Matric Maths – Notes
A general guide to the maths syllabus for IEB & CAPS grade 12 students.
Table of Contents
General Exam layout.............................................................................................................. 4
Acceptable reasons: Euclidean Geometry .............................................................................. 5
Paper 1 .................................................................................................................................... 8
Algebra, equations & inequalities ...................................................................................... 8
Patterns and Sequences .................................................................................................... 15
1. Arithmetic (linear) sequences ................................................................................ 15
2. Geometric (exponential) sequences ........................................................................ 15
3. Quadratic (parabolic) sequences ............................................................................ 16
Sigma Notation .............................................................................................................. 16
1. Arithmetic Series.................................................................................................... 16
2. Geometric Series..................................................................................................... 16
Infinite series ................................................................................................................. 17
Common questions ........................................................................................................ 17
Finance, Growth & Decay ................................................................................................. 18
Nominal & effective interest ......................................................................................... 18
Hire Purchase ................................................................................................................ 18
Sinking funds................................................................................................................. 18
Future Annuity.............................................................................................................. 19
Present Annuity ............................................................................................................ 19
Balance Outstanding ..................................................................................................... 19
Differing starting/ending times..................................................................................... 21
Functions and graphs ....................................................................................................... 22
Function notation .......................................................................................................... 22
Inverse functions ........................................................................................................... 22
Transformations ............................................................................................................ 22
Types of functions .......................................................................................................... 23
Differential Calculus ......................................................................................................... 26
Notation ......................................................................................................................... 26
First principles .............................................................................................................. 26
Short method ................................................................................................................. 27
Average gradient ........................................................................................................... 27
, Optimization .................................................................................................................. 28
Rates of change .............................................................................................................. 28
Probability ......................................................................................................................... 29
Types of events: ............................................................................................................. 29
Identities ........................................................................................................................ 29
Tree Diagrams ............................................................................................................... 30
Venn Diagrams .............................................................................................................. 30
Arrangements ................................................................................................................ 31
Paper 2 .................................................................................................................................. 32
Euclidean Geometry.......................................................................................................... 32
Revision ......................................................................................................................... 32
Proportionality theorem ................................................................................................ 37
Midpoint theorem .......................................................................................................... 37
Pythagoras extended ..................................................................................................... 38
Proofs ............................................................................................................................. 38
Analytical Geometry ......................................................................................................... 39
Revision ......................................................................................................................... 39
Equation of a circle ........................................................................................................ 39
Tangents to a circle ....................................................................................................... 40
Statistics............................................................................................................................ 41
Box & whisker diagram ................................................................................................. 41
Stem & leaf plot ............................................................................................................. 42
Frequency Polygon ........................................................................................................ 42
Ogive .............................................................................................................................. 42
Standard deviation ........................................................................................................ 42
Outliers .......................................................................................................................... 42
Correlation & Linear regression ................................................................................... 43
Trigonometry..................................................................................................................... 44
Identities ........................................................................................................................ 44
Solving Equations.......................................................................................................... 45
Graphs ........................................................................................................................... 46
Common Questions Types ............................................................................................. 47
,List of Shorthand & Abbreviations
LCD – Lowest Common Denominator
Pt. – Point
T.P. – Turning Point
LHS – Left-Hand Side
RHS – Right-Hand Side
a.k.a. – Also Known As
, General Exam layout
Mathematics exams will all generally be set with the mark breakdown seen in Table 1.
Difficulty Cognitive level IEB CAPS
1 Knowledge 20% 20%
2 Routine procedures 30% 35%
3 Complex procedures 35% 30%
4 Problem Solving 15% 15%
Total 100% 100%
Table 1: Weighting of exams according to cognitive level
The division of the content between paper 1 & paper 2 is identical between IEB and
CAPS. An estimate of the weighting of each section is given although this should be taken
as a rough guideline as this weighting can vary slightly from year to year. The breakdown
can be seen in Table 2 & 3.
Topics Marks Duration
Algebra, equations and inequalities ± 25
Patterns and sequences ± 25
Paper 1 Finance, growth and decay ± 15 3 hours
Functions and graphs ± 35
Differential calculus ± 35
Probability ± 15
Table 2: Paper 1 content weightings
Topics Marks Duration
Euclidean Geometry ± 50
Paper 2 Analytical Geometry ± 40 3 hours
Statistics and regression ± 20
Trigonometry ± 40
Table 3: Paper 2 content weightings
A general guide to the maths syllabus for IEB & CAPS grade 12 students.
