Cambridge IGCSE™ Mathematics Core and Extended
Suggested Scheme of Work
Cambridge IGCSE Core and Extended Mathematics – Core content
This Scheme of Work has been devised to follow a logical route through the textbook for students following the Core content of the syllabus and using the Core and
Extended textbook. Its aim is for students to complete the course by the end of the second term in the second year of study; this will then allow time for revision and
preparation for their exams. The chapters have been divided into fifteen blocks each with 14 hours of teaching time; this roughly equates to four weeks’ work, depending
upon individual timetables. The timings are generous to allow for some flexibility in this area.
If necessary, the blocks can be interchanged to allow for local conditions, preferences, etc. Where prior knowledge is required before starting a block, this is listed in the
‘Notes’ column in the Scheme of Work; please read this carefully to ensure necessary learning has taken place before attempting the work.
Similarly, the order in which each chapter is completed can be rearranged within each block if resources or timetabling dictates but, once again, some care needs to be
taken to ensure the necessary prior learning has taken place.
Please note that although the Core & Extended textbook covers all the Core syllabus content, this book is aimed particularly at students studying the Extended syllabus.
Our Cambridge IGCSE™ Core Mathematics Student’s Book provides a deeper level of support for the Core syllabus content and would be more suited for students
focusing on the Core syllabus only.
Cambridge International Education copyright material in this publication is reproduced under licence and remains the intellectual property of Cambridge International
Education.
This document has not been through the Cambridge International Education endorsement process.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
1
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 1: Total time 14 hours
Subject area
Chapter 1
Number and
language
Approx.
time
allocation Learning objectives © UCLES
Pages
Vocabulary
9 hours
Pages 4–12
cube number; cube root; Mystic Rose, Pages 102–104
factor; highest common This fully worked example
factor; integer; irrational takes students through the
number; lowest common process of carrying out a
multiple; multiple;
mathematical investigation and
natural number; negative the value of systematic
number; positive
working. Students should work
number; power; prime
through the problem and then
factor; prime number;
compare their methods with the
rational number;
worked solution.
reciprocal; square
Primes and squares, Page 104
number; square root
This is an investigation into
which prime numbers can be
written as the sum of two
squares.
C1.1 Types of number
Identify and use
 natural numbers
 integers (positive, zero and
negative)
 prime numbers
 square numbers
 cube numbers
 common factors
 common multiples
 rational and irrational numbers
 reciprocals.
C1.3 Powers and roots
Calculate with the following:
 squares
 square roots
 cubes
 cube roots
 other powers and roots of
numbers.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Mathematical investigations
and ICT
Notes
This chapter covers the
different types of number and
vocabulary that students need
to be familiar with.
In Exercise 1.6 (Page 8),
students need to recall some
work from Cambridge
Primary Lower Secondary
Mathematics including
Pythagoras’ theorem and the
formula for the circumference
and area of a circle.
This chapter covers noncalculator work as well as
giving the students the
opportunity to practice using
their calculator to find powers
and roots.
2
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 2
Accuracy
5 hours
C1.9 Estimation
Pages 13–19
1 Round values to a specified
degree of accuracy.
2 Make estimates for calculations
involving numbers, quantities
and measurements.
3 Round answers to a reasonable
degree of accuracy in the
context of a given problem.
accuracy; decimal place;
estimate; lower bound;
rounding; significant
figure; upper bound
C1.10 Limits of accuracy
Give upper and lower bounds for
data rounded to a specified
accuracy.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
This chapter involves
rounding to powers of 10,
decimal places and significant
figures. It also includes using
an appropriate degree of
accuracy and estimation. It is
important for students to use
estimation as a means of
checking their calculations.
In exercise 2.4 on Pages 16–
17, they need to find area and
volume of simple compound
2D and 3D shapes.
Remind students to round any
inexact answers to 3 s.f. Also
when working with angles,
give inexact angles correct to
1 d.p. – See Block 11 Chapter
25.
3
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 2: Total time 14 hours
Subject area
Chapter 3
Calculations
and order
Approx.
time
allocation Learning objectives © UCLES
6 hours
Pages
C1.5 Ordering
Pages 25–30
Order quantities by magnitude and
demonstrate familiarity with the
symbols =, ≠, >, < , ⩾, ⩽ .
