Table of Contents
- Calculation and Estimation
- Factors and Multiples
-
Powers and Roots
- Powers and Exponents
- Laws of Exponents
- Zero and Negative Exponents
- Simplifying Monomials: Zero Exponents
- Simplifying Monomials: Negative Exponents
- Fractional Exponents
- Simplifying Algebraic Expressions: Negative and Fractional Exponents
- nth Roots: Integers
- Scientific Notation
- Number Operations in Scientific Notation
-
Factorising and Expanding Expressions
- Simplifying Expressions: Rules of Exponents
- The Greatest Common Factor of Monomials
- Factoring Using the Highest Common Factor
- Rewriting Expressions Using the Distributive Property
- Multiplying Binomials
- Multiplying a Binomial by an Algebraic Expression
- Expanding an Expression to a Difference of Two Squares
- Difference of Two Squares
- Factoring Monic Quadratics
- Equations and Formulas
- Sequences
-
Fractions, Decimals, and Percentages
- Reciprocals
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Converting Decimals to Fractions
- Converting Fractions to Recurring Decimals
- Converting Recurring Decimals to Fractions
- Comparing and Ordering Rational Numbers
- Percentage Change
- Applications of Percentage
- Simple Interest
- Fractions to Percents
- Percents to Fractions
- Fractions, Decimals, and Percents
- Ratio and Proportion
-
Working with Data
- Stem-and-Leaf Plots
- Back-to-Back Stem-and-Leaf Plots
- Frequency Polygons
- Pie Charts
- Drawing Pie Charts
- Time Series Graphs
- Plotting Scatter Graphs
- Scatter Plots and Lines of Best Fit
- Best Measure of Central Tendency
- Mean, Median, and Mode
- Grouped Frequency Tables
- Grouped Frequency Tables: Estimating the Mean
- Grouped Frequency Tables: Estimating the Median
- Grouped Frequency Tables: Estimating the Mode
- Appropriate Data Display
- Angles in Polygons
-
Right-Angled Triangles
- The Pythagorean Theorem
- Applications on the Pythagorean Theorem
- Distance on the Coordinate Plane: Pythagorean Formula
- The Converse of the Pythagorean Theorem
- Right Triangle Trigonometry: Solving for a Side
- Right Triangle Trigonometry: Solving for an Angle
- Angles of Elevation and Depression
- Special Right Triangles
- Trigonometric Ratios of Special Triangles
- Trigonometric Ratios in Right Triangles
-
Area and Perimeter
- Perimeter of a Composite Figure
- Perimeter of Polygons
- Areas of Composite Polygons
- Area of a Trapezoid
- Areas of Composite Figures
- Converting and Comparing Area: Metric Units
- Areas in Hectares
- Upper and Lower Bounds
- Circumference of a Circle
- Area of a Circle
- Arc Lengths and Sectors: Degrees
- Areas of Circular Segments
- Area of Circular Segments: Degrees
- Volume
- Surface Area
-
Graphing Linear and Nonlinear Equations
- Equations of Vertical and Horizontal Lines
- Equation of a Straight Line: Slope–Intercept Form
- Slopes and Intercepts of Linear Functions
- Equation of a Straight Line: General Form
- Slope of a Line through Two Points
- Completing Function Tables
- Linear Functions
- Linear Functions in Different Forms
- Applications of Linear Functions
- Velocity–Time Graphs
- Average Speed
- Linear Relationships
- Midpoint on the Coordinate Plane
- Slopes of Parallel and Perpendicular Lines
- Equations of Parallel and Perpendicular Lines
- Graphing Quadratic Functions
- Features of Quadratic Functions
- Applications of Quadratic Equations
- Graphing Circles
- Properties of Tangents and Chords
- Geometric Constructions and Loci
- Bearings and Scale Drawings
- Geometric Transformations
- Solving Quadratic Equations
- Simultaneous Equations
- Linear Inequalities
-
Probability
- Introduction to Probability
- Probability of Simple Events
- Compound Events
- Mutually Exclusive Events
- Experimental Probability
- Prediction Using Probability
- Theoretical Probability
- Dependent and Independent Events
- Independent Events
- Tree Diagrams
- Conditional Probability: Tree Diagrams
- Conditional Probability
- Two-Way Frequency Tables
- Conditional Probability: Two-Way Tables
- Sets and Venn Diagrams
- Calculating Probability Using Venn Diagrams
- Expressing a Set
-
Collecting, Interpreting, and Representing Data
- Sampling Methods
- Simple Random Sample
- Stratified Random Sampling
- Biased versus Unbiased Samples
- Quartiles of a Data Set
- Interquartile Range
- Cumulative Frequency Graphs
- Box-and-Whisker Plots
- Comparing Two Distributions Using Box Plots
- Frequency Density and Histograms
- Comparing Data
- Comparing Data Sets Using the Mean and Range
- Multiplicative Reasoning
- Direct and Inverse Proportion
-
Congruence and Similarity
- Congruence of Triangles: SSS, SAS, and RHS
- Congruence of Triangles: ASA and AAS
- Applications of Triangle Congruence
- Congruent Polygons
- Similarity of Triangles
- Triangle Similarity Criteria and Their Applications
- Similar Polygons
- Areas of Similar Polygons
- Applications of Similar Polygons
- Similarity of Solids
-
Trigonometry
- Upper and Lower Bounds: Trigonometric Calculations
- Evaluating Trigonometric Ratios given the Value of Another Ratio
- Graphs of Trigonometric Functions
- Finding the Area of a Triangle Using Trigonometry
- Law of Sines
- Law of Cosines
- Applications on Sine and Cosine Laws
- Bearing in Trigonometry
- Applying the Pythagorean Theorem to Pyramids and Cones
- Trigonometry in Three Dimensions
- Transformation of Trigonometric Functions
- Circle Theorems
-
Graphs
- Solving Systems of Linear Equations Graphically
- Two-Variable Linear Inequalities
- Solving Systems of Linear Inequalities
- Quadratic Functions in Different Forms
- Solving Quadratic Equations Graphically
- Solving Quadratic Equations Iteratively
- Solving Systems of Nonlinear Equations Graphically
- Graphing Factorized Cubic Functions
- Solving Cubic Equations Graphically
- Solving Cubic Equations Iteratively
- Graphs of Direct and Inverse Variations
- Graphs of Rational Functions
- Graphs of Exponential Functions
- Function Transformations: Translations
- Function Transformations: Dilation
- Estimating Rates of Change and Areas Under Graphs
- Surds
- Algebraic Fractions
- Functions and Polynomials
- Vectors