LONGMAN MATHEMATICS for IGCSE Book 1

At the end of each unit is a useful revision and examination section

Unit / Name / Description / Page / Notes
1 / Number 1 / Fractions / 1 / Should all be revision, but worth a look
Directed numbers / 2
Percentages / 3
Standard Form / 5
Sig figs and dec places / 7
Algebra 1 / Collecting like terms / 10
Algebraic products / 12
Equations / 13
Graphs 1 / Gradients / 21
Y=mx+c / 24 / Introduces ax+by=c form
Shape and space 1 / Basic Principles / 31 / Done orally
Polygons / 32 / Revision
Constructions & Loci / 36 / Important work
Ruler and compass needed
Sets 1 / Basic ideas / 43 / Completely new, needs careful introduction
Venn diagrams / 46
2 / Number 2 / Standard form / 59
4 rules of fractions / 63 / Hopefully revision
Ratio / 64
Proportion / 66 / Mention inverse?
Algebra 2 / Fractions / 70 / Introduces algebraic fractions, but stress the method is the same as for numbers
Equations / 73 / Multiply by LCM to remove fractions
Formulae / 74
Indices / 79
Inequalities / 80
Graphs 2 / Simultaneous equations / 86
Inequalities / 88 / Students always struggle here
Shape and space 2 / Tangent of an angle / 95 / Stress labelling triangle o, a, h
Take care with angle of depression and elevation
Handling data 2 / Frequency tables / 105 / Simple work
Averages / 106
Displaying data / 108
3 / Number 3 / Percentage inc/dec / 119 / Important section
Multiples, factors, primes / 124 / All straightforward
HCF LCM / 126
Calculator work / 128
Algebra 3 / Factorising-common factor / 132
Algebraic fractions / 133
Equations with fractions / 134 / Multiply by LCD to remove denominators
Simultaneous equations / 137 / Use elimination not substitution
Graphs 3 / Travel graphs / 146
Shape & Space 3 / Sine and Cosine / 154 / Do plenty from the problems section
Handling Data 3 / Mean from freq tables / 168
Group boundaries / 170 / Take care here
4 / Number 4 / Inverse percentages / 183 / Always difficult, do not rush
Upper/lower bounds / 186
Estimating / 189
Algebra 4 / Change of subject / 194 / Students find this difficult, lots of examples needed
Circles / 198
Graphs 4 / Quadratics / 203
Solving quadratics graphically / 210
Shape and Space 4 / Circle Theorems / 214
Similar triangles / 226
Pythagoras / 234
Handling data 4 / Probability / 240
5 / Number 5 / Proportion / 257
Indices / 263
Recurring decimals / 264
Algebra 5 / Expanding brackets / 268 / No need for rectangle method
Factorising single ( ) and difference of 2 squares / 273 / Single bracket already done in Algebra 3
Factorising ( )( ) / 274 / X2 and only-X2 – give ax2 if you think they can handle it
Solving quadratics / 277
Sequences 5 / Continuing sequences / 283
Formulae for sequences / 285 / Nth term
Difference method / 287
Shape & Space 5 / Transformations / 295 / Make sure transformation is described completely
Combinations / 303
Enlargements / 305
Handling data 5 / Distributions / 313
Quartiles / 314
Cum. Freq. / 315 / Introduces quartiles

LONGMAN MATHEMATICS for IGCSE Book 2

At the end of each unit is a useful revision and examination section

Unit / Name / Description / Page / Notes
1 / Number 1 / Inverse proportion / 1 / Use reduction to unity method but mention formula method?
Recurring decimals / 5 / Standard method
Algebra 1 / Proportion / 9 / Use of formula and constant of proportionality
Graphs 1 / Cubics / 21 / Explain basic shapes – not just curves of y=x3 but also those with two turning points
Reciprocals / 24
Shape and space 1 / Congruence / 30 / Probably too formal for IGCSE but worth doing with better sets. Weaker students often struggle with formal proofs
Circles / 38 / Remind of old circle theorems
Alternate segment theorem / 43 / New theorem
Intersecting chord theorems / 49 / New theorems
Sets 1 / Revision / 57 / Definitely worth doing
Problems / 58
Shading Venn diagrams / 60 / Students find this difficult – even the good ones!
Set-Builder Notation / 62
2 / Number 2 / Negative and fractional indices / 72
Algebra 2 / Solving Quadratics - Factorising / 77 / All vital work
By the formula / 80
Problems / 83
Quadratic inequalities / 87 / By sketching the graph please
Graphs 2 / Solving equations / 91 / Introduces cubic equations later on
Shape and space 2 / Converting metric units / 105 / Straightforward – no need to do too much here, but take care with sq and cubed units
Circles, semi circles and quadrants / 110 / All fairly easy – no need to over do
Arcs and sectors of a circle / 115 / New work – for better sets talk about radians?
Surface areas and volumes / 124 / Introduces cones etc
Similar areas and volumes / 135 / Students often find this difficult
Handling data 2 / Compound probability / 152 / x and + laws and tree diagrams
3 / Number 3 / Leave this section out
Algebra 3 / Simultaneous equations / 188 / Algebraic solutions by substitution only
Functions / 196 / Calculating f(2) etc
Domain and range / 200 / Vital work
Composite functions / 204
Inverse functions / 207
Graphs 3 / Tangents to a curve / 212 / Links well with travel graphs
Shape and space 3 / Vectors / 224 / Lots of new ideas and notation to get across here – take your time
Handling data 3 / Histograms / 240 / Be able to work both ways and remember to give the key
4 / Number 4 / Irrational numbers / 258 / Not an easy topic for even the better students. Take time here.
Surds / 260
Rationalising the denominator / 266
Algebra 4 / Algebraic fractions / 269 / Always difficult – take your time here
Equations with fractions / 275 / Once again take your time – very difficult
Graphs 4 / Differentiation / 282 / Do not bother with p283 unless you have a very good set!
Tangents / 288 / All C1 work really – but still fine for all standards of student once they have learnt a few basic rules.
Max and min / 289
Motion of a particle / 296
Shape and space 4 / Trig ratios up to 180 / 302 / Use the graphs – possibly extend to 360 and beyond with better sets
Sine and Cosine rule / 305 / Omit the ambiguous case
Area of a triangle / 318
3D work / 320 / Definitely not easy – get them to draw a 2D diagram for each part
Handling data 4 / More probability / 329 / Harder questions from an earlier chapter
5 / Revision / This section can be used for revision of all topics covered if there is time