Research Guides: Academic Coaching: Handouts

Helpful Handouts

General Algebra Concepts

Algebra Cheat Sheet
A variety of formulas used for College Algebra
Mathematics Properties
A quick cheat-sheet for mathematical properties and what they mean
Integer Rules
Adding, Subtracting, Multiplying and Dividing Integers
Integer Rules Reloaded
Adding, Subtracting, Multiplying and Dividing Integers
Divisibility Rules
Quick rules to help you divide quickly and effectively
Fraction Rules
The rules for adding, subtracting, multiplying, and dividing fractions
Geometry Formulas
Formulas used in geometry, including perimeter, area, surface area, and volume
Variations
Direct and inverse variations
Set Notation, Interval Notation and Inequalities
How to express a solution to a graph or equation using set notation, interval notation, or inequalities

Lines and Graphs

Linear Equations
A list of the different types of linear equations and explanations on when to use them
Linear Equations part 2
How to generate the equation of a line and which equation to use
Graphs of Parent Functions
The shapes that various functions form
Transformation of graphs
Starting with a parent function, graph a new function by shifting, stretching, compressing and reflecting

Solving systems of equations

Solving systems of equations
Learn how to solve systems of equations by graphing, substitution or elimination methods.
Solving systems of Equations using Matrices
Learn how to use matrix operations to solve systems of equations.

Factoring and Solving Quadratic Equations

Factoring Polynomials - special cases
How to factor special polynomials such as sum and difference of cubes, sum and difference of squares, and perfect square trinomials
Factoring Methods - Trinomials
Several different methods for factoring trinomials
Completing the Square
How to use the "completing the square" method for quadratic formulas
Solving quadratic equations
How to solve quadratic equations using complete the square, factoring, or the quadratic formula

Rational Expressions and Equations

Simplifying Rational Expressions
How to simplify rational expressions
Asymptotes
How to find vertical, horizontal and oblique asymptotes
Graphing a Rational Equation
Steps to graph a rational equation
Rational and Polynomial Inequalities
Learn how to solve rational and polynomial inequalities using a chart and number line.

Functions

Finding Inverses of Functions
This worksheet walks you through the process to find an inverse a function.
Synthetic Division
This worksheet will show you how to use synthetic division to find a zero or to find a remainder.
Rational Roots Theorem
Learn how to tell how many real roots are possible from a given polynomial.
Law of Signs
Learn how to use Descartes' Law of Signs to determine how many positive or negative real roots a polynomial might have.
Find Bounds on Polynomial Roots
This handout will tell you how to find upper and lower bounds to the roots of a polynomial equation.
Finding Zeros of a Function
Utilize all of the tools available to you to find zeros of a function.
Finding the Domain
Learn how to find the domain of any equation.
Functions- Even, Odd, Neither
How to tell if a function is even, odd, or neither
Symmetry of Functions
How to determine if an equation or a graph has x-axis symmetry, y-axis symmetry or symmetry about the origin

Exponents, Radicals and Logs

Laws of Exponents and Radicals
Table of formulas to simplify exponential and fractional exponential expressions
Logarithm Rules
All the rules for logarithms
Solving Exponential and Logarithmic Equations
Use rules for and properties of exponents and logarithms to solve equations containing them

Word Problems

Understanding Word Problems
Key words to look for in understanding word problems
Mixture Word Problems
Learn how to interpret and solve word problems involving percents or money.
Work Flow Word Problems
Learn how to solve word problems that involve people working together to complete a job.
Uniform Motion Word Problems
Learn how to interpret and solve word problems that involve d=r*t.
Word Problem - Ballistics
How to work word problems that involve ballistic motion (parabolic).

PreCalculus Facts and Formulas sheet
A list of commonly used formulas and concepts for Precalculus. This is NOT a complete list of all precalculus concepts but is a handy starter reference.
Conics
Equations for parabolas, circles, ellipses and hyperbolas.
Symmetry in Polar Coordinates
Symmetry using the polar form of an equation

We are currently building additional content for this subject, but until we have specific documents, you can find many handouts that apply to Precalculus in our Algebra and Trigonometry tabs:

Algebra Tab
- Linear Equation Information
- Generating Equations of a line
- Variation functions
- Rational and Polynomial inequalities
- Factoring
- Complete the Square
- Solving Quadratic Equations
- Transformation of Graphs
- Symmetry of Functions
- Synthetic Division
- Rational Roots Theorem
- Descarte's Rule of Signs
- Asymptotes
- Graphing a Rational Function
- Finding Inverses of Functions
- Laws of Exponents and Radicals
- Solving Exponential Functions
- Logarithm Rules
- Solving Logarithmic Functions
- Solving Systems of Equations
- Matrices

