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IGCSE Revision Checklist
Revision checklists can be used to help you to focus on your revision. The checklist provides you with an overview of the skills and knowledge from
the syllabus that you should revise.
INTERNATIONAL MATHEMATICS (0607)
The table headings for International Mathematics are explained below:
Content You should be able R A G Comments
to
These are the general Content in the Tick the ‘R’, ‘A’, and ‘G’ column to record your progress. The
You can:
titles for items in the syllabus you need to ‘R’, ‘A’ and ‘G’ represent different levels of confidence, as• Add further information of your own, such
syllabus cover follows: as names of case studies needed.
• add learning aids, such as rhymes, poems
R = RED: means you are really unsure and lack confidence in
or word play
that area; you might want to focus your revision here and
• pinpoint areas of difficulty you need to
possibly talk to your teacher for help.
check further with your teacher or
A = AMBER: means you are reasonably confident in a topic but textbooks
need some extra practice. • include reference to a useful resource
G = GREEN: means you are very confident in a topic.
As your revision progresses, you can concentrate on the RED
and AMBER topics, in order to turn them into GREEN topics.
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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EXTENDED SYLLABUS
Number
Content You should be able to R A G Comments
Number Vocabulary and notation for different sets of numbers: natural
numbers, primes, squares, cubes, integers, rational numbers,
irrational numbers, real numbers, triangle numbers
Use of the four operations and brackets
Highest common factor (HCF), lowest common multiple (LCM)
Estimating, rounding, decimal places and significant figures
Ratio & Proportion e.g. Map scales
Percentages Equivalences between decimals, fractions and percentages
Use percentages for
profit & loss
simple & compound interest
Exponents Calculation of powers and roots
& Surds
Meaning of exponents (powers, indices) in Standard Form, a × 10n
where 1 ⩽ a < 10 and n ∈
Rules for exponents
Surds (radicals), simplification of square root expressions
Rationalisation of the denominator
Absolute The meaning of |x|
value
Time Calculations involving time: seconds (s), minutes (min), hours (h),
days, months, years including the relation between consecutive
units,
1 year = 365 days
Problems involving speed, distance and time
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Algebra
Content You should be able to R A G Comments
Inequalities Writing, showing and interpretation of inequalities, including those
on the real number line
Solution of linear and quadratic inequalities e.g. 2x2 + 5x – 3 < 0
Solution of inequalities using a graphic display calculator
Equations Solution of linear equations including those with fractional
expressions
Solution of simultaneous equations in two variables
Solution of quadratic equations: by factorisation
using a graphics display calculator
using the formula
Formulae Derivation, rearrangement and evaluation of formulae
Brackets Expansion of brackets, e.g. (x – 5)(2x – 1) including the square of a
binomial Factorisation:
common factor e.g. 6x2 + 9x = 3x(2x + 3)
difference of squares e.g. 9x2 – 16y2 = (3x – 4y)(3x + 4y)
trinomial e.g. 6x2 + 11x – 10 = (3x – 2)(2x + 5)
four term e.g. xy – 3x + 2y – 6 = (x + 2)(y – 3)
Algebraic Simplification, including use of factorisation
fractions
Addition or subtraction of fractions with integer denominators
Addition or subtraction of fractions with linear denominators or
single term
Multiplication or division and simplification of two fractions
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Content You should be able to R A G Comments
Indices Simple indices: multiplying and dividing e.g. 8x5 ÷ 2x3
Rules for indices
Graphic Use of a graphic display calculator to solve equations, including
display those which may be unfamiliar.
calculator e.g. 2x = x2
Sequences Continuation of a sequence of numbers or patterns
Determination of the nth term
Use a difference method to find the formula for
a linear sequence
a simple quadratic sequence
a simple cubic sequence
Identify a simple geometric sequence and find its formula
Variation Direct variation (proportion)
Inverse variation
Best variation model for
given data
Functions
Content You should be able to R A G Comments
Basic ideas Notation
Domain and range domain is R unless stated otherwise
Mapping diagrams
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Content You should be able to R A G Comments
Recognise these functions from their graphs
Recognition linear f(x) = ax + b
quadratic f(x) = ax2 + bx + c
cubic f(x) = ax3 + bx2 + cx + d
reciprocal f(x) = a
x
exponential f(x) = ax (0 <a < 1 or a > 1) includes
compound interest
absolute value f(x) = |ax + b|
trigonometric f(x) = asin(bx), f(x) = acos(bx), f(x) = tan(x)
includes period and amplitude
Find at most two of a, b, c or d in simple cases of these functions
Quadratic Finding the quadratic function given
function vertex and another point, y = a(x – h)2 + k has a vertex of
(h, k)
x-intercepts and a point
vertex or x-intercepts with a = 1
Graphic Use a graphic display calculator to
display sketch the graph of a function, including unfamiliar
calculator functions not mentioned explicitly in this syllabus
produce a table of values
find zeros, local maxima or minima including the vertex of a
quadratic
find the intersection of the graphs of functions
Asymptotes Understanding of the concept of asymptotes and graphical
identification of simple examples parallel to the axes
e.g. f(x) = tan x asymptotes at 90°, 270°, etc.
