Algebra
Substituting values
Evaluate algebraic expressions
If x
 
3 , find the value of x
2 x


1
1
If x
 
2 , find the value of
 x

3

2 
4 x
If x

2 , y
 
1 , and z
 
2 find the value of
3 x
2 z
2 y
3

1.
Parenthesis
2.
Exponents
3.
Multiplication and Division, left to right
4.
Addition and Subtraction, left to right
54

6
2 
4

6

3 ( 1

5 )
2 
4
2
10

6
5

3

4

7

2

Linear Equations
Equation – statement that two expressions are equal
Solve – find variable value(s) that make stmt true
Solution set – set of the values that make it true x
 x
2 
1 x
2 
1

0
Equivalent – two stmts with same solution set
Contradiction – equation with no solution set x

2
 x
Identity – equation with infinite solution set x
 x

2 x
A linear equation in one variable is an equation that can be written in the form ax
 b

0 , a , b
 
, a

0
(an equation that is not linear is called non-linear)
Addition property a
 b
 a
 c
 b
 c
Multiplication property a
 b
 ac
 bc

3 x

3

9
3
 x

4
 
2 x

1
3

2 x

5
 
10
  x

5

7

6 x

2

3 x

1

2

5
 x
 
25

3
 x

5
 
5 x

1. Familiarize yourself with the problem
Read problem Analyze situation
List given info and question to answer
Do we need a formula?
Sketch Chart Field a guess
2. Translate to Math - write the equation
Identify quantities
Label quantities
Model - write the equation
3. Do the math
4. State the answer
5. Check your work

Four students about to purchase concert tickets for $18.50 each, discover that they can purchase
5 tickets for $80. How much would each person save if they found a fifth person, and split the cost?
A $200 CD player is on sale for 20% off. What is the cost of the CD player?
Sarah purchases a camera for $90 on a 25% off sale. What is the normal price of the camera?
You take your family to a fancy restaurant, and receive a bill for $38. You decide to leave a
15% tip. How much is the tip?

Fractions and Rational Expressions
Write
38
7
as a mixed number.
Write
1
2

+,-,*,/ Fractions (LCD), Decimals, percent
2
3
3
4

4
5
5
6

How many yards of material from a 24-yard cloth remain after 3 pieces, each and 5 pieces, each

Averages
Mean, median, mode 8, 7, 3, 2, 7, 5, 2
You have taken 3 of 4 tests in your math course, and received 84, 72, and 75. How much must you score in your 4 th test to get a B in math?
An airplane flew for 8 hours at an airspeed of x mph, and for 7 more hours at 325 mph. The average airspeed was 350 mph. Solve for x .

Slope of a line; y
 mx
 b
Find the slope of the line 2 x

3 y

6 m

 y
 x
 y
2 x
2

 y
1 x
1
 x
1
 x
2

Find the slope of a line from the point the point

5 ,

1

.
 
3 , 7

to m
 y x

 y
1 x
1
Find the equation of a line from the point to the point

5 ,

1

.
 
3 , 7


Setting up equations linear modeling, y
 mx
 b
To model a quantity that is changing at a fixed rate, with a linear function f , f ( x )=(const rate of chg) x + (initial value)
A 100 gallon tank is initially full of water and being drained at 5 gallons per minute.
A driver of a car is initially in Wichita KS, 545 miles from home, traveling toward home on
I-35 at 70 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours.

direct variation, ratios, similar triangles
If you can buy 3 bottles of a sports drink for $7, how much will 12 bottles cost?
The cost of tuition is directly proportional to the number of credits taken. If 11 credits cost
$720.50, find the cost of taking 16 credits.
A person 6 feet tall stands 50 feet from a street lamp. If the person casts a shadow 10 feet long, how tall is the street lamp?

Linear equations/two variables
Solve 2x2 systems of equations
3 x
 y

8 x

2 y

5
2 x

3 x
 y y


3

8
In one day, Glovers, Inc., sold 20 pairs of gloves. Cloth gloves sold for $24.95 per pair, while pigskin gloves sold for $37.50 per pair.
The company took in $687.25. How many of each pair were sold?

Exponents, square roots, and scientific notation
Exponents as shorthand for multiplication
3

3 3
2
3

3

3
3

3

3

3
Square Roots
3
3
3
4
9
25
81
4 81

Exponents and radicals exponent manipulation
Product Rule: a m  a n  a
Quotient Rule: a m a n
 a
Neg Exponent Rule: a
 m 
1 a m
, a

0
Zero Exponent Rule: a
0 
1

   n
Power Rules:




  a b m m
 
2 
 a m
 n
 a m b m
 a m b m
   


10 x
3 y
5
5 x
4 y
2
 x

6  x
4 z
2 z

3



Scientific Notation
A real number r is in scientific notation when r is written as c

10 n
, where 1
 c

10 and n is an integer.
Dist to sun = 93,000,000
Pop of world in 2050 = 9,000,000,000
Mass of the earth – 5 .
98

10
24 kg

3 .
1

10
6

5 .
6

10

4



6

10
3
4

10
6



1 .
2

10
2

The solar wind carries particles from the sun at about 2 .
4

10
7 meters per minute. The distance from the sun to the earth is about 1 .
5

10
11 meters. How long does it take for a particle to travel from the sun to the earth?

Basic operations/polynomials
Add, sub, mult, div algebraic expressions
3 a

4 b
 
6 a

3 b
 

4 x
2 
6
 
3 x
2 
5 x

3

   x

4
 

3 x

4
  x
2 
2 x

1

 x
2  x
2 x

12

3


Factoring polynomials

FOIL x
2 
2

2 x
2 
3



3 x

2

3 x

2
 

3 x

2

2 
 x
 a
 x
 b
 

x
2
Factor quadratics x
2 
5 x

6

 x

20

4 x
2 
12 x

16
 x
2 
10 xy

25 y
2  x
2 
16


Solve quadratic equations x
2 
7 x

6

0 x
2 
4

5 x

Rational expressions
2 x
3

4
 x x


2
2

2 x

4
 x
2 x

3

9 x

20

2 x
4

1

5
3 x


Solve rational equations
Solve for x :
9
6
 x
8
3 x

6
3 x

1 x x

2

1 x x
1

3
 x
1

3
 x
2
6

9