Deck 12: Basic Algebra Review

Question 1

Provide an appropriate response.
Which of the following sets: N, Z, Q and I, together compose the set of real numbers?

A) N and Z together
B) I and Z together
C) I and Q together
D) Z and Q together

Answer 1

I and Q together

Question 2

Provide an appropriate response.
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 2

(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

Question 3

Provide an appropriate response.
Convert the repeating decimal 0.454 545 . . . into a reduced fraction.

Answer 3

Question 4

Provide an appropriate response.
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.

Question 5

Find the product.
(4x - 5y)(5x - 10y)

A)
B)
C)
D)

Question 6

Provide an appropriate response.

A)
B)
C)
D)

Question 7

Provide an appropriate response.
Given the sets N, Z, Q, and R, indicate to which set(s) each of the following numbers belong.
(A)
(B) e
(C) -2
(D) 8

Question 8

Provide an appropriate response.
Factor using integer coefficients:

Question 9

Simplify the expression by combining like terms, if possible.
-7(3r + 8) + 7(2r + 5)

A) -7r + 8
B) -77r
C) -7r - 21
D) -4r + 1

Question 10

Provide an appropriate response.
Factor by grouping:

Question 11

Find the product.

A)
B)
C)
D)

Question 12

Factor completely using grouping.

A) 2(2y + 1)(y - 5)
B) 2(2y - 1)(y + 5)
C) (4y - 2)(y + 5)
D) prime

Question 13

Provide an appropriate response.
Perform the indicated operation and reduce to lowest terms:

Question 14

Simplify the expression by combining like terms, if possible.
Perform the indicated operation and simplify: 3t - [5 - 3{t - t(6 + t)}].

Question 15

Provide an appropriate response.
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.

Question 16

Provide an appropriate response.

A)
B)
C)
D)

Question 17

Provide an appropriate response.
Which polynomial can be factored using integer coefficients? Find its factored form.
I) II) III)

Question 18

Provide an appropriate response.
Perform the indicated operation and reduce to lowest terms:

Question 19

Provide an appropriate response.
Factor the expression using integer coefficients:

Question 20

Provide an appropriate response.
Convert the repeating decimal 2.626 262 . . . into a reduced fraction.

Question 21

Provide an appropriate response.
Combine into a single fraction and simplify:

Question 22

Provide an appropriate response.
Change to simplest radical form:

Question 23

Use the square root property to solve the equation.

A)
B)
C)
D)

Question 24

Provide an appropriate response.
Change to simplest radical form: (

Question 25

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Write in the form a where a, b, and c are real numbers and p, q and r are integers.

Question 26

Provide an appropriate response.
Simplify and express the answer using positive exponents:

Question 27

Provide an appropriate response.
Write with positive exponents only, and as a single fraction reduced to lowest terms.

Question 28

Provide an appropriate response.

A)
B)
C)
D)

Question 29

Provide an appropriate response.
Write in standard notation.

Question 30

Provide an appropriate response.
Combine into a single fraction and simplify:

Question 31

Provide an appropriate response.

A)
B)
C)
D)

Question 32

Provide an appropriate response.
Simplify and express the answer using positive exponents only:

Question 33

Provide an appropriate response.
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.

Question 34

Provide an appropriate response.
Simplify and express using positive exponents:

Question 35

Provide an appropriate response.

A)
B)
C)
D)

Question 36

Provide an appropriate response.
Express as a simple fraction reduced to lowest terms:

Question 37

Provide an appropriate response.
Write in simplest radical form:

Question 38

Provide an appropriate response.
- -

A)
B)
C)
D)

Question 39

Provide an appropriate response.
Change to simplest radical form:

Question 40

Provide an appropriate response.
Simplify and express using positive exponents:

Question 41

Provide an appropriate response.
Factor, if possible, as the product of two first-degree polynomials with integer coefficients:

Question 42

Provide an appropriate response.
The supply and demand equations for a certain product are s = 2,500p - 14,500 and where p is the
price in dollars. Find the price where supply equals demand.

Question 43

Provide an appropriate response.
Solve by factoring:

Question 44

Provide an appropriate response.

A)
B)
C)
D)