Deck 8: Appendix A: Basic Algebra Review

Question 1

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Convert the repeating decimal 2.626 262 . . . into a reduced fraction.

Answer 1

Question 2

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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

Answer 2

(A) Q, R; (B) R; (C) Z, Q, R; (D) N, Z, Q, R

Question 3

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Factor using integer coefficients:

Answer 3

xx

Question 4

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Which polynomial can be factored using integer coefficients? Find its factored form.
I) II) III) + 7x - 5

Question 5

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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 6

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Factor by grouping:

Question 7

Factor completely using grouping.

A) 7(2y + 1)(y - 5)
B) (14y - 7)(y + 5)
C) 7(2y - 1)(y + 5)
D) prime

Question 8

Simplify the expression.

A)
B)
C)
D)

Question 9

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Perform the indicated operation and reduce to lowest terms: t terms:

Question 10

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

Question 11

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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)

Question 12

Simplify the expression by combining like terms, if possible.
-3(5r + 6) + 3(4r + 7)

A) -3r + 3
B) -33r
C) 2r + 3
D) -3r + 6

Question 13

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Factor the expression using integer coefficients: 24a

Question 14

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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 15

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Convert the repeating decimal 0.454 545 . . . into a reduced fraction.

Question 16

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Perform the indicated operation and reduce to lowest terms: t terms:

Question 17

Find the product.

A)
B)
C)
D)

Question 18

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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

Question 19

Factor the GCF from the polynomial.

A)
B)
C)
D)

Question 20

Find the product.
(5x + 3y)(9x + 12y)

A)
B)
C)
D)

Question 21

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Write in the formaxp + bxq + cxr, where a, b, and c are real numbers and p, q and are integers.

Question 22

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Change to simplest radical form: m:

Question 23

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Simplify and express using positive exponents: positive exponents:

Question 24

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.

A)
B)
C)
D)

Question 25

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Write in simplest radical form:

Question 26

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Write 7.214 × in standard notation.

Question 27

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Combine into a single fraction and simplify:

Question 28

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Simplify and express the answer using positive exponents only: (

Question 29

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Simplify and express using positive exponents: positive exponents:

Question 30

Simplify. The exponents in the answer should be positive integers.

A)
B)
C)
D)

Question 31

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Change to simplest radical form :

Question 32

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Simplify and express the answer using positive exponents:

Question 33

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Write te with positive exponents only, and as a single fraction reduced to lowest terms.

Question 34

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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 35

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Express as a simple fraction reduced to lowest terms:

Question 36

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Combine into a single fraction and simplify:

Question 37

Use the square root property to solve the equation.

A)
B)
C)
D)

Question 38

Simplify. The exponents in the answer should be positive integers.

A)
B)
C)
D)

Question 39

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Change to simplest radical form:

Question 40

Rewrite the expression with a positive rational exponent. Simplify, if possible.

A)
B)
C)
D)

Question 41

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Solve by factoring: Solve by factoring:

Question 42

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Factor, if possible, as the product of two first-degree polynomials with integer coefficients: :

Question 43

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

Question 44

Use the quadratic formula to solve the equation.
+ 10x + 15 = 0

A)
B)
C)
D)