Vocabulary
addition; division;
indices; inequality;
multiplication; order of
operations; subtraction
C1.6 The four operations
Use the four operations for
calculations with integers,
[fractions and decimals] including
correct ordering of operations and
use of brackets.
Mathematical investigations
and ICT
Football leagues, Page 104
Students use systematic
working to investigate how
many games there are in total
when t teams play each other
twice.
Notes
This chapter focuses on
ordering decimals and
fractions, and order of
operations with integers in
C1.6.
Content in square brackets is
covered in Chapter 4.
C2.6 Inequalities
Represent and interpret
inequalities, including on a number
line.
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4
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 35
4 hours
Mean, median,
mode and range
C9.2 Interpreting statistical data
Pages 506–508 average; discrete data;
and 510
frequency; grouped
1 Read, interpret and draw
frequency table; mean;
inferences from tables and
median; modal class;
statistical diagrams.
mode; range
2 Compare sets of data using
tables, graphs and statistical
measures.
3 Appreciate restrictions on
drawing conclusions from given
data.
Students learn about measures
of spread and types of
average. They learn to
calculate averages for raw,
frequency and grouped data
and how to determine which
average is the most suitable
for a given data set.
The Student assessment
material on Page 510 is
suitable for Core students.
Note the mean for grouped
data on Pages 509–510 is for
students following the
Extended syllabus.
C9.3 Averages and range
Calculate the mean, median, mode,
and range for discrete data and
distinguish between the purposes
for which these are used.
Chapter 26
Measures
4 hours
C5.1 Units of measure
Use metric units of mass, length,
area, volume and capacity in
practical situations and convert
quantities into larger or smaller
units.
Pages 350–354 area; capacity;
centimetre; gram;
kilogram; kilometre;
length; litre; mass;
metre; millilitre;
millimetre; volume
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Metal trays, Page 388
This is an investigation into a
maximum box for the same
surface area.
This chapter focuses on units
and conversions.
5
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 3: Total time 14 hours
Subject area
Chapter 4
Integers,
fractions,
decimals and
percentages
Approx.
time
allocation Learning objectives © UCLES
Pages
Vocabulary
8 hours
Pages 31–39
decimal; denominator;
Hidden treasure, Pages 286–
equivalent fraction;
287
fraction; improper
Students explore an algorithm
fraction; mixed number; to work out which contestant in
numerator; order of
a game show will win the
operations; percentage; hidden treasures.
proper fraction; recurring
decimal; simplest form
C1.4 Fractions, decimals and
percentages
1 Use the language and notation
of the following in appropriate
contexts:
 proper fractions
 improper fractions
 mixed numbers
 decimals
 percentages.
2 Recognise equivalence and
convert between these forms.
Mathematical investigations
and ICT
Notes
In this chapter, C1.6 is
revisited.
In Block 1, Chapter 3 on
Pages 25–30, students learnt
C1.6.
This objective is revisited to
include a greater focus on
non-calculator methods when
working with larger integers
and calculations with
fractions.
Content in square brackets is
covered in Block 2 Chapter 3.
C1.6 The four operations
Use the four operations for
calculations with [integers,]
fractions and decimals, including
correct ordering of operations and
use of brackets.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
6
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 11
Algebraic
representation
and
manipulation
6 hours
C2.1 Introduction to algebra
1 Know that letters can be used to
represent generalised numbers.
2 Substitute numbers into
expressions and formulas.
Pages 108–112 algebraic fraction;
and 113
bracket; expand;
Exercise 11.7 expression; factorise;
Q.1 and 2
formula; quadratic
expression; subject
C2.2 Algebraic manipulation
1 Simplify expressions by
collecting like terms.
2 Expand products of algebraic
expressions.
3 Factorise by extracting common
factors.
C2.5 Equations
4 Change the subject of formulas.
Chapter 11 is split between
Block 3 and Block 7. In this
first section, there is a focus
on expanding brackets, simple
factorisation, substitution into
formulas and changing the
subject of a simple formula.
The rest of C2.5 is covered in
Block 5, chapter 13:
1 Construct expressions,
equations and formulas.
2 Solve linear equations in
one unknown.
