An overview of all the areas under Academic Coaching, including the Math Lab, Math Hotspot, Science Hotspot, and Writing and Reading Hotspot.

- College Algebra
- Trigonometry
- Precalculus (creating handouts)
- Finite Math
- Calculus I - III
- Differential Equations
- Statistics
- Calculator Help
- TSI Math Prep
- Math tips and tricks

**General Algebra Concepts**

- Algebra Formula SheetA variety of formulas used for College Algebra compiled by Paul Dawkins http://tutorial.math.lamar.edu
- Integer RulesAdding, Subtracting, Multiplying and Dividing Integers
- Divisibility RulesQuick rules to help you divide quickly and effectively
- Fraction RulesThe rules for adding, subtracting, multiplying, and dividing fractions
- Mathematics PropertiesA quick cheat-sheet for mathematical properties and what they mean
- Geometry FormulasFormulas used in geometry, including perimeter, area, surface area, and volume
- Set Notation, Interval Notation and InequalitiesHow to express a solution to a graph or equation using set notation, interval notation, or inequalities
- Solving a linear equation in one variableThis 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 FormulasLearn how to use the midpoint and distance formulas in examples.

**Factoring and Solving Quadratic Equations**

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

**Word Problems**

- Understanding Word ProblemsKey words to look for in understanding word problems
- Word Problems - BallisticsHow to work word problems that involve ballistic motion (parabolic).
- Word Problems - MixturesLearn how to interpret and solve word problems involving percents or money.
- Word Problems - Work FlowLearn how to solve word problems that involve people working together to complete a job.
- Word Problems - Uniform MotionLearn how to interpret and solve word problems that involve d=r*t.

**Linear Equations**

- Linear EquationsA list of the different types of linear equations and explanations on when to use them
- Linear Equations part 2How to generate the equation of a line and which equation to use

- Symmetry of EquationsHow to determine if an equation or a graph has x-axis symmetry, y-axis symmetry or symmetry about the origin
- CirclesLearn the difference between the standard and general forms of a circle and how to transform one into the other.
- VariationsDirect and inverse variations
- What is my Domain? FlowchartHow to find the domain of a function using our flowchart
- Finding the DomainLearn how to find the domain of any equation.
- Functions- Even, Odd, NeitherHow to tell if a function is even, odd, or neither
- Graphs of Parent FunctionsThe shapes that various functions form
- Intercepts for piecewise functionsThis 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 graphsStarting with a parent function, graph a new function by shifting, stretching, compressing and reflecting

**Polynomials, Graphs and Roots/Zeros**

- Finding a polynomial from its graphLearn how to use the properties of the graph of a polynomial to determine an equation for the graph.
- Graphing a PolynomialLearn how to graph a polynomial given its equation.
- Synthetic DivisionThis worksheet will show you how to use synthetic division to find a zero or to find a remainder.
- Rational Roots TheoremLearn how to tell how many real roots are possible from a given polynomial.
- Law of SignsLearn how to use Descartes' Law of Signs to determine how many positive or negative real roots a polynomial might have.
- Find Bounds on Polynomial RootsThis handout will tell you how to find upper and lower bounds to the roots of a polynomial equation.
- Finding Zeros of a FunctionUtilize all of the tools available to you to find zeros of a function.
- Finding a polynomial from its zeros/roots/solutionsLearn how to find a polynomial when given only its solutions, also called zeros or roots.

**Rational Expressions and Equations**

- Simplifying Rational ExpressionsHow to simplify rational expressions
- Solving Rational EquationsLearn how to solve rational equations.
- AsymptotesHow to find vertical, horizontal and oblique asymptotes
- Graphing a Rational EquationSteps to graph a rational equation
- Rational and Polynomial InequalitiesLearn how to solve rational and polynomial inequalities using a chart and number line.

**Functions**

- Composite FunctionsLearn how to find a composite function and how to find the domain of that composite function.
- Finding Inverses of FunctionsThis worksheet walks you through the process to find an inverse a function.

**Exponents, Radicals and Logs**

- Laws of Exponents and RadicalsTable of formulas to simplify exponential and fractional exponential expressions
- Solving Exponential EquationsUse rules for and properties of exponents to solve equations containing them
- Logarithm RulesAll the rules for logarithms
- Solving Logarithmic EquationsUse rules for and properties of Logarithms to solve equations containing them

**Solving systems of equations**

- Solving systems of equationsLearn how to solve systems of equations by graphing, substitution or elimination methods.
- Solving systems of Equations using Matrices - OnesLearn 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 - ZerosLearn 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 formulasLearn how to use the distance and midpoint formulas.
- Finding Intercepts from a piecewise equationLearn how to find and check intercepts for a piecewise equation. Also reviews how to find intercepts from an equation in general.
- Symmetry of EquationsTest an equation for symmetry with respect to the x-axis, y-axis, and origin.
- Equations of CirclesLearn the difference between the standard and general forms of a circle and how to transform between the two.
- Find the domain of a functionLearn how to find the domain of a function.
- Domain Flow ChartFlow chart to summarize the process to find the domain of a function.
- Even and Odd functionsLearn how to determine whether a function is even, odd, or neither.
- Graphs of parent functionsLearn how to identify the graphs of various functions.
- Transformation of functionsLearn how to transform the graph a parent function into a given function.
- Inverse FunctionsLearn how to find the inverse of a function.