Table of Contents
General Exam layout.............................................................................................................. 4
Acceptable reasons: Euclidean Geometry .............................................................................. 5
Paper 1 .................................................................................................................................... 8
Algebra, equations & inequalities ...................................................................................... 8
Patterns and Sequences .................................................................................................... 15
1. Arithmetic (linear) sequences ................................................................................ 15
2. Geometric (exponential) sequences ........................................................................ 15
3. Quadratic (parabolic) sequences ............................................................................ 16
Sigma Notation .............................................................................................................. 16
1. Arithmetic Series.................................................................................................... 16
2. Geometric Series..................................................................................................... 16
Infinite series ................................................................................................................. 17
Common questions ........................................................................................................ 17
Finance, Growth & Decay ................................................................................................. 18
Nominal & effective interest ......................................................................................... 18
Hire Purchase ................................................................................................................ 18
Sinking funds................................................................................................................. 18
Future Annuity.............................................................................................................. 19
Present Annuity ............................................................................................................ 19
Balance Outstanding ..................................................................................................... 19
Differing starting/ending times..................................................................................... 21
Functions and graphs ....................................................................................................... 22
Function notation .......................................................................................................... 22
Inverse functions ........................................................................................................... 22
Transformations ............................................................................................................ 22
Types of functions .......................................................................................................... 23
Differential Calculus ......................................................................................................... 26
Notation ......................................................................................................................... 26
First principles .............................................................................................................. 26
Short method ................................................................................................................. 27
Average gradient ........................................................................................................... 27
, Optimization .................................................................................................................. 28
Rates of change .............................................................................................................. 28
Probability ......................................................................................................................... 29
Types of events: ............................................................................................................. 29
Identities ........................................................................................................................ 29
Tree Diagrams ............................................................................................................... 30
Venn Diagrams .............................................................................................................. 30
Arrangements ................................................................................................................ 31
Paper 2 .................................................................................................................................. 32
Euclidean Geometry.......................................................................................................... 32
Revision ......................................................................................................................... 32
Proportionality theorem ................................................................................................ 37
Midpoint theorem .......................................................................................................... 37
Pythagoras extended ..................................................................................................... 38
Proofs ............................................................................................................................. 38
Analytical Geometry ......................................................................................................... 39
Revision ......................................................................................................................... 39
Equation of a circle ........................................................................................................ 39
Tangents to a circle ....................................................................................................... 40
Statistics............................................................................................................................ 41
Box & whisker diagram ................................................................................................. 41
Stem & leaf plot ............................................................................................................. 42
Frequency Polygon ........................................................................................................ 42
Ogive .............................................................................................................................. 42
Standard deviation ........................................................................................................ 42
Outliers .......................................................................................................................... 42
Correlation & Linear regression ................................................................................... 43
Trigonometry..................................................................................................................... 44
Identities ........................................................................................................................ 44
Solving Equations.......................................................................................................... 45
Graphs ........................................................................................................................... 46
Common Questions Types ............................................................................................. 47
,List of Shorthand & Abbreviations
LCD – Lowest Common Denominator
Pt. – Point
T.P. – Turning Point
LHS – Left-Hand Side
RHS – Right-Hand Side
a.k.a. – Also Known As
, General Exam layout
Mathematics exams will all generally be set with the mark breakdown seen in Table 1.
Difficulty Cognitive level IEB CAPS
1 Knowledge 20% 20%
2 Routine procedures 30% 35%
3 Complex procedures 35% 30%
4 Problem Solving 15% 15%
Total 100% 100%
Table 1: Weighting of exams according to cognitive level
The division of the content between paper 1 & paper 2 is identical between IEB and
CAPS. An estimate of the weighting of each section is given although this should be taken
as a rough guideline as this weighting can vary slightly from year to year. The breakdown
can be seen in Table 2 & 3.
Topics Marks Duration
Algebra, equations and inequalities ± 25
Patterns and sequences ± 25
Paper 1 Finance, growth and decay ± 15 3 hours
Functions and graphs ± 35
Differential calculus ± 35
Probability ± 15
Table 2: Paper 1 content weightings
Topics Marks Duration
Euclidean Geometry ± 50
Paper 2 Analytical Geometry ± 40 3 hours
Statistics and regression ± 20
Trigonometry ± 40
Table 3: Paper 2 content weightings