3 Solve simultaneous linear
equations in two
unknowns.
C2.5.4 is also covered later in
Block 7, Chapter 11.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
7
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 4: Total time 14 hours
Subject area
Chapter 22
Geometrical
vocabulary and
construction
Approx.
time
allocation Learning objectives © UCLES
4 hours
C4.1 Geometrical terms
1 Use and interpret the
geometrical terms:
 point
 vertex
 line
 parallel
 perpendicular
 bearing
 right angle
 acute, obtuse and reflex
angles
 interior and exterior angles
 similar
 congruent
 scale factor.
2 Use and interpret the
vocabulary of:
 triangles
 special quadrilaterals
 polygons
 nets
 simple solids.
3 Use and interpret the
vocabulary of a circle.
Pages
Vocabulary
Mathematical investigations
and ICT
Pages 290–295 acute; bearing; centre;
Fountain borders, Page 345
circle; circumference;
This investigation looks at the
cone; congruent;
number of tiles needs to border
construction; cube;
different sized fountains.
cuboid; cylinder;
Students need to work
decagon; diameter; edge; systematically to solve the
equilateral triangle;
problem.
exterior angle; face;
frustum; hemisphere;
hexagon; interior angle;
irregular polygon;
isosceles triangle; kite;
line; net; obtuse and
reflex angles; octagon;
parallel; parallelogram;
pentagon; perpendicular;
perpendicular bisector;
plane; point; polygon;
prism; pyramid;
quadrilateral; radius
(plural radii); rectangle;
regular polygon;
rhombus; right angle;
right-angled triangle;
scale factor; scalene
triangle; similar; solid
shape; sphere; square;
surface; trapezium;
vertex; semi-circle
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Notes
This chapter is an introduction
to geometrical vocabulary and
properties of shapes.
Part of C4.3 is covered in
Block 11, Chapter 28:
2 Use and interpret threefigure bearings.
Chapter 22 is also in Block 5
where nets, constructions and
scale drawings are covered.
C4.3 Scale drawings
1 Draw and interpret scale
drawings.
8
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 23
Similarity and
congruence
3 hours
C4.4 Similarity
Pages 301–303 congruent; scale factor;
Calculate lengths of similar shapes.
similar
ICT activity 1, Pages 346–347
Students use a geometry
package to investigate the ratio
of corresponding sides in
similar triangles.
It is important that students
have a sound grasp of
similarity before they tackle
trigonometry in Block 11.
Chapter 7
Indices,
standard form
and surds
7 hours
C1.7 Indices I
1 Understand and use indices
(positive, zero, negative, and
fractional).
2 Understand and use the rules of
indices.
Towers of Hanoi, Pages 440–
441
Students investigate the classic
problem of the Towers of
Hanoi.
The rule for the number of
moves to move n discs is 2𝑛 −
1.
Core students are only
expected to calculate with
standard form on the
calculator paper.
Pages 63–68
index; powers; rules of
Student
indices; standard form
assessment 1
and 2 on Pages
76–77
C1.8 Standard form
1 Use the standard form A × 10n
where n is a positive or negative
integer, and 1 ⩽ A < 10.
2 Convert numbers into and out of
standard form.
3 Calculate with values in
standard form.
C2.4 Indices II
1 Understand and use indices
(positive, zero, negative and
fractional).
2 Understand and use the rules of
indices.
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9
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 5: Total time 14 hours
Subject area
Approx.
time
allocation Learning objectives © UCLES
Chapter 22
10 hours
Geometrical
vocabulary and
construction
C4.1 Geometrical terms
1 Use and interpret the geometrical terms:
 point
 vertex
 line
 parallel
 perpendicular
 bearing
 right angle
 acute, obtuse and reflex angles
 interior and exterior angles
 similar
 congruent
 scale factor.
2 Use and interpret the vocabulary of:
 triangles
 special quadrilaterals
 polygons
 nets
 simple solids.
