Research Guides: Academic Coaching: Handouts

Helpful Handouts

General Algebra Concepts

Algebra Formula Sheet
A variety of formulas used for College Algebra compiled by Paul Dawkins http://tutorial.math.lamar.edu
Integer Rules
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
Mathematics Properties
A quick cheat-sheet for mathematical properties and what they mean
Geometry Formulas
Formulas used in geometry, including perimeter, area, surface area, and volume
Set Notation, Interval Notation and Inequalities
How to express a solution to a graph or equation using set notation, interval notation, or inequalities
Solving a linear equation in one variable
This handout explains how to solve a linear equation in one variable and provides a list a steps that can be used for any linear equation solution process.
Midpoint and Distance Formulas
Learn how to use the midpoint and distance formulas in examples.

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
Completing the Square
How to use the "completing the square" method for quadratic formulas
Factoring Methods - Trinomials
Several different methods for factoring trinomials
Solving quadratic equations
How to solve quadratic equations using complete the square, factoring, or the quadratic formula

Word Problems

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

Linear Equations

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

Symmetry of Equations
How to determine if an equation or a graph has x-axis symmetry, y-axis symmetry or symmetry about the origin
Circles
Learn the difference between the standard and general forms of a circle and how to transform one into the other.
Variations
Direct and inverse variations
What is my Domain? Flowchart
How to find the domain of a function using our flowchart
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
Graphs of Parent Functions
The shapes that various functions form
Intercepts for piecewise functions
This handout reviews how to find intercepts for any function, and explains how to test if the potential intercepts are valid for a given piecewise function.
Transformation of graphs
Starting with a parent function, graph a new function by shifting, stretching, compressing and reflecting

Polynomials, Graphs and Roots/Zeros

Finding a polynomial from its graph
Learn how to use the properties of the graph of a polynomial to determine an equation for the graph.
Graphing a Polynomial
Learn how to graph a polynomial given its equation.
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 a polynomial from its zeros/roots/solutions
Learn how to find a polynomial when given only its solutions, also called zeros or roots.

Rational Expressions and Equations

Simplifying Rational Expressions
How to simplify rational expressions
Solving Rational Equations
Learn how to solve rational equations.
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

Composite Functions
Learn how to find a composite function and how to find the domain of that composite function.
Finding Inverses of Functions
This worksheet walks you through the process to find an inverse a function.

Exponents, Radicals and Logs

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

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 - Ones
Learn how to use matrix operations to solve systems of equations. This method finds the "ones" in the matrix first, and the "zeros" second
Solving Systems of Equations using Matrices - Zeros
Learn how to use matrix operations to solve systems of equations. This method finds the "zeros" in the matrix first, and the "ones" last.

Review

Distance and Midpoint formulas
Learn how to use the distance and midpoint formulas.
Finding Intercepts from a piecewise equation
Learn how to find and check intercepts for a piecewise equation. Also reviews how to find intercepts from an equation in general.
Symmetry of Equations
Test an equation for symmetry with respect to the x-axis, y-axis, and origin.
Equations of Circles
Learn the difference between the standard and general forms of a circle and how to transform between the two.
Find the domain of a function
Learn how to find the domain of a function.
Domain Flow Chart
Flow chart to summarize the process to find the domain of a function.
Even and Odd functions
Learn how to determine whether a function is even, odd, or neither.
Graphs of parent functions
Learn how to identify the graphs of various functions.
Transformation of functions
Learn how to transform the graph a parent function into a given function.
Inverse Functions
Learn how to find the inverse of a function.

Trigonometry Information Sheet
Definitions, formulas, properties, and identities compiled by Paul Dawkins http://tutorial.math.lamar.edu
Circular Motion
Convert angular speed to linear speed.
Unit Circle
Unit circle diagram
Trigonometric and Inverse Trigonometric Functions
Graphs of trigonometric and inverse trigonometric functions
Transforming Trigonometric Graphs
Using amplitude, period, phase shift and vertical shifts, this document explains how to graph a trignometric function based on its parent graph.
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.
Strategies for Proving Trigonometric Identities
Proving trigonomentric identities can be difficult because each problem is unique. This document discusses several strategies that can help lead to a solution.
Imaginary Roots
Learn how to use the DeMoivre formula to find the imaginary roots of an equation.

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.
DeMoivre's Theorem
Learn how to use DeMoivre's theorem to multiply out a complex number raised to a power.
Symmetry in Polar Coordinates
Symmetry using the polar form of an equation
Solving Partial Fractions - Equation Method
This handout walks you through solving a partial fraction decomposition example using equations.
Solving Partial Fractions using roots.
This handout walks you through solving a partial fraction decomposition example using roots.
Conics
Equations for parabolas, circles, ellipses and hyperbolas.
Induction
How to solve a series Induction problem.

