ELM: CSU Math Study Guide
About the Course
The ELM exam is required for incoming students at schools within the California State University system. The test is designed to assess your math skills and is used by the university to determine which mathematics classes you can register for. The ELM is a very important test; students who fail the exam are required to take summer courses in the university's Early Start program and then retake the exam. If you fail the exam a second time, you are required to take a developmental math course in your first semester, which does not count as credit towards your degree. Failure to pass this class can lead to being disenrolled from the university.
Who Takes the ELM?
The California State University system requires math proficiency for all incoming students, and there are several ways to demonstrate that proficiency instead of taking the ELM, including scoring above 550 on math portion of the SAT or 23 on the math portion of the ACT. Read more about university math requirements here or contact your college advisor for more information. Students who cannot demonstrate math proficiency through other means are required to take the ELM prior to starting their first semester.
How to Prepare for the ELM
Most students learn the math covered on the ELM in high school but may be rusty on some of the concepts. We offer a full collection of video lessons that will help you review or learn all of the math included on the exam. If you want a complete review, start at the beginning and take the quiz associated with each lesson to ensure you've mastered the material. You can also jump to specific chapters if you just need to review some of the material.
Here is a breakdown of the material covered in this course:
Basic Arithmetic Calculations
Review the rules of different types of numbers, including whole numbers and signed numbers. Practice factoring and learn how to find the greatest common factor and least common multiple.
Rational Numbers
Review the rules of factors and practice with like, unlike, and complex fractions as well as mixed numbers. This chapter also reviews ratios and proportions.
Decimals and Percents
Learn basics of decimals and percents, including arithmetic and ordering. Practice converting decimals to percents or fractions.
Irrational Numbers
Work with square roots, including evaluating, estimating, and simplifying square roots. Learn how to simplify complex expressions that contain square roots, and complete square root practice problems.
Data & Statistics
Practice reading bar graphs, pie charts, and representations of data. You'll also learn how to work with mean, median, and mode and use data to make predictions.
Basic Expressions in Algebra
Learn properties associated with algebraic expressions, including the commutative, associative, and distributive properties. This chapter also includes lessons on simplifying expressions and combining like terms.
Exponents
Use the five main properties of exponents to simplify expressions. Learn how to work with zero and negative exponents.
Linear Equations & Inequalities
Practice solving linear equations with one and two variables. Learn a simple stepbystep process for solving linear equations and inequalities.
Absolute Value Equations and Inequalities
Learn the rules of absolute value and applying them when solving and graphing absolute value equations. This chapter also teaches you how to solve and graph inequalities with absolute value.
Polynomials
Learn about polynomials, including quadratic equations. This chapter includes FOIL, synthetic division, and practice problems for the quadratic formula.
Rational Expressions
Practice adding, subtracting, multiplying, and dividing rational expressions and then review how to solve a rational equation. Apply rational expressions to the real world by solving problems using constant and average rates.
Perimeter, Area & Volume
Find the perimeter and area of basic shapes, including triangles and rectangles. Also practice finding area and circumference of circles. Learn how to find the volume of prisms, cylinders, and other 3dimensional shapes.
Properties of Objects
Review the properties of shapes such as circles and quadrilaterals and then dig deep into triangles, angles, and lines. Finally, use the Pythagorean theorem to find the area of triangles.
Graphing Basics
Learn how to read a graph or number line and practice plotting points on a coordinate plane.
Graphing Functions
Practice graphing functions and working with slope. Learn the different forms of linear equations, including standard form and pointslope formula. Then, learn about graphing parabolas and the different forms of quadratic functions.
Practice
We provide practice questions along with each lesson. You can also complete ELM sample questions provided by CSU.
100% developed This course is fully developed. You can use the lessons in this course to study for exams and supplement your learning right now.