3 Use and interpret the vocabulary of a circle.
Pages
Vocabulary
Pages 295–
300
acute; bearing; centre;
circle; circumference;
cone; congruent;
construction; cube;
cuboid; cylinder;
decagon; diameter; edge;
equilateral triangle;
exterior angle; face;
frustum; hemisphere;
hexagon; interior angle;
irregular polygon;
isosceles triangle; kite;
line; net; obtuse and
reflex angles; octagon;
parallel; parallelogram;
pentagon; perpendicular;
perpendicular bisector;
plane; point; polygon;
prism; pyramid;
quadrilateral; radius
(plural radii); rectangle;
regular polygon;
rhombus; right angle;
right-angled triangle;
scale factor; scalene
triangle; similar; solid
shape; sphere; square;
C4.2 Geometrical constructions
1 Measure and draw lines and angles.
2 Construct a triangle, given length of all sides,
using a ruler and pair of compasses only.
3 Draw, use and interpret nets.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Mathematical
investigations and
ICT
Notes
Chapter 22 is also covered
in Block 4 which must be
completed first.
This chapter is an
opportunity to revise
geometrical vocabulary and
properties of shapes. It also
covers constructions of
triangles and scale drawings.
C4.3.2 is covered in Block
11, Chapter 28.
10
Cambridge IGCSE™ Mathematics Core and Extended
C4.3 Scale drawings
1
Draw and interpret scale drawings.
Chapter 12
Algebraic
indices
4 hours
C2.4 Indices II
1 Understand and use indices (positive, zero
and negative).
2 Understand and use the rules of indices.
surface; trapezium;
vertex
Pages 128–
129
Student
assessment 1
on Page 131
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
index; powers; rules of
indices
Chequered boards,
Block 4 must be completed
Page 254
first.
This is an
investigation into the
total number of black
and white squares on
an m by n chequered
board. It is a
variation of the
problem ‘How many
square are there on a
chess board?’
11
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 6: Total time 14 hours
Subject area
Chapter 36
Collecting,
displaying and
interpreting
data
Approx.
time
allocation Learning objectives © UCLES
14 hours
C9.1 Classifying statistical data
Classify and tabulate statistical data.
C9.2 Interpreting statistical data
1 Read, interpret and draw inferences
from tables and statistical diagrams.
2 Compare sets of data using tables,
graphs and statistical measures.
3 Appreciate restrictions on drawing
conclusions from given data.
Page
Vocabulary
Pages
bar chart; class width;
512–514 composite bar chart;
and 515– correlation; dual bar chart;
528
frequency density; grouped
Student
frequency table; histogram;
assessment line of best fit; pictogram;
1 Qs1–3
pie chart; scatter diagram;
on Pages stem and leaf; tally table;
533–534 two-way table
Mathematical
investigations and ICT
Notes
This chapter focuses on the
collection, display and
interpretation of data. The
material on grouped data and
Histograms is for students
following the Extension
syllabus only.
C9.4 Statistical charts and diagrams
Draw and interpret:
(a) bar charts
(b) pie charts
(c) pictograms
(d) stem-and-leaf diagrams
(e) simple frequency distributions
C9.5 Scatter diagrams
1 Draw and interpret scatter diagrams.
2 Understand what is meant by positive,
negative and zero correlation.
3 Draw by eye, interpret and use a
straight line of best fit.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
12
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 7: Total time 14 hours
Subject area
Chapter 11
Algebraic
representation
and
manipulation
Approx.
time
allocation Learning objectives © UCLES
3 hours
C2.1 Introduction to algebra
1 Know that letters can be used to
represent generalised numbers.
2 Substitute numbers into
expressions and formulas.
C2.2 Algebraic manipulation
1 Simplify expressions by
collecting like terms.
2 Expand products of algebraic
expressions.
3 Factorise by extracting common
factors.
Page
Vocabulary
6 hours
C2.5 Equations
1 Construct simple expressions,
equations and formulas.
2 Solve linear equations in one
unknown.
3 Solve simultaneous linear
equations in two unknowns.
Notes
Pages 118–120 algebraic fraction;
Student
bracket; expand;
assessment 1
expression; factorise;
and 2, and Q.1 formula; quadratic
from Student expression; subject
assessment 3
on Pages 124–
126
This is an opportunity to
revisit the earlier Block 3
work on algebra. Pages 118–
120 further the work on
rearranging formulas. Use the
Student assessments for
consolidation.
Chapter 11 Pages 108–113 is
also covered in Block 3.
