Percent of problems which could have fractional coefficients 0 5 10 20 30 40 50 60 70 80 90 100 (Only where applicable)

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(Random) Review

a. Using Formulas: Slope/Distance/Midpoint
b. Graphing Parabolas
c. Parallel and Perpendicular Lines
d. Solving Linear Equations
e. Solving Quadratic Equations

A (Random) Functions and Relations

a. Identifying Functions
b. Identifying Domain/Range
c. Finding the Composition
d. Finding the Inverse
e. Identifying Transformations of Functions
f. Graphing Functions through Transformations
g. Writing Transformed Functions
h. Reading Graphs for Word Problems
i. Graphing Word Problems

B (Random) Polynomial and Rational Functions

a. Using the Rational Roots Theorem
b. Using Descartes's Rule of Signs
c. Finding Zeros of Polynomials
d. Determining Odd/Even Functions
e. Finding Vertical Asymptotes of Rational Functions
f. Finding Horizontal Asymptotes of Rational Functions
g. Finding Slant Asymptotes of Rational Functions
h. Writing Rational Functions from Graphs
i. Graphing Rational Functions
j. Creating Test Intervals of Rational Functions
k. Solving a System of Equations with Matrices
l. Graphing Linear Inequalities
m. Determining Symmetries of Functions

C (Random) More With Functions

a. Solving Nonlinear Systems of Equations using Linear Combination
b. Solving Nonlinear Systems of Equations using Substitution
c. Solving Nonlinear Systems of Equations using Graphing
d. Decompose Rational Expressions into Partial Fractions
e. Finding the n^th Term of a Binomial Expansion (Pascal's Triangle)
f. Finding the n^th Term of a Binomial Expansion (Combinatorics)
g. Expanding Binomials

D (Random) Exponential and Logarithmic Functions

a. Finding Asymptotes of Exponential and Logarithmic Functions
b. Finding Domain/Range of Exponential and Logarithmic Functions
c. Graphing Exponential Functions
d. Graphing Logarithmic Functions
e. Changing from Logarithmic to Exponential Form
f. Changing from Exponential to Logarithmic Form
g. Expanding Logarithmic Expressions
h. Contracting Logarithmic Expressions
i. Solving Equations with Logs
j. Solving Equations With Logs (More Complicated)
k. Exponential Word Problems
l. Solving Exponential Equations with Different Bases
m. Solving Exponential Equations Using Substitution
n. Using Change of Base Formula

E (Random) Sequences and Series

a. Writing the first n terms of an Arithmetic Sequence
b. Finding the n^th term formula for an Arithmetic Sequence
c. Evaluating Summations of Arithmetic Series (Number Arches Video)
d. Writing the first n terms of a Geometric Sequence
e. Finding the n^th term formula for a Geometric Sequence
f. Evaluating Finite Summations of Geometric Series
g. Evaluating Infinite Summations of Geometric Series

F (Random) Induction and Recursion

a. Writing Terms from Recursion form
b. Finding Recursive Formulas
c. Using Induction in Proofs
d. Finding Polynomial Formulas for a Finite Sequence

G (Random) Preparation for Calculus

a. Finding Limits from Graphs
b. Finding Limits Algebraically
c. Finding Limits Numerically (Using a Calculator)
d. Describing End Behavior as Limits
e. Finding Points of Discontinuity (Graphs)
f. Finding Points of Discontinuity (Expressions)
g. Calculating Average Rate of Change
h. Calculating Instantaneous Rate of Change
i. Finding Limits of Sequences
j. Writing a composite function as the Composition of 2 Functions
k. Fixing [f(x+h)-f(x)]/h for Polynomials
l. Fixing [f(x+h)-f(x)]/h for Rationals
m. Fixing [f(x+h)-f(x)]/h for Radicals
n. Applying Intermediate Value Theorem to find Zeros