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
Trigonometry Tab
- Graphs of Trigonometric and Inverse Trigonometric Functions
- Transformation of Trigonometric Functions
- Trigonometric Identities and More sheet
- Strategies for Proving Trig Identities
- Solving Half Angle - Double Angle Trigonometric Equations - COMING SOON
- Trigonometric Equations - COMING SOON
- Inverse Trigonometric Functions - COMING SOON
- Law of Sines Ambiguous Case
- Vectors - COMING SOON
Finite Tab
- Permutations
- Combinations

Finite Math Information Sheet
This document contains many useful formulae and explanation on their usage in finite math applications.
Mean, Variance, Standard Deviation - Grouped Data
How to calculate the mean, variance, and standard deviation of grouped data.

Probability

Permutation Examples
Probability of an event when order matters.
Combination Examples
Probability of an event when order does NOT matter.
Baye's Theorem Example
Utilize Baye's Theorem to calculate a probability.
Probability and Expected Value Examples
A number of examples, with explanation, for permutation and combination probability as well as expected value.

Matricies

Operations on Matrices
This document explains adding, subtracting, and multiplication of matrices.
Inverse of a 2x2 Matrix
How to find the inverse of a 2x2 matrix.
Inverse of a Square Matrix (Determinant Method)
Shows the process of finding the inverse of a square matrix using determinants.
Inverse of a Square Matrix (Identity Matrix Method)
Shows the process of finding the inverse of a square matrix by appending an identity matrix.
Input Output Example
Solving an industry example utilizing the identity matrix method to find the inverse of a square matrix.
Determinant of a 2x2 Matrix and 2x2 Cramer's rule
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
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
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 (intro to Simplex)
This document explains the Table Method which can be used to maximize or minimize a variable.
Maximization Problem using Simplex Method
Displays how to solve a maximization problem using the Simplex Method.
Minimization Dual Problem (using Simplex Method)
Displays how to solve a dual problem (minimization) using transposition and the Simplex Method.
Maximization with Mixed Constraints
Displays how to solve a maximization problem using Simplex Method when the problem constraints have mixed signs.

Financial Equations

Future Value Problems
Calculating n (number of payments) for a future value problem.
Build an Amortization Schedule
Learn how to build an Amortization Schedule.
Yearly Interest Paid on an Amortized Loan
Learn how to calculate how much interest one has paid on an Amortized loan.

Calculus Information Sheet - Limits
Limits and evaluation techniques compiled by Paul Dawkins http://tutorial.math.lamar.edu
Calculus Information Sheet - Derivatives
Derivatives formulas and variants compiled by Paul Dawkins http://tutorial.math.lamar.edu
Calculus Information Sheet - Integrals
Definitions and techniques for integrals compiled by Paul Dawkins http://tutorial.math.lamar.edu
Common Derivatives & Integrals
Properties/rules/formulas for derivatives and integrals compiled by Paul Dawkins http://tutorial.math.lamar.edu

Calculus I

Continuity and Differentiability of Functions
This document explains continuity and differentiability of a function and shows graphically what these terms mean.
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.
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.
Sketch a Function Curve Based on 1st Derivative Graph
Using the graph of a 1st derivative, sketch one of the possible curves for f(x).

Calculus II

Rewrite Integrands
Different ways to rewrite your equation to make integration easier
Integration Methods Summary
A summary of various integration methods.
Series Convergence/Divergence
Calculus Integration Techniques
This is a document from a presentation given by one of our coaches for students. Looking into uploading the 2 video components

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

Laplace Transformations
A list of Laplace Transformations compiled by Paul Dawkins http://tutorial.math.lamar.edu

Statistical Functions on TI-83-84
How to locate and utilize numerous statistical functions on the TI83 or 84.
Sampling Methods
A document that illustrates and describes various statistical sampling methods.
Graphical Summaries
A document that illustrates and describes important statistical charts and diagrams.
Building a Frequency Distribution Table
Process to build a frequency distribution table from a set of data elements.
Mean, Variance, Standard Deviation - Frequency Distribution
How to calculate the mean, variance, and standard deviation of a frequency distribution.
Using the Binomial Distribution Theorem
Examples of how to utilize the Binomial Distribution Theorem to calculate probability.
Establishing Hypotheses for One-Sample Tests
Describes a simple 3-step process to establish null and alternative hypotheses.

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 TI83/84 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

TSIA2 Learning Resources
Excerpt from their site: "TSIA2 Learning Resources provides thousands of learning resources to help Texas students, parents and teachers. All of the learning resources have been aligned to Texas state academic standards. Students identified as not college ready on the TSIA2 assessments can use the powerful Learning Locator™ to find specific materials targeted to the growth areas identified on their score reports."
more...less...
If you haven't taken the TSIA2 yet, you can click on the "Enter Student Site" button to browse study materials at your leisure.

TSIA2 Sample Math Questions
This document has a set of sample math questions, a page with the answers to the questions, and several pages that explain how to work each problem.

