Beginner

Mathematics Content Domain

Diagnostic Test

The following topics would be tested for entry into Pre Algebra



Basic Arithmetic: Addition, subtraction, multiplication, and division of whole numbers.
Fractions: Understanding, simplifying, and performing basic operations (addition, subtraction, multiplication, division).
Decimals: Basic operations, converting between fractions and decimals.
Integers: Understanding positive and negative numbers, basic operations.
Factors and Multiples: Prime numbers, GCF, and LCM.
Basic Geometry: Identifying shapes, understanding perimeter and area of basic shapes.
Ratios and Proportions: Writing ratios, solving simple proportions.
Percentages: Understanding and calculating percentages, simple percentage problems.
Basic Measurement: Understanding units of measurement, simple conversions.
Reading Graphs: Basic interpretation of bar and line graphs, plotting points on a coordinate plane.

Syllabus

Pre Algebra

Chapter 1: Whole Numbers

  1. Introduction to Whole Numbers
  • Definition and Properties
  • Number Line
  1. Addition and Subtraction of Whole Numbers
  • Basic Operations
  • Word Problems
  1. Multiplication and Division of Whole Numbers
  • Basic Operations
  • Long Multiplication and Division
  • Word Problems
  1. Order of Operations
  • PEMDAS/BODMAS Rules
  • Solving Complex Expressions
  1. Prime Numbers and Composite Numbers
  • Definitions and Examples
  • Prime Factorization
  1. Factors and Multiples
  • Greatest Common Factor (GCF)
  • Least Common Multiple (LCM)

Chapter 2: Integers and Algebraic Expressions

  1. Introduction to Integers
  • Positive and Negative Numbers
  • Number Line and Opposites
  1. Operations with Integers
  • Addition and Subtraction
  • Multiplication and Division
  1. Order of Operations with Integers
  • Solving Expressions
  1. Introduction to Algebraic Expressions
  • Variables and Constants
  • Writing and Evaluating Expressions
  1. Simplifying Algebraic Expressions
  • Combining Like Terms
  • Distributive Property

Chapter 3: Solving Equations

  1. Introduction to Equations
  • Definition and Examples
  1. One-Step Equations
  • Solving with Addition and Subtraction
  • Solving with Multiplication and Division
  1. Two-Step Equations
  • Solving with Combined Operations
  1. Multi-Step Equations
  • Solving Complex Equations
  1. Equations with Variables on Both Sides
  • Balancing Equations
  1. Word Problems Involving Equations
  • Setting Up and Solving

Chapter 4: Fractions and Mixed Numbers

  1. Introduction to Fractions
  • Definition and Types
  • Simplifying Fractions
  1. Operations with Fractions
  • Addition and Subtraction
  • Multiplication and Division
  1. Mixed Numbers
  • Converting Between Improper Fractions and Mixed Numbers
  • Operations with Mixed Numbers
  1. Complex Fractions
  • Simplifying and Operations
  1. Word Problems Involving Fractions
  • Practical Applications

Chapter 5: Decimals

  1. Introduction to Decimals
  • Place Value and Representation
  1. Operations with Decimals
  • Addition and Subtraction
  • Multiplication and Division
  1. Converting Between Fractions and Decimals
  • Techniques and Examples
  1. Rounding and Estimating with Decimals
  • Rules and Applications
  1. Word Problems Involving Decimals
  • Practical Applications

Chapter 6: Ratio and Proportion

  1. Introduction to Ratios
  • Definition and Examples
  1. Writing and Simplifying Ratios
  • Techniques and Practice
  1. Introduction to Proportions
  • Definition and Examples
  1. Solving Proportions
  • Cross-Multiplication Method
  1. Applications of Ratios and Proportions
  • Word Problems and Real-Life Examples

Chapter 7: Percents

  1. Introduction to Percents
  • Definition and Conversion between Fractions, Decimals, and Percents
  1. Calculating Percentages
  • Finding Percent of a Number
  • Percentage Increase and Decrease
  1. Applications of Percents
  • Discounts, Sales Tax, and Interest
  1. Word Problems Involving Percents
  • Practical Applications

Chapter 8: Measurement and Geometry

  1. Units of Measurement
  • Customary and Metric Systems
  • Conversions
  1. Perimeter and Area
  • Basic Shapes
  • Compound Shapes
  1. Volume and Surface Area
  • Prisms, Cylinders, and Other Solids
  1. Introduction to Geometry
  • Basic Geometric Terms and Definitions
  1. Angles and Lines
  • Types of Angles
  • Parallel and Perpendicular Lines
  1. Polygons and Circles
  • Properties and Formulas

Chapter 9: Graphs and Statistics

  1. Introduction to Graphs
  • Types of Graphs: Bar, Line, Pie
  1. Reading and Interpreting Graphs
  • Analyzing Data
  1. Plotting Points and Graphing on a Coordinate Plane
  • Cartesian Coordinates
  1. Introduction to Statistics
  • Mean, Median, Mode, and Range
  1. Collecting and Organizing Data
  • Tables and Charts

Chapter 10: Exponents and Polynomials

  1. Introduction to Exponents
  • Definition and Rules
  1. Operations with Exponents
  • Multiplication and Division
  • Powers and Roots
  1. Introduction to Polynomials
  • Definition and Terminology
  • Adding and Subtracting Polynomials
  1. Multiplying Polynomials
  • Distributive Property and FOIL Method
  1. Factoring Polynomials
  • Common Factors and Special Cases