This study guide provides an overview of topics that will be covered on an upcoming math test, including: [1] writing expressions, [2] evaluating expressions, [3] solving algebra equations, [4] writing formulas from patterns, and [5] writing two-step expressions. It defines key terms like variables, coefficients, expressions, and equations. It also provides examples and explanations for how to work through different types of algebra problems that may appear on the test.

1. Name __________________________________________ Date ____________
Polizzi/Woska Math – 6
Study Guide Math Test
ALGEBRA
***Extra Review at mrpolizzi.wikispaces.com
* Do not limit yourself to using only this study guide to prepare for the test. You also need to review
your homework book, your notes, the materials provided in class, as well as remembering class
discussions.
Topics on Test:
1. Writing expressions
2. Evaluating expressions
3. Solving Algebra equations
4. Writing formulas from patterns
5. Writing 2 step expressions
variable – a quantity that you can change; you can use a letter to represent a number
Ex: 4 + x (x is the variable)
coefficient – the number that appears before the variable
Ex: 3n (3 is the coefficient; n is the variable)
expression – a mathematical phrase that has variables and operation signs but no equal sign
Ex: 9 – r
equation – a mathematical sentence with an equal sign and an answer
Ex: 3n = 9
Common Words or Phrases
Addition Subtraction
plus, combined, added to, and, minus, difference, less than,
greater than, more than, total, fewer than, take away, decreased by
increased by, sum
Multiplication Division
times, product, double, multiply, quotient of, half of, goes into, per,
factor, of out of
 Writing an expression

2. -You are ordering clothes online. The total cost is $43. You must pay shipping costs to have the
clothes delivered.
shipping expression
Overnight shipping is $12 43 + 12
3 day shipping is $7 43 + 7
Standard shipping is $3 43 + 3
If you don’t know which you will choose, you simply write 43 + x
-You go grocery shopping and spend $105. The cashier will randomly give you a coupon that can have
one of three values.
coupon expression
$10 off $105 - $10
$5 off $105 - $5
$1 off $105 - $1
Since you don’t know which coupon you will get, your expression will be $105 - c
-Your family is going to the movies. Adult tickets cost $9.
amount of adults expression
3 adults 9(3)
5 adults 9(5)
x adults 9x
-You and your friends are going out to eat. Your group is 5 people including yourself. Write an
expression that will show how much each person pays.
amount of people expression
Bill is $30 30  5
Bill is $50 50  5
Bill is x x5
 Evaluating expressions

3. Evaluate an algebraic expression by replacing the variable in the expression with its numerical value and solve.
Remember 5y is the same as 5 times y (multiplication).
Example: 3t – 4 for t = 9 Evaluate: 4 (y + 6) for y = 2
3x9–4
27 – 4
23 You should have gotten: 32
*Remember to use the order of operations when you solve the expression.
x = 3:
x+5 12 – x 4x
3 + 5 __8__ 12 – 3 __9__ 4(3) __12__
 Solving addition equations
To solve, find the value of the variable that makes it balance and subtract it from both sides of the
equation.
Example: x + 4 = 11 Try it: y + 3 = 14
x + 4 - 4 = 11 – 4
x=7 You should have gotten: 11
*Remember to subtract the same number from both sides!
 Solving subtraction equations
To solve, find the value of the variable that makes it balance and add it to both sides of the equation.
Example: b – 16 = 4 Try it: w – 9 = 35
b – 16 + 16 = 4 + 16
b = 20 You should have gotten: 44
*Remember to add the same number to both sides!
 Solving multiplication equations

4. To solve, find the value of the variable that makes it balance and divide both sides by that value.
Example: 4x = 12 Try it: 6h = 24
4x ÷ 4 = 12 ÷ 4
x=3
check: 4(3) = 12 You should have gotten: 4
12 = 12
 Solving division equations
To solve, find the value of the variable that makes it balance and multiply both sides by that value.
Example: r9=4 Try it: a ÷ 6 = 42
r÷9x9=4x9
r = 36
check: 36 ÷ 9 = 4 You should have gotten: 252
4 =4
 Writing formulas from patterns
x Answer
1 3
2 6
3 9
4 12
Formula: 3x = Answer
 Writing 2 step expressions
7 more than the product of a number f and 39
Equation: 39f + 7
8 less than a number m times 22
Equation: 22m – 8
Lauren took her car for repairs. The mechanic who worked on the car charged $40 per hour of labor.
Lauren is also responsible for the cost of the required parts. The parts of her car costs $430. If H
represents the amount of hours the mechanic worked on the car, write an algebraic equation to
represent Lauren’s car repair costs.
Equation: $40H + 430