1. Arithmetic, Exponents, Equations and Inequalities
Math concepts
Arithmetic, Exponents, Equations and Inequalities

2. Absolute Values
For any number a, exactly one of the following is true:
A is negative
A = 0
A is positive
The absolute value of a number is the distance between a and 0 on the number line so the answer is always POSITIVE
Two unequal numbers that have the same absolute value are called opposites
The only number that is equal to its opposite is 0

3. Exponents For any number b:
b1 = b
bn = b ×b ×b … ×b, where b is used as a factor n times
For any numbers b and c and positive integers m and n:
bm bn = bn+m
bm / bn = bm-n
(bm )n = bmn
bmcm =(bc)m

4. Square Roots
√ab = √a x √b
√(a-b) = √a ÷ √b

5. PEMDAS Pemdas: Please Excuse My Dear Aunt Sally
When a calculation requires performing more than one operation, carry them out in the correct order.
Parentheses
Exponents
Multiplication and Division:
Do all multiplications and divisions in order from left to right – do not multiply first then divide
Addition and Subtraction:
Do all additions and subtractions in order from left to right – do not add first then subtract

6. Six Steps to Equations and Inequalities
**Note: If you start with an inequality and in step 6 you divide by a negative number, remember to reverse the inequality

7. Inequalities
Adding a number to an inequality or subtracting a number from an inequality preserves it.
If a < b, then a + c < b + c
Adding inequalities in the same direction preserves them.
If a < b and c < d, then a + c < b + d

8. Inequalities
Multiplying or dividing an inequality by a positive number preserves it
If a < b, and c is positive, then ac < bc and (a/c) < (b/c)
Multiplying or dividing an inequality by a negative number reverses it.
If a < b and c is negative then ac > bc and (a/c) > (b/c)

9. Inequalities Taking negatives reverses an inequality
If a < b, then –a > -b and if a > b, then –a < -b
If two numbers are each positive or negative then taking the reciprocals reverses an inequality
If a and b are both positive or both negative and a < b, then (1/a) > (1/b)

10. Lets Practice
Complete the problems from the worksheet (Click Next Page to view the worksheet)