Trigonometry Tab
- Graphs of Trigonometric and Inverse Trigonometric Functions
- Transformation of Trigonometric Functions
- Trigonometric Identities and More sheet
- Law of Sines Ambiguous Case

Finite Tab
- Permutations
- Combinations

Trigonometry Cheat Sheet
Definitions, formulas, properties, and identies
Unit Circle
Unit circle diagram
Trigonometric and Inverse Trigonometric Functions
Graphs of trigonometric and inverse trigonometric functions
Trigonometric Transformations
Displays the process to graph a trigonometric function using graph transformations.
Conics
Summary of the types of Conics and their equations.
Law of Sines - Ambiguous Case
When using the law of Sines to solve a triangle, there are 3 possible outcomes. This document discusses the process.

Finite Math Cheat Sheet - F1
This document contains many useful formulae and explanation on their usage in finite math applications.
Inverse of a 2x2 Matrix - F2a
How to find the inverse of a 2x2 matrix.
Inverse of a Square Matrix (Determinant Method) - F2b
The process to find the inverse of a square matrix using determinants.
Input Output - F3
Future Value Problems - F4
Calculate n for future value problem
Permutation Examples - F5
Probability of an event when order matters
Combination Examples - F6
Probability of an event when order does NOT matter
Baye's Theorem Example - F7
Probability Examples - F8
More examples of permutations and combinations and explanations
Maximization using Simplex Method - F9
Displays how to solve a maximization problem using the Simplex Method.
Mean, Variance, Standard Deviation - Grouped Data - F11
Mean, Variance, Standard Deviation - Grouped Data
Determinant of a 2x2 Matrix and 2x2 Cramer's rule - 15a
This handout first describes how to find the determinant of a 2x2 matrix and then explains how to solve a system of two equations in 2 variables to using Cramer's rule. Cramer's rule uses matrices and determinants to solve systems of equations that have the same number of variables as equations.
Determinant of a 3x3 Matrix - 15b
This document illustrates two methods used to find the Determinant of a 3x3 or larger square matrix.
Solve a system of 3 equations in 3 variables using Cramer's rule - 15c
Cramer's rule is a method that can be used to solve a system of equations with the same number of variables as equations using matrices and determinants. This handout explains the process using a 3x3 matrix.
Table Method (into to Simplex) - F16
This document explains the Table Method which is used to maximize or minimize a variable
Build an Amortization Schedule - F17
Learn how to build an Amortization Schedule.
Yearly Interest Paid on an Amortized Loan - F18
Learn how to calculate how much interest one has paid on an Amortized loan.

Calculus Cheat Sheet - Limits
Limits and evaluation techniques
Calculus Cheat Sheet - Derivatives
Derivatives formulas and variants
Calculus Cheat Sheet - Integrals
Definitions and techniques for integrals
Common Derivatives & Integrals
Properties/rules/formulas for derivatives and integrals
Find the equation of a tangent line
This document explains the process of finding an equation of a line that is tangent to a function at a point using the slope.
Series Convergence/Divergence
Rewrite Integrands
Different ways to rewrite your equation to make integration easier
Continuity and Differentiability of Functions
This document explains continuity and differentiability of a function and shows graphically what these terms mean.
What can the first and second derivatives tell us about a function?
This document summarizes the properties of a function based upon the function itself and the first and second derivatives of the function.
Curve Sketching Techniques
This document explains how to use the function and its first and second derivatives in order to sketch the function.

We hope to add some great resources to this page soon!

Statistical Functions on TI-83-84 - S1
Frequently used statistics functions on the TI83/84 and how to use them.
Building a Frequency Distribution Table - S2
Process to build a frequency Distribution Table from a set of data elements
Mean, Variance, Standard Deviation - Frequency Distribution - S3

Graphing Equations in your Calculator
Instructions on graphing an equation in a TI83/84 calculator
Finding x-intercepts
Use a TI83/84 graphing calculator to find the x-intercepts of an equation
Finding y-intercepts
Use a TI83/84 graphing calculator to find the y-intercepts of an equation
Scatter Plots
How to graph Scatter Plots on a TI83/84 calculator
ERROR-Mistakes in Data Entry
What does this ERROR message mean on my TI83/83 calculator
ERROR-Missing info on a graph
What does this ERROR message on my TI83/84 calculator mean?
ERROR-that Tells You Something Important
These error messages tell you something about your graph or your data because they return an error
Find the Vertex of a Quadratic Function
These steps tell you how to use the Min/Max feature of the TI83/84 calculator to find the vertex of a parabola
Solve Matrices using a TI83/84 Calculator
Use a TI83/84 Calculator to solve matrices in one step or step by step
TI83/84 General Info Sheet
An introduction to all the amazing things the calculator can do for you