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Grade 11 and 12 MathematicsSummary
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summary, notes and practice past papers all in one. this document summarises the grade 11 and 12 maths work into understandable, easy to read notes.
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GR 11 MATHEMATICS- UP TO DATE -
SUMMARIES &
EXAM PREPARATION GUIDE
1
,Contents
Topic 1: Exponents and surds ............................................................................. 6
The number system .......................................................................................................... 6
Definitions and laws of exponents .................................................................................. 6
Simplifying expressions involving rational exponents ................................................... 7
Products and factors involving rational exponents......................................................... 8
Simplifying expressions using factors ........................................................................... 10
Exponential equations .................................................................................................... 12
Surds ............................................................................................................................... 17
Factorisation: complex procedures and problem solving ............................................. 19
Fractions: complex procedures and problem solving ................................................... 20
Complex equations involving exponents and surds...................................................... 21
Content and breakdown as for exam ............................................................................. 22
Topic 2: Quadratic equations, simultaneous equations, inequalities and
nature of roots ................................................................................................... 24
Quadratic equations ....................................................................................................... 24
Quadratic equations: complex procedures .................................................................... 29
Inequalities ..................................................................................................................... 31
Inequalities: complex procedures .................................................................................. 33
Simultaneous equations: one linear and one quadratic ................................................ 35
Problems involving minimum and maximum values .................................................... 37
The nature of the roots of 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0 ..................................................................... 39
Test: Content and breakdown as for exam .................................................................... 43
Departmental Examination Questions with Memo ........................................... 45
EASTERN CAPE 2014 ..................................................................................................... 45
EASTERN CAPE 2015 ..................................................................................................... 49
EASTERN CAPE 2016 ..................................................................................................... 54
GAUTENG PAPER 2015 .................................................................................................. 58
GAUTENG PAPER 2016 .................................................................................................. 62
GAUTENG PAPER 2017 .................................................................................................. 66
GAUTENG PAPER 2018 .................................................................................................. 71
TOPIC 3: Number Patterns ................................................................................. 77
Departmental Examination Questions with Memo ........................................... 78
EASTERN CAPE – 2014 .................................................................................................. 78
EASTERN CAPE – 2015 .................................................................................................. 81
EASTERN CAPE – 2016 .................................................................................................. 83
GAUTENG PAPER – 2015 ............................................................................................... 84
GAUTENG PAPER – 2016 ............................................................................................... 88
GAUTENG PAPER – 2017 ............................................................................................... 91
GAUTENG PAPER – 2018 ............................................................................................... 93
2
,TOPIC 4: Analytical Geometry ........................................................................... 97
Relevant Formulae: ......................................................................................................... 97
Finding Equations Of Straight Lines............................................................................... 97
Special Lines ................................................................................................................... 98
Parallel and Perpendicular Lines .................................................................................... 99
Collinear points and Intersection lines ........................................................................ 100
Lines in triangles .......................................................................................................... 101
Angle of Inclination ...................................................................................................... 102
Departmental Examination papers with Memo ..............................................104
EASTERN CAPE – 2014 ................................................................................................ 104
EASTERN CAPE – 2015 ................................................................................................ 108
EASTERN CAPE – 2016 ................................................................................................ 111
GAUTENG PAPER – 2015 ............................................................................................. 114
GAUTENG PAPER – 2016 ............................................................................................. 117
GAUTENG PAPER – 2017 ............................................................................................. 122
GAUTENG PAPER – 2018 ............................................................................................. 125
TOPIC 5: Functions ...........................................................................................131
Straight Line function................................................................................................... 131
Parabolic function ........................................................................................................ 133
Hyperbolic function ..................................................................................................... 139
Exponential function .................................................................................................... 142
Departmental Examination papers with Memo ..............................................144
EASTERN CAPE – 2014 ................................................................................................ 144
EASTERN CAPE – 2015 ................................................................................................ 149
EASTERN CAPE – 2016 ................................................................................................ 153
GAUTENG PAPER – 2015 ............................................................................................. 155
GAUTENG PAPER – 2016 ............................................................................................. 161
GAUTENG PAPER – 2017 ............................................................................................. 165
GAUTENG PAPER – 2018 ............................................................................................. 170
TRIGONOMETRIC FUNCTIONS .................................................................................... 176
TOPIC 6: Trigonometry – reduction formulae, special angle, identities and
equations ..........................................................................................................183
Trigonometry Identities: .............................................................................................. 184
Reduction formulas: ..................................................................................................... 184
Using a given diagram to evaluate expressions: .......................................................... 186
Problems that require you to sketch your own diagram ............................................. 188
Proving Trig Identities ................................................................................................. 189
General Solution of a function: .................................................................................... 191
Departmental examinations papers with Memos ...........................................195
EASTERN CAPE -2014 .................................................................................................. 195
EASTERN CAPE – 2015 ................................................................................................ 199
3
, EASTERN CAPE – 2016 ................................................................................................ 201
GAUTENG PAPER – 2015 ............................................................................................. 204
GAUTENG PAPER – 2016 ............................................................................................. 209
GAUTENG PAPER - 2017 .............................................................................................. 213
GAUTENG PAPER – 2018 ............................................................................................. 217
TOPIC 7: Measurement .....................................................................................223
Area formula of 2D shapes........................................................................................... 223
Volume and Surface area formula ................................................................................ 223
Multiplying by a scale factor ........................................................................................ 225
TOPIC 8: TRIGONOMETRY – Sine, cosine and area rules ...............................232
Solving problems involving triangles that have no right angles ................................. 234
Departmental Examination Questions with Memo .........................................241
EASTERN CAPE – 2014 ................................................................................................ 241
EASTERN CAPE – 2015 ................................................................................................ 243
EASTERN CAPE – 2016 ................................................................................................ 245
GAUTENG PAPER – 2015 ............................................................................................. 248
GAUTENG PAPER – 2016 ............................................................................................. 251
GAUTENG PAPER – 2017 ............................................................................................. 254
GAUTENG PAPER – 2018 ............................................................................................. 257
TOPIC 9: Euclidean geometry ..........................................................................261
Lines, parallel lines and triangles ................................................................................ 261
Circle Geometry ............................................................................................................ 263
SUMMARY ON CIRCLE GEOMETRY ............................................................................. 275
Departmental examinations papers with Memos ...........................................276
EASTERN CAPE -2014 .................................................................................................. 276
EASTERN CAPE – 2015 ................................................................................................ 282
EASTERN CAPE – 2016 ................................................................................................ 287
GAUTENG PAPER – 2015 ............................................................................................. 292
GAUTENG PAPER – 2016 ............................................................................................. 296
GAUTENG PAPER – 2017 ............................................................................................. 300
GAUTENG PAPER – 2018 ............................................................................................. 305
TOPIC 10: Financial Mathematics ....................................................................313
SIMPLE INTEREST .......................................................................................................... 313
COMPOUND INTEREST .................................................................................................. 314
NOMINAL AND EFFECTIVE INTEREST RATES ................................................................ 318
STRAIGHT LINE/ REDUCING BALANCE DEPRECIATION ................................................ 319
Departmental examinations papers with Memos ...........................................320
EASTERN CAPE – 2014 ................................................................................................ 320
EASTERN CAPE – 2015 ................................................................................................ 322
EASTERN CAPE – 2016 ................................................................................................ 323
4
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