IGCSE Mathematics – SIS units of learning
Student resources:
● Hodder textbooks – all students will have their own copy of the Hodder Student Book (electronic version) which is valid for the two
years of IGCSE. References in the table below will point you to the relevant chapters for each unit.
● www.myimaths.com (username: island password: minus) – this website is not just for homework, students are able to attempt
questions and view lessons to support their learning outside of lessons. It is great for reviewing a topic at home.
● www.mangahigh.com (School ID: 40417) - this website has lots of games and activities to support learning beyond the lesson.
● www.drfrostmaths.com – this website has lots of practice and teaching videos.
● www.mrcartermaths.com – this website provides a lot of skill practice.
Topics covered previously in Year 9 to be re-visited at appropriate times throughout Y10 and Y11:
YEAR 9:
Unit 0. Number Skills (Fractions, Decimals and Rounding)
- Chapter 1
Unit 1. Sequences
- Chapter 9
Unit 2. Coordinate Geometry
- Chapters 5, 6, 10
Unit 3. Systems of Linear Equations
- Chapters 7, 8
Unit 4. Probability
- Chapters 18, 20
Unit 5. Pythagoras and Right Triangle Trigonometry
- Chapters 15, 16
Topics covered in Years 10 & 11:
Students on the Extended and Standard Courses will cover all outcomes in this document (classes 201-208).
The Foundation Course students (class 209) will only cover the concepts printed in black. You can find detailed information about the SIS
classes and pathways at www.sis.edu.hk > Learning at SIS > Learning pathways > Mathematics.
YEAR 10
Unit 1. Number Skills
Unit 2. Non-Linear Algebra
Unit 3. Advanced Algebra
Unit 4. Geometry
Unit 5. Circle Theorems
YEAR 11
Unit 6. Trigonometry II
Unit 7: Functions
Unit 8: Calculus
Unit 9: Statistics
Unit 10: Vectors
YEAR 10 Unit 1. Number Skills
Objectives
Themes
1.1. Ratios and
Percentages
Chapter 2
Recurring
Decimals
(Section 1.3)
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Use ratio notation, including reduction to its simplest form and its various links to
fraction notation
Divide a quantity in a given ratio or ratios
Solve word problems using ratio
Understand that ‘percentage’ means ‘number of parts per 100’
Express a given number as a percentage of another number
Express a percentage as a fraction and as a decimal
Convert between recurring decimals and fractions using an algebraic method
Understand the multiplicative nature of percentages as operators
Solve simple percentage problems, including percentage increase and decrease
Use reverse percentages
Use compound interest and depreciation
Use repeated percentage change
Solve compound interest problems
Examples
Express in the form 1 : n
Share £416 in the ratio 5 : 3 or 4 : 3 : 1
s varies directly as t
Including maps and scale diagrams
15% of 120 = 15/100 120
In a sale, prices were reduced by 30%. The
sale price of an item was £17.50 Calculate
the original price of the item
Calculate the total percentage increase
when an increase of 30% is followed by a
decrease of 20%
1.2. Powers and
Roots and
Standard Form
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Chapter 3
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Identify square numbers and cube numbers
Calculate squares, square roots, cubes and cube roots
Use index notation and index laws for multiplication and division of positive and
negative integer powers including zero
Express integers as a product of powers of prime factors
Find highest common factors (HCF) and lowest common multiples (LCM)
Use index notation for positive and negative integer powers (including zero)
Use index laws in simple cases
Use index laws to simplify and evaluate numerical expressions involving integer,
fractional and negative powers
Use index notation involving fractional, negative and zero powers
Calculate with and interpret numbers in the form a × 10n where n is an integer and
1 ≤ a ≤ 10
Solve problems involving standard form
720 = 24 × 32 × 5
150 000 000 = 1.5 × 108
1.3. Direct and
Inverse
Proportions
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Use the process of proportionality to evaluate unknown quantities
Calculate an unknown quantity from quantities that vary in direct proportion
Solve word problems using proportion
Set up problems involving direct or inverse proportion and relate algebraic solutions
to graphical representation of the equations
s varies directly as t Find the missing value
in a table
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Identify upper and lower bounds where values are given to a degree of accuracy
Solve problems using upper and lower bounds where values are given to a degree of
accuracy
The dimensions of a rectangle are 12 cm
and 8 cm to the nearest cm Calculate, to 3
significant figures, the smallest possible
area as a percentage of the largest possible
area
Chapter 21
1.4 Upper and