The rest of C2.5 is covered in
Chapter 13:
1 Construct simple
expressions, equations and
formulas.
2 Solve linear equations in
one unknown.
3 Solve simultaneous linear
equations in two
unknowns.
Pages 132–143 completing the square;
Student
elimination; inequality;
assessments 1 linear equation;
and 2 Pages
quadratic equation;
150–151
quadratic formula;
simultaneous equation;
substitution
Block 6 must be completed
first.
The rest of C2.5 is covered in
Blocks 3 and 7, Chapter 11:
4 Change the subject of
simple formulas.
C2.5 Equations
4 Change the subject of simple
formulas.
Chapter 13
Equations and
inequalities
Mathematical investigations
and ICT
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
13
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 6
Ratio and
proportion
5 hours
C1.11 Ratio and proportion
Pages 53–162
Understand and use ratio and
proportion to:
 give ratios in their simplest
form
 divide a quantity in a given ratio
 use proportional reasoning and
ratios in context.
average speed;
compound measure;
density; direct
proportion; inverse
proportion; population
density; pressure; rate;
ratio
ICT activity 2 Page 105
Students use a graphing
package to investigate
velocities at different points of
a 100 m sprint.
This chapter involves solving
problems involving direct and
inverse proportion and the use
of compound measures.
C1.12 Rates
1 Use common measures of rate.
2 Apply other measures of rate.
3 Solve problems involving
average speed.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
14
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 8: Total time 14 hours
Subject area
Chapter 15
Sequences
Approx.
time
allocation Learning objectives © UCLES
3 hours
C2.7 Sequences
1 Continue a given number
sequence or pattern.
2 Recognise patterns in
sequences, including the termto-term rule, and relationships
between different sequences.
3 Find and use the nth term of
sequences:
(a) linear
(b) simple quadratic
(c) simple cubic.
Pages
Vocabulary
Pages 157–159 cubic; exponential
and 161–164
sequence; linear
Student
sequence; nth term;
assessment 1
quadratic; term-to-term
on Pages 168- rule
169
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Mathematical investigations
and ICT
House of cards, Page 254
Students can explore the
sequences produced from
building houses of cards.
Notes
Subscript notation is on the
Extended syllabus only.
Students following the Core
syllabus will work with simple
quadratic and cubic sequences
only.
15
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 27
Perimeter, area
and volume
11 hours
C5.2 Area and perimeter
Carry out calculations involving
the perimeter and area of a
rectangle, triangle, parallelogram
and trapezium.
C5.3 Circles, arcs and sectors
1 Carry out calculations involving
the circumference and area of a
circle.
2 Carry out calculations involving
arc length and sector area as
fractions of the circumference
and area of a circle, where the
sector angle is a factor of 360°.
Pages 355–
370, 372–380
and 383–387
arc; area; circumference; Tennis balls, Pages 388–389
compound shape; cone; This is an investigation into a
cuboid; cylinder;
packing problem involving 12
diameter; frustrum;
tennis balls.
parallelogram;
ICT activity, Page 389
perimeter; prism;
This is an ICT investigation in
pyramid; radius;
which students find the
rectangle; sector; sphere; maximum volume cone made
surface area; trapezium; from a sector with a fixed
triangle; volume
radius.
Answers may be need to be
given in terms of .
Formulae for
 curved surface area of a
cone;
 surface area of a sphere;
 volume of a sphere;
 volume of a pyramid;
 volume of a cone;
will be given.
C5.4 Surface area and volume
Carry out calculations and solve
problems involving the surface area
and volume of a:
 cuboid
 prism
 cylinder
 sphere
 pyramid
 cone.
C5.5 Compound shapes and parts
of shapes
1 Carry out calculations and solve
problems involving perimeters
and areas of:
 compound shapes
 parts of shapes.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
16
Cambridge IGCSE™ Mathematics Core and Extended
2 Carry out calculations and solve
problems involving surface
areas and volumes of:
 compound solids
 parts of solids.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
17
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 9: Total time 14 hours
Subject area
Chapter 25
Angle
properties
Approx.
time
allocation Learning objectives © UCLES
14 hours
Pages
Vocabulary
C4.6 Angles
Pages 322–330 alternate angles; centre;
circumference;
1 Calculate unknown angles and
corresponding angles;
give simple explanations using
cyclic quadrilateral;
the following geometrical
exterior angle; interior
properties:
angle; parallel; polygon;
 sum of angles at a point =
radius; segment;
360°
semicircle;
 sum of angles at a point on a
supplementary; tangent;
straight line = 180°
vertically opposite
 vertically opposite angles are
angles
equal
 angle sum of a triangle =
180° and angle sum of a
quadrilateral = 360°.
