1. Make time in your schedule to learn; you
cannot take shortcuts.
2. Read each section in your textbook and answer the questions in the
study
guide before you go to class.
3. Take notes in class, trying to understand as the teacher presents
examples and explains concepts.
4. Do your homework (It should be easier after the previous two steps).
Make sure to understand what you are doing and be able to solve each
problem completely and correctly by yourself.
5. Carry on a conversation with yourself as you work, asking as you
start
each problem, “What is this? What is my goal? What should my answer look
like when I am done?” Then, as you work a problem ask, “What property
al lows me to take this step?” And at the end, “ Does my answer make
sense?
How can I check it?”
6. Maintain a great attitude about learning Algebra; people who have a
good
attitude find it easier to learn, and those who learn algebra well
usually
enjoy it.
7. Go to the lab or your instructor’s office and get help when you need
it. |
Section 2.1 Writing and evaluating Algebraic Expressions
Read section 2.1, pages 62 – 67 and answer the following questions as you
read:
1. What are symbols used to represent in Algebra?
2. What is an algebraic expression? Give two examples of algebraic
expressions different from the examples in the book.
3. Complete the table by identifying the terms of the expressions .
| Expression |
How many
terms? |
List the terms separated by
commas. |
 |
4. Identify the coefficients of the following terms.
5.
a. Write 
as repeated multiplication.
b. Write 
as repeated multiplication.
c. Write 
as repeated multiplication.
d. Write 
as repeated multiplication.
d. Write 
as repeated multiplication.
e. Write
as repeated multiplication.
f. Write 
as repeated multiplication.
6. What does it mean to evaluate an expression?
For each of the following, show your work neatly.
7. Evaluate the expression in example 5 e when y=-2.
8. Evaluate the expression in example 6 d when x=5 and y=2.
9. Evaluate the expression in 7a when x=5, y=2 and z=-3.
10. Example 8, which is about __________________, if the
table
included one more x -value, what would it be? What is the value of
5x+2 for this x?
Section 2.2 Simplifying Algebraic Expressions
Read section 2.2, pages 71 – 79 and answer the following questions as you
read:
1. Make three note cards, one for each rule of exponent on page 71. Be
sure to include on each note card a verbal description of the
expression to be simplified and at least two examples.
2. Simplify each of the following expressions, if possible. If it is not
possible, explain why.
3. If you made note cards in chapter 1 for each of the
properties, get
them out and add an algebraic example to each one. If you did not
make cards in chapter 1, make one now for each property. You should
have nine cards when you are done. Be sure to include a way to
remember each property.
4. Use the Distributive property to rewrite the following expressions.
a. 3(x-7)
b. –3(x-7)
c. –3x(x-7)
5. Draw an area model (like those in example 5) for the multiplication
3a(2a+b).
6. What is the definition of like terms?
7. Identify the like terms in each of the following expressions by
underlining terms that are like. If other terms are also like terms,
double under line them .
Example:
8. Combine like terms in the last problem.
a.
b.
9. Simplify each expression.
10. What number must we multiply by
to get x? (Hint: look at example
10a.) What property are we using?
11. Example 11 talks about symbols of grouping. List all grouping symbols
you know of.
12.To simplify an algebraic expression means to remove symbols of
grouping and combine like terms. Simplify the following expressions.
Section 2.3 Algebra and Problem Solving
Read section 2.3, pages 85 – 95 and answer the following questions as you
read:
1. What is algebra?
2. How do you tell an equation from an expression?
3. You are participating in a fundraiser where your
employer pays $2 for
each mile you run and $1.50 for each mile you bike ride for a week,
write an expression that represents the total amount of money your
employer will pay the charity. (Declare variables and write a verbal
model first.)
4. Write the ope ration indicated by each of the following words:
a. Sum
b. Product
c. Difference
5. Translate the phrases into algebraic expressions:
a. The sum of 12 and a number
b. The product of a number and 5
c. 5 less than a number
d. A number less than 5
e. 10 less than the product of 3 and a number
6. Write a verbal description for each of the following algebraic
expressions:
a. 2x+4
b. 2(x+4)
7. In example 6a give a verbal description of the ‘value of nickel’
multiplied by ‘number of nickels’. That is, after the multiplication, how
can you describe the meaning of the quantity?
8. If you drive 60 miles per hour for three hours, how far
have you gone? If
you travel r miles per hour for t hours, write an expression for how far you
have gone?
Section 2.4 Introduction to Equations
Read section 2.4, pages 99 - 104 and answer the following questions as you
read:
1. What is an equation?
2. What does it mean to solve an equation?
3. What is an identity?
4. What is a conditional equation?
5. State whether each of the following is an expression, an identity, or a
conditional equation and state how you know.
a. 2x+4=2(x+2)
b. 8-3x+4(x-7)
c. x-7=3
6.
a. Determine whether 3 is a solution to the equation x - 5 = -2
b. Determine whether –3 is a solution to -4(4-x)=4
7. What are equivalent equations ?
8. List the four ways an equation can be transformed into an equivalent
equation.
9. To solve each of the following equations, state your goal, state the
step you are going to take and why you are going to take it. Then solve
the equation
Example:
x+4=2
My goal is to get x on one side of the equation by itself.
I am going to subtract 4 from each side since 4 is being
added to x.
X+4-4=2-4
X=-2
a. x-3=-5
b. 2x=5
c. x/3=15
10. Write a verbal model for each of the problems.
a. The sale price of a football is $15. The sale price is $4 less
than the original price. What is the original price?
b. The original price of a shirt is $45. The original price is marked
down by $12. What is the sale price?
Chapter 2 Review
1. What is different about solving equations and simplifying expressions?
2. What properties can you use to solve equations that you cannot use to
simplify expressions?
3. What topics in chapter 2 are still confusing to you? (you may list
problems you do not understand.)
