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-- ax² + 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 = r²

Lines:

equations of 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:

Logarithmic equation :

Properties:

Change of base formula:

b