2 Calculate unknown angles and
give geometric explanations for
angles formed within parallel
lines:
 corresponding angles are
equal
 alternate angles are equal
 co-interior (supplementary)
angles sum to 180°.
3 Know and use angle properties
of regular polygons.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Mathematical investigations
and ICT
Notes
Material from Chapter 25 on
Circle theorems are covered in
Block 15.
18
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 10: Total time 14 hours
Subject area
Approx.
time
allocation Learning objectives © UCLES
Pages
Vocabulary
complement; element;
empty set; intersection;
set; subset; union;
universal set; Venn
diagram
Mathematical investigations
and ICT
Chapter 10
5 hours
Set notation and
Venn diagrams
C1.2 Sets
Understand and use set language,
notation and Venn diagrams to
describe sets and represent
relationships between sets.
Definition of sets
e.g.
A = {x: x is a natural number}
B = {(x, y): y = mx + c}
C = {x: a ⩽ x ⩽ b}
D = {a, b, c, …}
Pages 92–96
and 98–100
Chapter 33
Probability
C8.1 Introduction to probability
1 Understand and use the
probability scale from 0 to 1.
2 Calculate the probability of a
single event.
3 Understand that the probability
of an event not occurring = 1 –
the probability of the event
occurring.
Pages 480–490 event; expected
ICT activity: Buffon’s needle
frequency; outcome;
experiment, Page 503
probability scale; relative Buffon’s needle is a classic
frequency; Venn
probability experiment used to
diagram
produce an estimate for .
5 hours
Notes
Numbered balls Page 440
Venn diagrams will be limited
Students investigate number
to two sets only.
sequences using the rule:
If the last term was even: divide
by 2 to find the next term
If the last term was odd: add 1
to find the next term
Students need to study
Chapter 33 before they study
probability further in Block
10, Chapter 34
C8.2 Relative and expected
frequencies
1 Understand relative frequency
as an estimate of probability.
2 Calculate expected frequencies.
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19
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 34
Further
probability
4 hours
C8.3 Probability of combined
events
Calculate the probability of
combined events using, where
appropriate:
 sample space diagrams
 Venn diagrams
 tree diagrams.
Pages 491–495 conditional probability;
and Student
event; outcome;
assessment1
probability; sample
on Pages 499– space diagram; tree
500
diagram; Venn diagram
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Probability drop, Page 501
An investigation into Pascal’s
triangle.
Students study combined
events, conditional probability
is extension content only.
20
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 11: Total time 14 hours
Approx.
time
allocation Learning objectives © UCLES
Pages
Vocabulary
Chapter 28
Bearings
3 hours
C4.3 Scale drawings
2 Use and interpret three-figure
bearings.
Page 392
three-figure bearings
The rest of C4.3 is covered
in Chapter 22:
1 Draw and interpret scale
drawings.
Chapter 29
Trigonometry
11 hours
C6.1 Pythagoras’ theorem
Know and use Pythagoras’
theorem.
Pages 394–405
adjacent; cosine;
Student assessment depression; elevation;
1 and 2 on Pages
hypotenuse; opposite;
417–419
Pythagoras’ theorem;
sine; tangent
Block 10 must be completed
first.
Angles will be given in
degrees. Answers should be
written in degrees and
decimals to one decimal
place.
Subject area
C6.2 Right-angled triangles
1 Know and use the sine, cosine
and tangent ratios for acute
angles in calculations involving
sides and angles of a rightangled triangle.
2 Solve problems in two
dimensions using Pythagoras’
theorem and trigonometry.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Mathematical
investigations and ICT
Notes
21
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 12: Total time 14 hours
Subject area
Chapter 4
Integers,
fractions,
decimals and
percentages
Approx.
time
allocation Learning objectives © UCLES
2 hours
C1.4 Fractions, decimals and
percentages
1 Use the language and notation
of the following in appropriate
contexts:
 proper fractions
 improper fractions
 mixed numbers
 decimals
 percentages.
