# Math Final Exam Review

**Chapter 1
**Exponents:

**Radicals:**

**Polynomials:**

adding , subtracting, multiplying , dividing

factoring -- look for common factors first

three terms--trial and error

two terms --formula or common factor

** Rational expressions (fractions with polynomials):**

adding, subtracting, multiplying, dividing

Complex fractions (fraction over a fraction)

Rationalizing

**Chapter 2
Solving equations :**

linear

rational equations (fractions with variable in denominator)--either an answer

you can use, an answer you can’t use ( no solution ) or all real x except x =??

Applications

Solving quadratic equations-- ax^{2} + bx + c = 0

(1) solve by factoring

(2) solve by completing the square (do not have to)

(3) solve by quadratic formula

Imaginary numbers

Radical equations, absolute value equations, etc.

Inequalities, absolute value inequalities:

Inequalities using a sign chart

**Chapter 3
**distance formula:

midpoint formula:

circles: (x − h)^{2} + ( y − k )^{2} = r^{2}

Lines:

(1)

(2) y = mx + b

general form

Finding function values or expressions

Domain, range, increasing, decreasing...

Stretching, shifting, reflecting of graphs

piece-wise functions

Parabolas :

Standard form:

Quadratic form:

Vertex : or find average
of x-int.

plug in to find y

Add, subtract, multiply, divide two functions

Composition of functions f ○ g

**Chapter 4**

Directly proportional: y = kx

Inversely proportional:

Solving (graphing) inequalities using a sign chart

**Chapter 9
**Two equation/two unknowns

substitution/elmination

**Chapter 5
**Inverse functions

Exponential equation:

Properties:

Change of base formula:

b

Only formulas given :
Any 3D volume/surface area with the exception of a box. |

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