Deck 12: Appendix A: Basic Algebra Review

Question 1

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 - b = b - a

Answer 1

False

Question 2

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 - b) - c = a - (b - c)

Answer 2

False

Question 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 + b = b + a

Answer 3

True

Question 4

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 - b) - c = a - (b - c)

Question 5

Indicate True (T) or False (F) by each statement.

-Every real number is a natural number.

Question 6

Indicate True (T) or False (F) by each statement.

-An irrational number is not a real number.

Question 7

Indicate True (T) or False (F) by each statement.

-Every natural number is an integer.

Question 8

Indicate True (T) or False (F) by each statement.

-An integer is a rational number.

Question 9

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 10

Find the product:

-( 3x + 12y)( 5x + 8y)

A)
B)
C)
D)

Question 11

Find the product:

-

A)
B)
C)
D)

Question 12

Find the product:

--3( 10r + 2) + 5( 2r + 3)

A) 7r - 1
B) -36r
C) -20r + 9
D) -20r + 2

Question 13

Factor the GCF from the polynomial:

-

A)
B)
C)
D)

Question 14

Factor completely using grouping:

-18y² + 81y - 45

A) ( 18y - 9)(y + 5)
B) 9(2y + 1)(y - 5)
C) 9(2y - 1)(y + 5)
D) prime

Question 15

Factor by grouping:

Question 16

Factor the expression using integer coefficients:

Question 17

Which polynomial can be factored using integer coefficients? Find its factored form.

A)
B)
C)

Question 18

Factor using integer coefficients:

Question 19

Simplify the expression:

-

A)
B)
C)
D)

Question 20

Perform the indicated operation and reduce to lowest terms:

Question 21

Perform the indicated operation and reduce to lowest terms:

Question 22

Combine into a single fraction and simplify:

Question 23

Combine into a single fraction and simplify:

Question 24

Express as a simple fraction reduced to lowest terms:

Question 25

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

-

A)
B)
C)
D)

Question 26

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

-

A) -
B)
C)
D)

Question 27

Simplify and express using positive exponents:

Question 28

Simplify and express the answer using positive exponents:

Question 29

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

Question 30

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

Question 31

Write 7.214 × in standard notation.

Question 32

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 33

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

-

A)
B)
C) 3a²b⁴
D)

Question 34

Simplify and express using positive exponents:

Question 35

Change to simplest radical form:

Question 36

Simplify and express the answer using positive exponents only:

Question 37

Change to simplest radical form:

Question 38

Write in simplest radical form:

Question 39

Change to simplest radical form:

Question 40

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

-

A)
B)
C)
D)

Question 41

Use the square root property to solve the equation:

-(x + 3)² = 12

A)
B)
C)
D)

Question 42

Solve by factoring:

Question 43

Use the quadratic formula to solve the equation:

-x² + 18x + 71 = 0

A)
B)
C)
D)

Question 44

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

Question 45

The supply and demand equations for a certain product are and where p is the price in dollars. Find the price where supply equals demand.