2 Recognise equivalence and
convert between these forms.
Pages
Vocabulary
Pages 40–41
and 44
decimal; denominator;
equivalent fraction;
fraction; improper
fraction; mixed number;
numerator; order of
operations; percentage;
proper fraction; recurring
decimal; simplest form
Mathematical investigations
and ICT
Notes
Students have already studied
the rest of this chapter in
Block 3.
Work on Pages 40–42 is on
converting between fractions
and decimals.
Use questions 1–8 of the
Student assessment on Page
44 as revision of all the work
on integers, fractions,
decimals and percentages.
C1.6 The four operations
Use the four operations for
calculations with integers, fractions
and decimals, including correct
ordering of operations and use of
brackets.
Chapter 5
Further
percentages
4 hours
C1.13 Percentages
Pages 45–50
percentage; percentage
increase / decrease;
1 Calculate a given percentage of Student
assessment 1
reverse percentage
a quantity.
and 2 on Pages
2 Express one quantity as a
51–52
percentage of another.
3 Calculate percentage increase or
decrease.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
Blocks 1, 4 and 10 must be
completed first.
Part of C1.13 is covered in
Block 12, Chapter 8:
4 Calculate with simple and
compound interest.
22
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 8
Money and
finance
8 hours
C1.13 Percentages
Pages 79–88
1 Calculate a given percentage of
a quantity.
2 Express one quantity as a
percentage of another.
3 Calculate percentage increase or
decrease.
4 Calculate with simple and
compound interest.
compound interest; cost
price; currency
conversion; deposit;
depreciation; discount;
earnings; exponential
decay; exponential
growth; profit and loss;
selling price; simple
interest
ICT activity 1 Page 105
In this activity students
investigate how the share price
of their chosen company
changes over time.
It is important that students
are confident with the work
from Chapter 5 before moving
onto this chapter.
C1.14 Using a calculator
1 Use a calculator efficiently.
2 Enter values appropriately on a
calculator.
3 Interpret the calculator display
appropriately.
C1.16 Money
1 Calculate with money.
2 Convert from one currency to
another.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
23
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 13: Total time 14 hours
Subject area
Chapter 21
Straight-line
graphs
Approx.
time
allocation Learning objectives © UCLES
11 hours
C3.1 Coordinates
Use and interpret Cartesian
coordinates in two dimensions.
Pages
Pages 258–
260, 265–271
and 273
Student
C3.2 Drawing linear graphs
assessment 1
Draw straight-line graphs for linear on Pages 282–
equations.
283
Vocabulary
axes; bisector;
coordinates; gradient;
intercept; midpoint;
origin; parallel;
perpendicular; segment
Mathematical investigations
and ICT
Notes
Block 2 must be completed
first.
C3.3 Gradient of linear graphs
Find the gradient of a straight line.
C3.5 Equations of linear graphs
Interpret and obtain the equation of
a straight-line graph in the form
𝑦 = 𝑚𝑥 + 𝑐.
C3.6 Parallel lines
Find the gradient and equation of a
straight line parallel to a given line.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
24
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 9
Time
3 hours
C1.14 Using a calculator
1 Use a calculator efficiently.
2 Enter values appropriately on a
calculator.
3 Interpret the calculator display
appropriately.
Pages 89–91
12-hour clock; 24-hour
clock; distance; speed;
time
Painted cube Page 475
Students investigate how many
faces of small cubes making up
a larger cube are painted when
the outside of the larger cube is
painted.
Ensure students understand
that say 1.25 hours is not 1
hour 25 minutes.
Students may need to solve
problems involving different
time zones.
C1.15 Time
1 Calculate with time: seconds
(s), minutes (min), hours (h),
days, weeks, months, years,
including the relationship
between units.
2 Calculate times in terms of the
24-hour and 12-hour clock.