Lower Bounds
Upper and
Lower Bounds
(Section 1.6)
Unit 2. Non-Linear Algebra
Objectives
Themes
2.1
Working
with
Algebra
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Understand that symbols may be used to represent numbers in equations or
variables in expressions and formulae
Understand that algebraic expressions follow the generalised rules of arithmetic
Use index laws in simple cases
Chapter 4
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Evaluate expressions by substituting numerical values for letters, substitute positive
and negative integers, decimals and fractions for words and letters in expressions
and formulae
Collect like terms
Multiply a single term over a bracket, expand the product of two or more linear
expressions
Take out common factors
Expand the product of two simple or more linear expressions
Understand the concept of a quadratic expression and be able to factorise such
expressions (ie: ax2 + bx + c, where a = 1), including where a ≠ 1
Manipulate algebraic fractions where the numerator and/or the denominator can be
numeric, linear or quadratic
Complete the square for a given quadratic expression
Use algebra to support and construct proofs
Examples
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2.2 Quadratic
Equations and
Inequalities
Use correct notational conventions for algebraic expressions and formulae
Use formulae from mathematics and other real-life contexts expressed initially in
words or diagrammatic form and convert to letters and symbols
Derive a formula or expression
Change the subject of a formula where the subject appears once
Solve x2 + x – 30 = 0
2x2 – 3x + 1 = 0, x(3x – 2) = 5
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Solve quadratic equations by factorisation (ie: ax2 + bx + c, where a = 1), including where
a≠ 1
Solve quadratic equations by using the quadratic formula or completing the square
Form and solve quadratic equations from data given in a context
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Interpret information presented in a range of linear and non-linear graphs
Recognise, generate points, plot and draw graphs with the equation: y = ax2 + bx +c
To include speed/time and distance/time
graphs
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Solve quadratic inequalities in one unknown and represent the solution set on a number
line
x2 ≤ 25, 4x2 > 25, x2 + 3x + 2 > 0
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Chapter 22
Unit 3. Advanced Algebra (Higher Tier Only)
Objectives
Themes
3.1 Working
with surds
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Understand the meaning of surds
Manipulate surds, including rationalising a denominator
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Manipulate algebraic fractions where the numerator and/or the denominator can be
numeric, linear or quadratic
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Solve simultaneous equations in two unknowns, one equation being linear and the other
being quadratic
Chapter 23
3.2 Algebraic
fractions
Chapter 23
3.3
Simultaneo
us
equations,
linear +
quadratic
Chapter 23
Examples
3.5 Changing
the subject of
an equation
where the
symbol occurs
twice
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Understand the process of manipulating formulae or equations to change the subject, to
include cases where the subject may appear twice or a power of the subject occurs
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Use algebra to support and construct proofs
Chapter 23
3.6 Algebraic
proofs
Chapter 23
Unit 4. Geometry
Objectives
Themes
4.1 Geometric
constructions
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Chapter 13
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4.2 Angles and
shape
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Chapter 11
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4.3 Area,
perimeter and
surface area
Chapter 11
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Examples
Measure and draw lines to the nearest millimetre
Construct triangles and other two-dimensional shapes using a combination of a ruler, a
protractor and compasses
Solve problems using scale drawings
Use straight edge and compasses to:
(i) construct the perpendicular bisector of a line segment
(ii) construct the bisector of an angle
Distinguish between acute, obtuse, reflex and right angles
Use angle properties of intersecting lines, parallel lines and angles on a straight line
Understand the exterior angle of a triangle property and the angle sum of a triangle property
Understand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties
of these triangles
Recognise and give the names of polygons
Understand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals
Understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium
and kite
Understand the term ‘regular polygon’ and calculate interior and exterior angles of regular