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Content You should be able to R A G Comments
Combination Simplify expressions such as f(g(x)) where g(x) is a linear function
& inverse Inverse function f -1
Logarithmic Logarithmic function as inverse of the exponential function: y = ax
Function equivalent to x = logay
Rules for logarithms corresponding to rules for exponents
Solution to ax = b as x = log b
log a
Transformat Description and identification, using the language of
ions transformations, of the changes to the graph when y = f(x) when y =
f(x) + k, y = f(x + k) (k an integer)
Coordinate Geometry
Content You should be able to R A G Comments
Graph Plotting of points and reading from a graph
Distance Distance between two points
Mid-point Mid-point of a line segment
Gradient Gradient of a line segment
Gradient of parallel and perpendicular lines
Equation Equation of a straight line as y = mx + c
ax + by = d (a, b and d integer)
Symmetry Symmetry of diagrams or graphs
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Geometry
Content You should be able to R A G Comments
Vocabulary Use and interpret the geometrical terms:
acute, obtuse, right angle, reflex, parallel, perpendicular, congruent,
similar
Use and interpret vocabulary of triangles, quadrilaterals, polygons
and simple solid figures e.g. pyramids including tetrahedrons
Symmetry Line symmetry
Rotational symmetry
Angles Measurement in degrees
Angles round a point, on a straight line, vertically opposite angles
Alternate and corresponding angles on parallel lines
Angle sum of a triangle, quadrilateral and polygons
Interior and exterior angles of a polygon including regular polygons
Similarity Calculation of lengths of similar figures
Use of area and volume scale factors
Pythagoras Pythagoras’ Theorem in two dimensions
Chord length & distance of a chord from the centre of a circle
Distances on a grid
Circles Use and interpret the vocabulary of circles, including sector and
segment
Properties of circles
tangent perpendicular to radius at the point of contact
tangents from a point are equal
angle in a semicircle is 90°
angles at the centre and at the circumference on the same arc
cyclic quadrilateral
alternate segment
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Vectors
Content You should be able to R A G Comments
Notation
Vector Addition and subtraction of vectors
operations Negative of a vector
Multiplication of a vector by a scalar
Transformat Transformations of the Cartesian plane:
ions translation
reflection
rotation
enlargement (reduction)
stretch
Description of a transformation
Combining these transformations
Inverse of these transformations
Mensuration
Content You should be able to R A G Comments
Units Convert between units:
mm, cm, m, km
mm2, cm2, m2, ha, km2
mm3, cm3, m3
ml, cl, l
g, kg, t
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Content You should be able to R A G Comments
Perimeter & Perimeter and area of
Area rectangle
triangle formula given
compound shapes derived from rectangles and triangles
Circumference and area of circle formula given
Arc length and area of sector
Volume & Surface area & volume
surface area prism and pyramid (in particular cuboid, cylinder and cone)
sphere and hemisphere
Note that in the examination the formulae will be given for:
the curved surface areas of cylinder, cone and sphere
the volume of prism, pyramid, cylinder, cone and sphere
Areas and volumes of compound shapes
Trigonometry
Content You should be able to R A G Comments
Trigonometry Right-angled triangle trigonometry
Three-figure bearings, and North, East, South, West
Problems in two and three dimensions
Angles Extension to the four quadrants (0° to 360°)
Exact values of sine, cosine and tangent of 0°, 30°, 45°, 60°, 90°
Graphs Properties of the graphs of y = sin x, y = cos x, y = tan x (x in
degrees)
Triangle Area of triangle formula given
Formulae Sine rule, including ambiguous case formula given
Cosine rule for two sides and included angle given, or for three
sides given formula given
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Sets
Content You should be able to R A G Comments
Notation Notation and meaning for
number of elements in A, (n(A))
is an element of (∈ ), is not an element of (∉)
empty set (∅ or { }), universal set (U)
complement of A, (A′)
is a subset of (⊆), is a proper subset of (⊂)
Sets in descriptive form: {x | } or as a list
Combining Venn diagrams of at most three sets
Sets Intersection and union of sets
Probability
Content You should be able to R A G Comments
Probability Probability P(A) as a fraction, decimal or percentage
Significance of the value of probability
Relative frequency as an estimate of probability
Expected frequency of occurrences
Combining Tree diagrams including successive selection with and without
Events replacement
Probabilities from Venn diagrams and tables
The addition rule P(A or B) = P(A) + P(B) when mutually exclusive
events
The multiplication rule P(A and B) = P(A) × P(B) when independent
events
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
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Statistics
Content You should be able to R A G Comments
Diagrams Reading and interpretation of graphs or tables of data
Discrete or continuous data
Pictogram
Bar graph
(Compound) bar chart
Pie chart
Line graph
Scatter diagram
Stem-and-leaf diagram
Mean, Mean, mode, median, quartiles and range from lists of discrete data
mode, Mean, mode, median and range from grouped discrete data
median Mean from continuous data
Cumulative Cumulative frequency table and curve
Frequency Median, quartiles and interquartile range (read from curve)
Graphic Use of a graphics display calculator to calculate
display mean, median, quartiles for discrete data
calculator mean for grouped data
Correlation Understanding and description of correlation (positive, negative or
zero) with reference to a scatter diagram. The coefficient of
correlation is not required.
Straight line of best fit (by eye) through the mean on a scatter
diagram
Use a graphic display calculator to find the equation of linear
regression
IGCSE International Mathematics Revision Checklist https://schoolsupporthub.cambridgeinternational.org/