3 Read clocks and timetables.
Cambridge IGCSE Mathematics Core and Extended Fifth edition © Hodder & Stoughton Limited 2023
25
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 14: Total time 14 hours
Subject area
Chapter 24
Symmetry
Approx.
time
allocation Learning objectives © UCLES
4 hours
Chapter 32
10 hours
Transformations
Pages
Vocabulary
C4.5 Symmetry
Pages 314–315 bisector; centre; tangent;
Recognise line symmetry and order Q.1 and
chord; cone; cylinder;
of rotational symmetry in two
Student
equidistant; line
dimensions.
assessment on symmetry; order of
Page 321 Q.1 rotational symmetry;
perpendicular; prism;
pyramid; rotational
symmetry
Mathematical investigations
and ICT
Notes
Tiled walls, Page 346
Students can investigate the
number of spacers (T shaped or
+ shaped) used to separate the
tiles in different tiling patterns.
C7.1 Transformations
Pages 456–457 clockwise; enlargement; Triangle count, Pages 476–477 Students need to know that
Recognise, describe and draw the and 459–467
reflection; rotation; scale Students investigate the number horizontal lines are in the form
following transformations:
Student
factor; transformation;
of triangles formed when a
y = a and vertical lines are in
assessment 1
translation; vector;
larger triangle is divided
the form x = b.
1 reflection of a shape in a
and 2 on Pages vertex
according to two different
vertical or horizontal line.
471–472
rules.
2 rotation of a shape about the
origin, vertices or midpoints of
edges of the shape, through
multiples of 90°.
3 enlargement of a shape from a
given centre by a given scale
factor.
4 translation of a shape by a given
𝑥
vector (𝑦).
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26
Cambridge IGCSE™ Mathematics Core and Extended
Resources in Cambridge IGCSE Core and Extended Mathematics Fifth Edition
Block 15: Total time 14 hours
Subject area
Approx.
time
allocation Learning objectives © UCLES
Pages
Vocabulary
Chapter 17
Graphs in
practical
situations
5 hours
C2.9 Graphs in practical situations
1 Use and interpret graphs in
practical situations including
travel graphs and conversion
graphs.
2 Draw graphs from given data.
Pages 176–181 conversion graph;
Student
distance; distance–time
assessment 1
graph; gradient; speed;
on Page 192
time; travel graph
Chapter 18
Graphs of
functions
6 hours
C2.10 Graphs of functions
1 Construct tables of values, and
draw, recognise and interpret
graphs for functions of the
forms:
 𝑎𝑥 + 𝑏
 ±𝑥 2 + 𝑎𝑥 + 𝑏
𝑎
 𝑥 (𝑥 ≠ 0)
where a and b are integer
constants.
2 Solve associated equations
graphically, including finding
and interpreting roots by
graphical methods.
Pages 197–
200, 202 –203,
205–206 and
212–214
Student
assessment 1
on Page 220
Mathematical investigations
and ICT
Notes
Blocks 8 and 11 must be
completed first.
intersection; linear
function; quadratic
function; reciprocal
function; root;
simultaneous equations;
symmetry
C2.11 Sketching curves
Recognise, sketch and interpret
graphs of the following functions:
(a) linear
(b) quadratic.
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27
Cambridge IGCSE™ Mathematics Core and Extended
Chapter 25
Angle
properties
3 hours
C4.6 Angles
Pages 331–333 alternate angles; cointerior angles;
1 Calculate unknown angles and Student
corresponding angles;
give simple explanations using assessment 1
on Pages 340– exterior angle; interior
the following geometrical
341
angle; parallel; polygon;
properties:
radius; semi-circle;
 sum of angles at a point =
supplementary; tangent;
360°
vertically opposite
 sum of angles at a point on a
angles
straight line = 180°
 vertically opposite angles are
equal
 angle sum of a triangle =
180° and angle sum of a
quadrilateral = 360°.
2 Calculate unknown angles and
give geometric explanations for
angles formed within parallel
lines:
 corresponding angles are
equal
 alternate angles are equal
 co-interior (supplementary)
angles sum to 180°.
3 Know and use angle properties
of regular polygons.
The focus here is on circle
theorems but angle
properties were also
covered in Block 9 and this
is an opportunity to review
that work.
C4.7 Circle theorems
Calculate unknown angles and give
explanations using the following
geometrical properties of circles:
 angle in a semi-circle = 90°
 angle between tangent and
radius = 90°.
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28