polygons
Understand and use the angle sum of polygons
Understand congruence as meaning the same shape and size
Understand that two or more polygons with the same shape and size are said to be congruent to
each other
Identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional
figure
Understand angle measure including three-figure bearings
Measure an angle to the nearest degree
Provide reasons, using standard geometrical statements, to support numerical values for angles
obtained in any geometrical context involving lines, polygons and circles (unit 5)
Angles at a point, vertically
opposite angles, alternate
angles, corresponding angles,
allied angles
Convert measurements within the metric system to include linear and area units
Find the perimeter of shapes made from triangles and rectangles
Find the area of simple shapes using the formulae for the areas of triangles and rectangles
Find the area of parallelograms and trapezia
Recognise and give the names of solids
Understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids
Find the surface area of simple shapes using the area formulae for triangles and rectangles
Convert between units of volume within the metric system
cm2 to m2 and vice versa
To include parallelogram,
rectangle, square, rhombus,
trapezium, kite, pentagon,
hexagon and octagon
The four angles of a
quadrilateral are 90°, (x + 15)°,
(x +25)° and (x + 35)° Find the
value of x
For a polygon with n sides, the
sum of the interior angles is (2n
– 4) right angles
Name a quadrilateral with no
lines of symmetry and order of
rotational symmetry of 2
To include cube, cuboid, prism,
pyramid, cylinder, sphere and
cone
cm3 to m3 and vice versa and 1
litre = 1000 cm3
4.4 Circles,
cylinders,
cones and
spheres
Chapter 12
4.5
Transformation
and similarity
Chapter 14
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Find circumferences and areas of circles using relevant formulae; find perimeters and areas
of semicircles
Find the surface area of a cylinder
Find the volume of prisms, including cuboids and cylinders, using an appropriate formula
Find the volume of prisms, including cuboids and cylinders, using an appropriate formula
Find perimeters and areas of sectors of circles
Find the surface area and volume of a sphere and a right circular cone using relevant
formulae
Understand that rotations are specified by a centre and an angle rotate shapes
Recognise that an anti-clockwise rotation is a positive angle of rotation and a clockwise
rotation is a negative angle of rotation
Understand that reflections are specified by a mirror line
Construct a mirror line given an object and reflect a shape given a mirror line (horizontal,
vertical and y = x)
Understand that translations are specified by a distance and direction translate shapes
Understand and use column vectors in translations
Understand that rotations, reflections and translations preserve length and angle so that a
transformed shape under any of these transformations remains congruent to the original
shape
Understand that enlargements are specified by a centre and a scale factor (positive scale
factors including fractions)
Understand that enlargements preserve angles and not lengths
Enlarge a shape given the scale factor (with or without a centre given)
Identify and give complete descriptions of transformations
Understand and use the geometrical properties that similar figures have corresponding
lengths in the same ratio but corresponding angles remain unchanged
Understand that areas of similar figures are in the ratio of the square of corresponding sides
Understand that volumes of similar figures are in the ratio of the cube of corresponding sides
Use areas and volumes of similar figures in solving problems
Unit 5. Circle Theorems
Objectives
Themes
5.1 Circle
properties
Chapter 17
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Recognise the terms “centre”, “radius”, “chord”, “diameter”, “circumference”, “tangent”, “arc”,
“sector”, and “segment” of a circle
Understand the chord and tangent properties of circles
Give informal reasons, where required, when arriving at numerical solutions to geometrical
problems
Recognise the term “cyclic quadrilateral”
Understand and use angle properties of the circle including
○ Angle subtended by an arc at the centre of a circle is twice the angle subtended at any
point on the remaining part of the circumference
○ Angle subtended at the circumference by a diameter is a right angle
○ Angels in the same segment are equal
○ The sum of the opposite angles of a cyclic quadrilateral is 180
○ The alternate segment theorem
Understand and use the internal and external intersecting chord properties
Provide reasons, using standard geometrical statements, to support numerical values for angles
obtained in any geometrical context involving lines, polygons and circles
Examples
Two tangents from a point to a
circle are equal in length
