Chapter 1.1 Sets of Numbers
1. Copy the section objective
2. Copy each of the bold faced number
categories in the boxes opposite page 1 and
write the definition of each category. Give 2
more examples of each category ( do not use
the ones in the book). You will be expected
to know all of these definitions.
Chapter 1.2 Field Axioms
1. Copy the section objective
2. Copy the field axioms from the blue
boxes on pages 4 and 5 and restate them in
your own words. For each axiom give an
example using real numbers.
3. Define field in your own words. (Be sure
you understand what closure means.)
4. Do the elements of a field have to be
numbers? Why?
5. Is the set of positive numbers a field?
Why or why not?
Chapter 1.3 Variables and Expressions
1. Copy the section objective
2. Design a “task” that would show whether
a person understands this objective
3. Copy the definition of variable on page
9, and restate it in your own words. Give an
example of a situation where you would use a
variable.
4. What is the domain of a variable? Give
an example.
5. Copy the definition of an expression on
page 10 and restate it in your own words.
Give an example of an expression.
6. What does evaluate the expression
mean?
Example1. Evaluate 2x2+4x-3 if x= -4
7. Copy the order of operations agreement
blue box from page 11.
Example 2. Carry out the following
operations
a. 2+6x3 b. 6+2x4÷3 c. 5-6x4÷3-7
8. Define absolute value of a number and
write the mathematical notation for it.
9. Define the absolute value of a variable.
Example 3. Evaluate 11 3x  4 if a.
x=6 b. x= -2
10. Describe what it means to simplify an
expression. Give an example of an
expression which can be simplifiedand
simplify it.
Example 4. Simplify 5x  4  (2x)
Example 5. Simplify
4  22x  6  3x  4
11. “A vinculum is a symbol of inclusion”

Explain. Give an example.
** The notes on pages 16-17 are important.
Chapter 
1.4 Polynomials
1. Copy the section objective
2. Define polynomial in your own words.
Give two examples of polynomials (not from
the book) and three examples of expressions
which are not polynomials for different
reasons.
3. Define term. Give 2 different examples
of terms and two examples of expressions
with more than one term..
4. Define degree of a polynomial. Give an
example of a 7th degree polynomial with no
single exponent equal to 7.
5. Give an example of a single term
expression with more than one variable and
degree 4
6. How is multiplying two binomials a
double use of the distributive property?
Explain in complete clear English sentences.
Example: Multiply (x-7)(3x+2)
Chapter 1.5 Equations
1. Write a section objective.
2. Explain how solving an equation can be
thought of as the reverse of evaluating an
expression.
3. What is a solution set? And what is the
math notation for a solution set?
Example 1: Solve 4x+7=39 and write the
solution set.
4. How do you verify that the solution set is
correct?
5. What is the proper notation for the
solution set of an equation which has no
solution?
6. What does it mean to say that 2 equations
are equivalent?
Example 2: Solve 3x+2 = 3x and write
the solution set in two different formats.
Example 3: Solve (2x-7)(x+6)=0 and write
the solution set.
Suppose the domain in example 3 were
x  int egers, what would the solution set
be?

Suppose the domain in example 3 were
xnaturalnumbers, what would the
solution set be?
Example 4: Solve x  3  7 and write the
solution set.
7. Copy the definition of extraneous
solution and restate in your own words.

Create an example of an extraneous solution
for an equation.
8. Copy the definition of irreversible step
in your own words. Create two examples for
equations; one where the irreversible step
creates an extraneous solution, and another
one where the irreversible step causes you to
lose a solution.
Chapter 1.6 Inequalities
1. Copy the section objective
2. Define inequality and restate in your own
words. Give two examples of inequality
statements.
Example 1: Graph the solution set of
2x+7>10
How would the graph be different if the
inequality was 2x+7≥10?
3.Copy the multiplication property of order
from page 28. Then write out the similar
property for x>y.
4.Explain (in complete sentences in English)
why you flip the inequality sign when you
multiply or divide by a negative number, but
you do not flip the inequality sign when you
add or subtract a negative number.
Example 2: Graph the solution set of –
3x≤12
Example 3: Graph the solution set of 4≤
3x+1<9
Example 4: Graph the solution set of
x  13
Example 5: Graph the solution set of
x  13
5. Copy 
the blue box on page 30.
Example 6: Graph the solution set of
2x  3  10 when the domain of x is

a. { real numbers}
b. {positive numbers}
c. {integers}

Chapter 1.7 Proofs of Properties
1. Copy the section objective
2. Copy each of the blue boxes on pages 33
and 34. For each one explain in your own
words(In complete sentences in English)
what the axiom means.
3. What does Q.E.D. stand for and how is it
used in mathematics?
4. Look up the words positive, inverse,
converse, and contrapositive with respect to
if…..then….. statements. (use either a
mathematical dictionary or the internet.).and
write the definition and an example for each.
Example 1: If you are sixteen then you go
to high school. Write the converse, inverse
and contrapositive of this statement.
5. When can you write a statement as if and
only if?
6. Write down the theorem proving
techniques from the blue box on page 37.
Example 2: Prove that if x=y then xz=yz.
Example 3: Prove that if 7+3x=16 then
x=3
Example 4: Prove that 5x+7=
(2x+3)+(3x+4)