Sample questions for the TSIA2/Accuplacer from College Board's official website.

Accuplacer Arithmetic sample questions
Answers are provided at the end as well as explanations on solving each problem.
Accuplacer Quantitative Reasoning sample questions
Answers are provided at the end as well as explanations on solving each problem.
Accuplacer Advanced Algebra and Functions sample questions
Answers are provided at the end as well as explanations on solving each problem.

TSIA Math Test prep materials from other LSC campuses.

TSI Sample Math Prep - Tomball
A document from LSC-Tomball with sample questions and a formula sheet.
TSIA2 Test Prep - CyFair
TSI Test Prep 2020 - CyFair
A document from LSC-CyFair with sample questions and a formula sheet.

Free online TSI math study materials and practice exams.

Note: Because these websites provide study materials free of charge to students, they often have in-site and popup ads. In addition, some of these websites may also advertise other products that are not free. These sites are not endorsed by or affiliated with Lone Star College in any way.

MathHelp.com TSI math test prep
This webpage takes you through over 100 sample questions and has videos on the concepts. To begin practicing, press the purple "Start Course" button.
Alternatively, if you know which concepts you need to practice, you can simply click on the concepts individually.
Mometrix.com TSI practice exam
Mometrix has a free practice test, and links to other paid services; flash cards, online course, and study guide.
To access the free practice test, press the yellow "Start Test" button.
After taking the test, each question you missed will have an explanation on the correct method to work that problem.
TSI Math Practice Test
This website has links to paid content and other miscellaneous ads. The test appears below the introductory text information.

Relations and Functions
- Difference between a relation and a function
- Function notation
- Domain
- Range
- Independent variable
- Dependent variable
Evaluating Functions
Defining Linear Equations
Graphing Functions and Relations
- origin of a graph
- vertical line test
Forms of Linear Equations
Solving Linear Equations
Solving Linear Inequalities
Linear Systems of Equations
Algebraic Expressions and Equations
Word Problems and Applications

Polynomials
- Defining terms
  - Monomial
  - Polynomial
    - equation versus function
  - Terms of a polynomial
  - Degree of a polynomial
- FOIL - how to multiply two binomials
- Factors of polynomials
- Factoring special cases
- Factoring trinomials
Quadratic Functions
- Definition
- Standard Form of a polynomial
- Discriminant
- Finding the vertex from a polynomial equation or function
Solving Quadratic Equations
Exponents and Roots
Order of Operations (PEMDAS or Pretty Please My Dear Aunt Sally)
Solving Equations with Exponents and Roots
Rational Expressions
Rational Equations
Rational Functions
- Asymptotes
- Graphing

Plane Geometry
- Points
- Distance Formula
- Line Segment
- Ray
- Circumference
- Angle
- Vertex
- Arc length
- Parallel
- Perpendicular
- Polygon
  - Vertices of
  - Interior angles of
- Regular polygon
- Triangle
  - Right
  - Isosceles
  - Equilateral
- quadrilateral
  - Rectangle
  - Square
  - Parallelogram
Transformations of a Plane
- Rotations
- Pre-image
- Image
- Translation
- Reflection
  - Line of Reflection
- Congruent figures
Dilation
- Definition
- Reduction
- Scale factor
Symmetry
- Line symmetry
- Rotational symmetry
Perimeters and Areas, Volumes and Surface Areas
The Pythagorean Theorem
- Hypotenuse
Similar Figures and Proportions

What are Statistics?
- Descriptive statistics
- Inferential statistics
Mean, Median and Mode
Quartiles and Percentiles
- First quartile
- Second quartile
- Third quartile
- Fourth quartile
- nth percentile
Standard Deviation
- Variance
Fitting Functions to Data
- Independent variable
- Dependent variable
- Correlation
Linear Data Fitting
- Linear correlation
Probabilities
- Probability distribution
  - Uniform probability distribution
Conditional Probabilities
Addition Rule
Multiplication Rule

Content from Lonestar College-University Park coaches.

How to read a Math Textbook
Reading a math text is different from reading other types of books or texts. This document gathers several "how to" lists from online sources, displays them, and summarizes similarities and differences.

Presentation on How To Read a Math Textbook
Watch a video by Allyn and Terri from the SLRC Math Lab to learn how to read a Math Textbook and why it is good to do so.

Below is a short list of websites that provide various tips on studying, note taking, overcoming test anxiety and more. Much of what we have included below are related to math.

These sites are not endorsed by or affiliated with Lone Star College in any way.

Testtakingtips.com is a website that provides visitors with tips for test taking, study skills, note taking, reducing test anxiety and more.

Here are several websites that provide tips and trick on how to succeed in Math Courses. For more sites, google "How to succeed in math".

Here are some websites from other colleges that talk about reducing math anxiety.

Here are some websites that provide information on reducing test anxiety.