Tangents are perpendicular to the
radius at the point of contact
The line from the centre of a circle
which is perpendicular to a chord
bisects the chord (and the
converse)
Reasons will only be required for
geometrical calculations based on
lines (including chords and
tangents), triangles and polygons
YEAR 11 Unit 6. Trigonometry II
Objectives
Themes
6.1 Re-Cap
Primary Trig
Ratios
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Know, understand and use sine, cosine and tangent of acute angles to determine lengths and
angles of a right-angled triangle
Understand and use sine, cosine and tangent of obtuse angles
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Understand and use the sine and cosine rules for any triangle
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Understand and use the formula A =
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Understand and use angles of elevation and depression
Use Pythagoras’ theorem in two and three dimensions
Apply trigonometric methods to solve problems in two and three dimensions, including
finding the angle between a line and a plane
Examples
Chapter 16
6.2 The Sine and
Cosine Rules
Chapter 25
6.3 Area of
Triangle
1
ab sin C for the area of a triangle
2
Chapter 25
6.4
Application
and Trig in 3D
Chapter 25
To include bearings
The angle between two
planes will not be required
Unit 7. Functions
Objectives
Themes
7.1 Functions
and function
notation
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Chapter 24
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Understand the concept that a function is a mapping between elements of two sets
Use function notations of the form f(x) = … and f : x …
Understand the terms ‘domain’ and ‘range’ and which values may need to be excluded from a
domain
Understand and find the composite function fg and the inverse function f -1
Examples
7.2 Graphs and
transformations
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Chapter 26
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Recognise, plot and draw graphs of the following types of functions:
○ Linear
○ Quadratic
○ Cubic
○ Reciprocal
Recognise, plot and draw the follow trigonometric functions (in degrees):
○ y = sin x
○ y = cos x
○ y = tan x
Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for
linear, quadratic, sine and cosine functions
Interpret and analyse transformations of functions and write the functions algebraically
Find the intersection points of two graphs, one linear (y1) and one non-linear (y2), and recognise
that the solutions correspond to the solutions of (y2 - y1) = 0
○ Recap algebraic methods
Unit 8. Calculus
Objectives
Themes
8.1 Calculus
Chapter 28
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Find the gradients of non-linear graphs by drawing a tangent
Understand the concept of a variable rate of change
Differentiate integer powers of x
Determine gradients, rates of change, stationary points, turning points (maxima and
minima) by differentiation and relate these to graphs
Distinguish between maxima and minima by considering the general shape of the
graph only
Apply calculus to linear kinematics and to other simple practical problems
Examples
Unit 9. Statistics
Objectives
Themes
9.1 Graphical
representation
of data and
statistical
measure
Chapter 19
9.2 Graphical
representation
of data and
statistical
measure
(Higher)
Chapter 19
Examples
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Use different methods of presenting data
Use appropriate methods of tabulation to enable the construction of statistical diagrams
Interpret statistical diagrams
Understand the concept of average
Calculate the mean, median, mode and range of a discrete data set
Calculate an estimate for the mean for grouped data
Identify the modal class for grouped data
Pictograms, bar charts and pie
charts, and only two-way tables
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Construct and interpret histograms
Construct cumulative frequency diagrams from tabulated data
Use cumulative frequency diagrams
Estimate the median from a cumulative frequency diagram
Understand the concept of a measure of spread
Find the interquartile range from a discrete data set
Estimate the interquartile range from a cumulative frequency diagram
For continuous variables with
unequal class intervals
Data could be in a list or
tabulated form
Includes simple problems using
these measures
The terms ‘upper quartile’ and
‘lower quartile’ may be used
Unit 10. Vectors
Objectives
Themes
10.1 Vectors
Chapter 27
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Understand that a vector has both magnitude and direction
Understand and use vector notation including column vectors
Multiply vectors by scalar quantities
Add and subtract vectors
Calculate the modulus (magnitude) of a vector
Find the resultant of two or more vectors
Apply vector methods for simple geometrical proofs
Examples