LESSONS	CONTENTS – CAPS
Lesson 1	Topic:  Algebra, Equations, Inequalities, Exponents, Surds
	Revision of Gr 11 work
	Algebraic Expressions
	Equations
	Quadratic Equations
	Completing the Square
	Quadratic Formula
	Surd Equations
	Nature of Roots
	Quadratic Inequalities
	Simultaneous equations
	Exponents
	Surds
	Problem Solving
	Exam Questions
Lesson 2& 3	Topic: Number Patterns , Sequences and Series
	Revision from Gr 11 work
	Linear Patterns
	From Sketches to Patterns
	Quadratic Patterns
	Sigma Notation
	Arithmetic Sequences & Series
	Geometric Sequences & Series
	Real Life Applications
	Exam Questions
Lesson 4, 5, & 6	Topic:  Functions and Graphs
	Revision of Gr 11 work
	Drawing Graphs
	Finding equations of graphs
	Functions& Transformations
	Essential Concepts
	Inverse Functions
	Logarithms
	Exponential & Logarithmic Graphs
	Exam Questions
Lesson 7 & 8	Topic:  Finance, Growth, Decay
	Revision of Gr 11 work
	Simple and Compound Growth & Decay
	Growth and Decay (Part 1&2)
	Timelines (Part 1&2)
	Nominal and Effective Interest Rates
	Number of Time Periods
	Sinking funds and Annuities
	Future Value Annuity ( Part 1 & 2)
	Present Value Annuity ( Part 1 & 2)
	Outstanding Balance
	Variations of the default formulae
	Exam Questions
Lesson 9, 10 & 11	Topic:  Differential Calculus
	Limits
	First Principles
	Derivative rules & Average gradients
	Tangents
	Curve sketching
	Concavity & Points of Inflection
	A summary: f / f’ / f’’
	Practical applications- Maximum  and Minimum
	Exam Questions
Lesson 12, 13 & 14	Topic:  Analytical Geometry
	Revision of Gr 11 work
	Formulae and the < of inclination( Part 1 &2 )
	Graph Concepts
	Equations of Straight lines graphs
	Quadrilaterals( Part 1 & 2)
	Equations of Circles
	General and Standard form
	A tangent to a Circle
	Points of Intersection
	Exam Questions
Lesson 15, 16, 17 & 18	Topic:  Trigonometry
	Trig Theory Revision (Gr 10 & Gr11)
	Trig Theory – The theory of Compound and Double Angles
	Sketches
	Reduction
	Equations
	Identities
	Graphs
	Solution of Triangles
	Exam Questions
Lesson 19 & 20	Topic: Polynomials – 3rd Degree
	Revision of Gr 11 work
	Cubic Equations
	Factorising Expressions and Solving Equations
	Sketches
	The Remainder & Factor Theorems
	Exam Questions
Lesson 21.22,23,24 & 25	Topic:  Euclidean Geometry and Measurement
	Revision of Gr10 & Gr11  work
	Parallel lines
	Circle Geometry, no tangents (Part1)
	Circle Geometry, including tangents (Part2)
	Circle Geometry (Part 3)
	Proportionality (Part 1 & 2)
	Similarity (Part 1 & 2)
	All Geometry ( Part 1&2)
	Exam Questions
Lesson 26,27 & 28	Topic:  Probability
	Revision of Gr 11 work
	Introduction to probabilities
	Introduction to probabilities /values/sums/terminology/symbols
	Venn Diagrams – intersections/unions/complementary/mutuals
	Tree Diagrams
	Independent events/Not independent events
	Contingency Tables
	Fundamental Counting Principle ( Part 1 & 2)
	Probabilty Rules and Product Rule
	Exam Questions
Lesson 29 & 30	Topic:  Statistics and Regression
	Revision of Gr10 & Gr11  work
	Univariate data ( Part 1; 2; 3)
	Bivariate Data ( Part 1 & 2)
	Regression and Correlation
	Exam Questions
Lesson 31+ more	Topics:   Revisions and Past Exams Papers