MATHS HANDBOOK & STUDY GUIDE


Overview and Table of Contents

Maths-Homepage-New-230

Grade 10 

Number Relationships and Patterns

The Number System
Rewriting Rational Number
Rounding of
Number Line Revision
Number Patterns

Exponents and Financial Mathematics

Exponent Laws
Financial Mathematics

Manipulations of Algebraic Expression

Revision of Grade 9 work
Grade 10 Algebra
Simplifying Algebraic
Fractions

Equations

Linear Equations
Quadratic Equations
Literal Equations
Linear Inequalities
Exponential Equations
Simultaneous Equations
Mathematical Modelling

Functions

Graphs and notation
The Linear Function
The Quadratic Function
The Hyperbolic Function
The Exponential Function
Determining equations of functions
Characteristics of Functions
Graph Interpretation
Mathematical modelling with functions
Trigonometric Functions

Trigonometry

Trigonometric Ratios
Trigonometric equations
Special Angles
Reciprocals
Trigonometric Functions in the Cartesian Plane
Angles of Elevation and
Depression

Geometry

Euclidean Geometry
Analytical Geometry

Surface Area and Volume

Right Prisms
Cylinders
Spheres and Hemispheres
Pyramids
Cones

Data Handling

Representations of Data
Measures of Central Tendency
Measures of Dispersion
The Five Number Summary
Misleading Statistics

Probability

Terminology
Calculating Probability
Venn Diagrams

Grade 11

The Number System, Exponents and Surds

The Number System
Definitions and Laws of Exponents and Surds

Equations and Inequalities

Grade 10 Revision
Quadratic Equations
Simultaneous Equations
Completing the Square
The Quadratic Formula
Inequalities
Mathematical Modelling

Number Patterns

Arithmetic Sequences
Quadratic Sequences

Analytical Geometry

Summary of Formulas
Properties of Quadrilaterals
Grade 10 Revision
Determining the Equation of a Straight Line
Angle of Inclination

Functions

Grade 10 Revision
The Quadratic Function
The Hyperbolic Function
The Exponential Function
Translations and Reflections of Graphs
Graph Interpretation
Trigonometric Functions
Interpretation of Trigonometric Functions

Trigonometry

Grade 10 Revision
Identities
Reduction Formulas
Trigonometric Equations
Restrictions in Trigonometric Equations

Measurement

Surface Area and Volume
Right Prisms
Scaling Factors
Cylinders
Pyramids
Spheres
Hemispheres
Cones

Euclidean Geometry

Revision of Lines and
Triangles
Circle Terminology
Circle Theorems

Sine, Cosine and Area Rules

Revision
The Sine Rule
The Cosine Rule
The Area Rule

Financial Mathematics

Simple and Compound
Growth and Decay
The Effects of Different
Compounding Periods
Time Lines
Probability
Grade 10 Revision
Dependant and
Independent Events
Venn Diagrams
Tree Diagrams
Contingency Tables

Statistics

Revision of Terminology
Histograms and Frequency
Polygons
Ogives
Variance and Standard
Deviation

Calculator Tips

Grade 12

Number Patterns

Grade 11 revision
Sequences
Series
Sigma Notation
Infinite Geometric Series
Applications of Sequences and Series

Functions, Inverses and Logarithms

Grade 11 Revision
Functions
Inverse Graphs
The Logarithmic Function
Laws of Logarithms

Financial Mathematics

Grade 11 Revision and the use of Logarithms
Future Value and Present Value
Comparing Investment and Loan Options
Applications of Finance

Trigonometry

Grade 11 Revision
Compound Angles
Double Angles
Trigonometric Identities using Double Angles
Trigonometric Equations

Term 1 Assessment

Two and Three Dimensional Trigonometry

Grade 11 Revision
Three Dimensional Trigonometry

Algebra and Differential Calculus

The Remainder and Factor Theorem
Limits
Average Gradient
Differentiation
Tangents to Graphs of Functions
Stationary Points and Points of Inflection

Curve Sketching and Graph Interpretation

Sketching Graphs of Cubic Functions
Graph Interpretation

Optimisation of Functions and Rate of Change

Maxima and Minima Problems
Rates of Change
Calculus of Motion

 

Analytical Geometry

Summary of Formulas
Grade 11 Revision
The Circle

Exemplar June Exams

Euclidean Geometry

Grade 11 Revision
Ratios and Proportion
Similarity

Statistics

Grade 11 Revision
Scatter Plots

Probability

Grade 11 Revision
The Fundamental Counting Principles

Exemplar Preliminary Examinations

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