Topic

Helpful Information

Example

Absolute Value

Absolute value = the distance a number is from 0 on a number line

The absolute value of 5 and -5 equals 5 because they are both 5 units from 0

Axiom-Additive axiom

If a > b, then a + c > b + c.

Axiom-Positive multiplication axiom:

If c > 0, then a > b

if, and only if, ac > bc.

Axiom-Transitive axiom

If a > b and b > c, then a > c

Binomials-Multiplying two binomials

Formula =

(a+b) (c+d) =ac + ad + bc + bd

Use the FOIL method

First Outside Inside Last

(b+2) ( b +3)

F b*b = b²

O b*3 = 3b

I 2*b =2b

L 3*2 =6 Combine: b² + 5b +6

Combining like terms

In order to combine they must have like variables and exponents.

1. Place like terms together.

2.Combine each set

3. Put the answers to each combine set together

2a + 4b + 5a – 2b - 2c + 4c

Step 1.2a + 5a +4b – 2b -2c + 4c
Step 2. 2a + 5a= 7a

4b -2b =2b

4c -2c =2c
Step 3. Combine 7a + 2b + 2c

Equations-Linear equations

Slope-intercept form y = mx +b
Standard form ax + by =c

Y = 3x + 9 where m=3 and b=9

4x + y = 20, a=4 and b=1 and c = 20

Equations-Solving Equations

Step 1 All variables can be moved to the left of the equal sign and the numbers can be on the right.

Move integers by adding the opposite sign of the integer.

Step 2. Divide both sides by the coefficient.

Step 1. 2b + 3 =7
-3 -3
Step 2 2b = 4
b =2

Equations-Solving literal equations

Step 1 The desired variable should be on the left
Place all other variables on the right of the equal
sign by adding opposites
Step 2 Divide both sides by the value of any other variable on the left to “isolate” the desired variable.

Solve for a
x = aw
aw =x
a =x/w

Equations-Writing Equations

Look for key words, for example “the product of” means you should place the constant before a variable “less than” and “ more than” means you should flip the order Substitute equal when you see “is” If there are not any key words create an equation in the order that the words are written.

The product of 5 and x is 14

5x = 14
y more than three is 15

3 + y =15
Ten less than x is 5

x - 10 = 5
The sum of 11 and y is 13

11 + y =13

Exponents

And Rules for Exponents

Exponents tell you how many times to use the number in multiplication

The Rules

x^m * xⁿ = x^(m+n)

(xⁿ)^m = x^(nm)

(xy)^m = x^my^m

3^2 = 3*3 =9

3^3 = 3*3*3= 27

3^4 = 3*3*3*3 = 81

2² * 2³ = 2⁽²⁺³⁾ = 2⁵

(2³)² = 2^(2*3) = 2⁶

(2*3)³ = 2³*3³ = 8*27 = 216

Exponents-Negative exponents

Move the term to the denominator, make the exponent positive then apply the power.

3^-2 = 1/3*3 = 1/9

3^-3 = 1/3*3*3= 1/27