- Trigonometry Information SheetDefinitions, formulas, properties, and identities compiled by Paul Dawkins http://tutorial.math.lamar.edu
- Circular MotionConvert angular speed to linear speed.
- Unit CircleUnit circle diagram
- Trigonometric and Inverse Trigonometric FunctionsGraphs of trigonometric and inverse trigonometric functions
- Transforming Trigonometric GraphsUsing 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 CaseWhen using the law of Sines to solve a triangle, there are 3 possible outcomes. This document discusses the process.
- Strategies for Proving Trigonometric IdentitiesProving trigonomentric identities can be difficult because each problem is unique. This document discusses several strategies that can help lead to a solution.
- Imaginary RootsLearn how to use the DeMoivre formula to find the imaginary roots of an equation.

- PreCalculus Facts and Formulas sheetA 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 TheoremLearn how to use DeMoivre's theorem to multiply out a complex number raised to a power.
- Symmetry in Polar CoordinatesSymmetry using the polar form of an equation
- Solving Partial Fractions - Equation MethodThis 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.
- ConicsEquations for parabolas, circles, ellipses and hyperbolas.
- InductionHow 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**- Linear Equation Information
- Generating Equations of a line
- Set Notation
- Domain of a function
- Variation functions
- Rational and Polynomial inequalities
- Factoring - Special Cases
- Complete the Square
- Factoring trinomials
- 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 - solving "ones" first
- Matrices - solving "zeros" first

**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 SheetThis document contains many useful formulae and explanation on their usage in finite math applications.
- Mean, Variance, Standard Deviation - Grouped DataHow to calculate the mean, variance, and standard deviation of grouped data.

**Probability**

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

**Matricies**

- Operations on MatricesThis document explains adding, subtracting, and multiplication of matrices.
- Inverse of a 2x2 MatrixHow 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 ExampleSolving 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 ruleThis 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 MatrixThis 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 ruleCramer'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 MethodDisplays 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 ConstraintsDisplays how to solve a maximization problem using Simplex Method when the problem constraints have mixed signs.

**Financial Equations**

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

- Calculus Information Sheet - LimitsLimits and evaluation techniques compiled by Paul Dawkins http://tutorial.math.lamar.edu
- Calculus Information Sheet - DerivativesDerivatives formulas and variants compiled by Paul Dawkins http://tutorial.math.lamar.edu
- Calculus Information Sheet - IntegralsDefinitions and techniques for integrals compiled by Paul Dawkins http://tutorial.math.lamar.edu
- Common Derivatives & IntegralsProperties/rules/formulas for derivatives and integrals compiled by Paul Dawkins http://tutorial.math.lamar.edu

**Calculus I**

- Continuity and Differentiability of FunctionsThis document explains continuity and differentiability of a function and shows graphically what these terms mean.
- Find the equation of a tangent lineThis 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 TechniquesThis 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 GraphUsing the graph of a 1st derivative, sketch one of the possible curves for f(x).

**Calculus II**

- Rewrite IntegrandsDifferent ways to rewrite your equation to make integration easier
- Integration Methods SummaryA summary of various integration methods.
- Calculus Integration TechniquesThis 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 TransformationsA list of Laplace Transformations compiled by Paul Dawkins http://tutorial.math.lamar.edu

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

- Graphing Equations in your CalculatorInstructions on graphing an equation in a TI83/84 calculator
- Finding x-interceptsUse a TI83/84 graphing calculator to find the x-intercepts of an equation
- Finding y-interceptsUse a TI83/84 graphing calculator to find the y-intercepts of an equation
- Scatter PlotsHow to graph Scatter Plots on a TI83/84 calculator
- ERROR-Mistakes in Data EntryWhat does this ERROR message mean on my TI83/84 calculator
- ERROR-Missing info on a graphWhat does this ERROR message on my TI83/84 calculator mean?
- ERROR-that Tells You Something ImportantThese error messages tell you something about your graph or your data because they return an error
- Find the Vertex of a Quadratic FunctionThese 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 CalculatorUse a TI83/84 Calculator to solve matrices in one step or step by step
- TI83/84 General Info SheetAn introduction to all the amazing things the calculator can do for you

- TSIA2 Learning ResourcesExcerpt 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."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 QuestionsThis 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 questionsAnswers are provided at the end as well as explanations on solving each problem.
- Accuplacer Quantitative Reasoning sample questionsAnswers are provided at the end as well as explanations on solving each problem.
- Accuplacer Advanced Algebra and Functions sample questionsAnswers 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 - TomballA document from LSC-Tomball with sample questions and a formula sheet.
- TSI Test Prep 2020 - CyFairA 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 prepThis 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 examMometrix 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 TestThis website has links to paid content and other miscellaneous ads. The test appears below the introductory text information.

**Here is a list of math concepts covered in the TSI Study Guide by Test Prep Books (2023-24). **

Where applicable, there are links to Math Lab handouts.

**Elementary Algebra and Functions**

- 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

**Intermediate Algebra and Functions**

- 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

- Defining terms
- 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
**P**retty**P**lease**M**y**D**ear**A**unt**S**ally) - Solving Equations with Exponents and Roots
- Rational Expressions
- Rational Equations
- Rational Functions

**Geometric and Spatial Reasoning**

- 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

**Probabilistic and Statistical Reasoning**

- 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

- Probability distribution
- Conditional Probabilities
- Addition Rule
- Multiplication Rule

**Content from Lonestar College-University Park coaches.**

- How to read a Math TextbookReading 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 TextbookWatch 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.

- Last Updated: Oct 3, 2023 1:58 PM
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