H (Random) The Derivative

a. Finding the Limit of (f(x+h) - f(x))/h for a Polynomial
b. Finding the Derivative of a Polynomial
c. Finding the Limit of (f(x+h) - f(x))/h for a Radical
d. Finding the Derivative of a Radical
e. Finding the Limit of (f(x+h) - f(x))/h for a Rational
f. Finding the Derivative of a simple Rational
g. Finding the Derivative of a Polynomial at a point
h. Finding points where the Tangent Line is Horizontal (Polynomials)

I (Random) Triangular and Circular Trigonometric Functions

a. Finding Trigonometric Functions in a Triangle
b. Finding Trigonometric Functions of an Angle
c. Draw an angle in Standard Position
d. Find the Reference Angle
e. Given a Trigonometric Function, find all others
f. Find Coterminal Angles
g. Converting from Radians to Degrees
h. Converting from Degrees to Radians
i. Converting with Degrees, Minutes, and Seconds

j. Angle Of Elevation/Depression Word Problems
k. Finding Area of an Isosceles Triangle
l. Finding Trigonometric Functions given coordinates on the Terminal side of an angle in Standard Position
m. Finding Trigonometric Functions given coordinates on a Unit Circle
n. Finding Trigonometric Functions of Special Angles (Degrees)
o. Finding Trigonometric Functions of Special Angles (Radians)
p. Applying the Unit Circle to find Domain/Range Even/Odd Period
q. Relationships Between Trig Functions
r. Finding Arc Length
s. Finding Linear Speed & Angular Velocity
t. Linear Speed and Angular Velocity Word Problems

J (Random) Solving Triangles

a. Solve Right Triangles
b. Finding the Number of Solutions in A.S.S. Case
c. Using Law of Sines
d. Using Law of Cosines
e. Finding Area using Sine
f. Finding Area using Heron's Formula
g. Word Problems

K (Random) Trigonometric Identities, Equations and Inverses

a. Using Reciprocal Identities
b. Using Pythagorean Identities
c. Using Quotient Identities
d. Using Sum and Difference Formulas
e. Using Double Angle Formulas
f. Using Half Angle Formulas
g. Solving Trigonometric Equations with Restricted Domains
h. Solving Trigonometric Equations with Infinite Solutions
i. Finding Domain and Range of Trig and Inverse Trig Functions
j. Using Inverse Functions
k. Using Inverse Functions with Variables
l. Solving Trigonometric Inequalities involving Sin/Cos/Tan

L (Random) Proving Trigonometric Identities

a. Simplifying Pythagorean Identities
b. Proving Pythagorean Identities
c. Simplifying Basic Trigonometric Identities
d. Proving Basic Trigonometric Identities
e. Simplifying Harder Basic Trigonometric Identities
f. Proving Harder Basic Trigonometric Identities
g. Simplifying Identities involving CoFunction and Even/Odd
h. Proving Identities involving CoFunction and Even/Odd
i. Proving Identities involving Sum/Difference Formulas
j. Proving Identities involving Double/Half Angle Formulas

M (Random) Graphs of Trigonometric Functions and Inverses

a. Basic Facts and Graphs of parent Trigonometric Functions
b. Determining Amplitude in Graph and Equation
c. Writing Equations of Amplitude and Vertical Stretch Changes
d. Sketching Graphs with Amplitude Changes, Vertical Stretches, and Vertical Flips
e. Determining Period in Graph and Equation
f. Writing Equations of Period Changes
g. Sketching Graphs with Period Changes
h. Determining Phase Shift in Graph and Equation
i. Writing Equations of Phase Shift Changes
j. Sketching Graphs with Phase Shift Changes
k. Determining Vertical Shift in Graph and Equation
l. Writing Equations of Vertical Shift Changes
m. Sketching Graphs with Vertical Shift Changes
n. Sketch the Graph of a Trigonometric Function
o. Writing Equations of Trigonometric Functions From Graphs
p. Graphing Cos/Sin by Chart
q. Graphing Sec/Csc by Chart
r. Graphing Tan/Cot by Chart
s. Finding key values in Compound Trigonometric Functions
t. Inverse Trigonometric Functions
u. Using the Chart-- finding phase shift, period, vertical asymptotes, and domains
v. Using the Chart-- finding vertical shift, amplitude, vertical stretch, and ranges

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