Course Chapters
ELM Test  Numbers and Data: Basic Arithmetic Calculations
All Videos in ELM Test  Numbers and Data: Basic Arithmetic Calculations
 1. What are the Different Types of Numbers?
 2. Arithmetic with Whole Numbers
 3. Arithmetic Calculations with Signed Numbers
 4. What Is The Order of Operations in Math?  Definition & Examples
 5. How to Find the Prime Factorization of a Number
 6. How to Find the Greatest Common Factor
 7. How to Find the Least Common Multiple
ELM Test  Numbers and Data: Rational Numbers
All Videos in ELM Test  Numbers and Data: Rational Numbers
 1. How to Build and Reduce Fractions
 2. How to Find Least Common Denominators
 3. Comparing and Ordering Fractions
 4. Changing between Improper Fraction and Mixed Number Form
 5. How to Add and Subtract Like Fractions and Mixed Numbers
 6. How to Add and Subtract Unlike Fractions and Mixed Numbers
 7. Multiplying Fractions and Mixed Numbers
 8. Dividing Fractions and Mixed Numbers
 9. Practice with Fraction and Mixed Number Arithmetic
 10. Estimation Problems using Fractions
 11. Solving Problems using Fractions and Mixed Numbers
 12. How to Solve Complex Fractions
 13. Calculations with Ratios and Proportions
ELM Test  Numbers and Data: Decimals and Percents
All Videos in ELM Test  Numbers and Data: Decimals and Percents
 1. What is a Decimal Place Value?
 2. Comparing and Ordering Decimals
 3. Arithmetic with Decimal Numbers
 4. Solving Problems Using Decimal Numbers
 5. What is a Percent?  Definition & Examples
 6. Changing Between Decimals and Percents
 7. Solve Problems Using Percents
 8. Changing Between Decimals and Fractions
ELM Test  Numbers and Data: Irrational Numbers
All Videos in ELM Test  Numbers and Data: Irrational Numbers
ELM Test  Numbers and Data: Data & Statistics
All Videos in ELM Test  Numbers and Data: Data & Statistics
 1. Statistical Analysis with Categorical Data
 2. Understanding Bar Graphs and Pie Charts
 3. Summarizing Categorical Data using Tables
 4. How to Calculate Percent Increase with Relative & Cumulative Frequency Tables
 5. What is a TwoWay Table?
 6. Make Estimates and Predictions from Categorical Data
 7. What is Quantitative Data?  Definition & Examples
 8. What is a Histogram in Math?  Definition & Examples
 9. What are Center, Shape, and Spread?
 10. How to Calculate Mean, Median, Mode & Range
 11. Describing the Relationship between Two Quantitative Variables
 12. Reading and Interpreting Line Graphs
 13. Making Estimates and Predictions using Quantitative Data
ELM Test  Algebra: Basic Expressions
All Videos in ELM Test  Algebra: Basic Expressions
 1. What is a Variable in Algebra?
 2. Expressing Relationships as Algebraic Expressions
 3. Evaluating Simple Algebraic Expressions
 4. The Commutative and Associative Properties and Algebraic Expressions
 5. The Distributive Property and Algebraic Expressions
 6. Combining Like Terms in Algebraic Expressions
 7. Practice Simplifying Algebraic Expressions
 8. Negative Signs and Simplifying Algebraic Expressions
ELM Test  Algebra: Linear Equations & Inequalities
All Videos in ELM Test  Algebra: Linear Equations & Inequalities
 1. What is a Linear Equation?
 2. How to Write a Linear Equation
 3. Problem solving using Linear Equations
 4. Solving Linear Equations with Literal Coefficients
 5. Solving Linear Equations: Practice Problems
 6. What is a System of Equations?
 7. How Do I Use a System of Equations?
 8. Solving a System of Equations with Two Unknowns
 9. Solving Problems involving Systems of Equations
 10. What is an Inequality?
 11. Solving Linear Inequalities: Practice Problems
ELM Test  Algebra: Absolute Value Equations & Inequalities
All Videos in ELM Test  Algebra: Absolute Value Equations & Inequalities
ELM Test  Algebra: Polynomials
All Videos in ELM Test  Algebra: Polynomials
 1. What are Polynomials, Binomials, and Quadratics?
 2. How to Add, Subtract and Multiply Polynomials
 3. Multiplying Binomials Using FOIL and the Area Method
 4. Multiplying Binomials Using FOIL & the Area Method: Practice Problems
 5. How to Factor Quadratic Equations: FOIL in Reverse
 6. Factoring Quadratic Equations: Polynomial Problems with a Non1 Leading Coefficient
 7. How to Divide Polynomials with Long Division
 8. How to Use Synthetic Division to Divide Polynomials
 9. Dividing Polynomials with Long and Synthetic Division: Practice Problems
 10. How to Solve a Quadratic Equation by Factoring
 11. How to Solve Quadratics That Are Not in Standard Form
 12. How to Complete the Square
 13. Completing the Square Practice Problems
 14. How to Use the Quadratic Formula to Solve a Quadratic Equation
 15. Using the Quadratic Formula to Solve Equations with Literal Coefficients
 16. Solving Problems using the Quadratic Formula
ELM Test  Algebra: Rational Expressions
All Videos in ELM Test  Algebra: Rational Expressions
 1. How to Add and Subtract Rational Expressions
 2. Practice Adding and Subtracting Rational Expressions
 3. How to Multiply and Divide Rational Expressions
 4. Multiplying and Dividing Rational Expressions: Practice Problems
 5. How to Solve a Rational Equation
 6. Rational Equations: Practice Problems
 7. Solving Rational Equations with Literal Coefficients
 8. Solving Problems Using Rational Equations
 9. Finding Constant and Average Rates
 10. Solving Problems Using Rates
ELM Test  Geometry: Perimeter, Area & Volume
All Videos in ELM Test  Geometry: Perimeter, Area & Volume
ELM Test  Geometry: Properties of Objects
All Videos in ELM Test  Geometry: Properties of Objects
 1. Properties of Shapes: Rectangles, Squares and Rhombuses
 2. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons
 3. How to Identify Similar Triangles
 4. Applications of Similar Triangles
 5. Properties of Congruent and Similar Shapes
 6. Parallel, Perpendicular and Transverse Lines
 7. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
 8. Angles and Triangles: Practice Problems
 9. The Pythagorean Theorem: Practice and Application
 10. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
ELM Test  Geometry: Graphing Basics
All Videos in ELM Test  Geometry: Graphing Basics
ELM Test  Geometry: Graphing Functions
All Videos in ELM Test  Geometry: Graphing Functions
 1. Graph Functions by Plotting Points
 2. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative
 3. Linear Equations: Intercepts, Standard Form and Graphing
 4. How to Find and Apply The Slope of a Line
 5. How to Find and Apply the Intercepts of a Line
 6. Graphing Undefined Slope, Zero Slope and More
 7. Equation of a Line Using PointSlope Formula
 8. How to Use The Distance Formula
 9. How to Use The Midpoint Formula
 10. What is a Parabola?
 11. Parabolas in Standard, Intercept, and Vertex Form
 12. How to Graph Cubics, Quartics, Quintics and Beyond

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