer using positive exponents: 5m–4
m–8
Answer:
5m4
28)
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.
Answer:
x3–4
3x +3x–1
29)
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.
Answer:
x2(x – 2)(x + 4)
30)
Write 7.214 ×107 in standard notation.
Answer:
72,140,000
31)
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.
Answer:
2.81422 ×108, 7.6212 ×107; 3.6926
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rewrite the expression with a positive rational exponent. Simplify, if possible.
32)
16a2b–4
a–2b4
1/2
A)
16b4
a
B)
16a
b2
C)
4a2b4
D)
4a2
b4
Answer:
D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
33)
Simplify and express using positive exponents: 4x2/3
10x–1/4
–1
Answer:
5
2x11/12
34)
Change to simplest radical form: (2xy6z35)3/7
Answer:
y2z1578x3y4
35)
Simplify and express the answer using positive exponents only: (2x–5/8y3/4)8
Answer:
256y6
x5
36)
Change to simplest radical form: 49x4y
7x
Answer:
7x3y7x
37)
Write in simplest radical form: 5243x13y22
Answer:
3x2y45x3y2
38)
Change to simplest radical form: 12m8n63m8n2
Answer:
6m8n4
5
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
39)
2
3+5
A)
5+3
B)
2
C)
5–3
D)
3–5
Answer:
C
Use the square root property to solve the equation.
40)
(x + 2)2=24
A)
{2 6–2, 2 6+2}
B)
{–2– 2 6, –2+ 2 6}
C)
{–2 6, 2 6}
D)
{–2– 2 12, –2+ 2 12}
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
41)
Solve by factoring: 4y2= 10y
Answer:
y = 0 or 5
2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the quadratic formula to solve the equation.
42)
x2+ 10x + 15 = 0
A)
{–5–10, –5+10}
B)
{5 –15, 5+15}
C)
{5 +10}
D)
{–10 +15}
Answer:
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
43)
Factor, if possible, as the product of two first–degree polynomials with integer coefficients: 4x2– 131x + 435
Answer:
(4x – 15)(x – 29)
44)
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.
Answer:
$6
6