**MATHS HANDBOOK & STUDY GUIDE
**

**Overview and Table of Contents**

**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**