Number

use
natural numbers, integers (positive, negative and zero), prime
numbers, common factors and common multiples, rational and
irrational numbers, real numbers;
continue
given number sequences, recognise patterns within and across
different sequences and generalise to simple algebraic statements
(including expressions for the nth term) relating to such
sequences.
prime
and prime factorization
finding
Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
calculation
with the use of calculator

Set
language and notation

A
= {x : x is a natural number}
B
=
C
=
D
= {a, b, c... }
Notation:
Union
of A and B: A ∪
B
Intersection
of A and B: A ∩
B
Number
of elements in set A: n(A)
“ .
. . is an element of . . . ”
: ∈
“ .
. . is not an element of . . . ”:
Complement
of set A
: A’
The
empty set: Ø
Universal
set
A is a subset of B
: A ⊆
B
A
is a proper subset of B
: A ⊂
B
A
is not a subset of B
: A ⊈
B
A
is not a proper subset of B: A
B

Function
notation

^{ }and
^{
}to
describe their inverses.

Squares,
square roots, cubes and cube roots


Decimal,
fractions, and percentages


Ordering

order
quantities by magnitude and demonstrate familiarity with the
symbols =,≠
, ^{>},
^{<},
≤, ≥

Standard
form


The
four operations


Estimation

make
estimates of numbers, quantities and lengths, give approximations
to specified numbers of significant figures and decimal places
and round off answers to reasonable accuracy in the context of a
given problem.

Limits
of accuracy

give
appropriate upper and lower bounds for data given to a specified
accuracy (e.g. measured lengths);
obtain
appropriate upper and lower bounds to solutions of simple
problems (e.g. the calculation of the perimeter or the area of a
rectangle) given data to a specified accuracy.

Ratio,
proportion, rate

demonstrate
an understanding of the elementary ideas and notation of ratio,
direct and inverse proportion and common measures of rate;
divide
a quantity in a given ratio;
use
scales in practical situations, calculate average speed;
express
direct and inverse variation in algebraic terms and use this form
of expression to find unknown quantities.

Percentages

calculate
a given percentage of a quantity;
express
one quantity as a percentage of another,
percentages
greater than 100%
calculate
percentage increase or decrease;
carry
out calculations involving reverse percentages, e.g. finding the
cost price given the selling price and the percentage profit.
problems
involving percentage

Measures

use
current units of mass, length, area, volume and capacity in
practical situations and express quantities in terms of larger or
smaller units.

Time


Money,
personal, and household finance

solve
problems involving money and convert from one currency to
another.
use
given data to solve problems on personal and household finance
involving earnings, simple interest, discount, profit and loss,
taxation;
extract
data from tables and charts.

Graphs
in practical situations

demonstrate
familiarity with cartesian coordinates in two dimensions;
interpret
and use graphs in practical situations including travel graphs
and conversion graphs;
draw
graphs from given data;
apply
the idea of rate of change to easy kinematics involving
distancetime and speedtime graphs, acceleration and
retardation;
calculate
distance travelled as area under a linear speedtime graph.

Graphs
of functions

construct
tables of values and draw graphs for functions of
the form ^{
}where
n =
–2,
–1, 0, 1, 2, 3, and simple sums of not more than three of
these and for functions of the form , where a is a positive
integer;
interpret
graphs of linear, quadratic, reciprocal and exponential
functions;
find
the gradient of a straight line graph;
the
gradient of a linear graph as the ratio of the vertical change to
the horizontal change (positive and negative gradients)
graphs
of linear equations in two unknowns
graphs
of quadratic functions and their properties
∗ positive
or negative coefficient of x^{2
}
∗ maximum
and minimum points
∗ symmetry
∗ y=±(x
^{_}p)^{2}+q
∗ y
= ±(x ^{_
}a)(x
^{_
}b)

Straight
line graphs

calculate
the gradient of a straight line from the coordinates of two
points on it;
interpret
and obtain the equation of a straight line graph in the form
calculate
the length and the coordinates of the midpoint of a line segment
from the coordinates of its end points.

Algebraic
representation and formulae

transform
simple and more complicated formulae;
translation
of simple realworld situations into algebraic expressions
construct
equations from given situations.

Algebraic
manipulation

addition
and subtraction of linear algebraic expressions
simplification
of linear algebraic expressions, e.g.
− 2(3x
− 5)+
4x
manipulate
directed numbers;
use
brackets and extract common factors;
expand
products of algebraic expressions;
factorise
expressions of the form

Indices


Solutions
of equations and inequalities

solve
simple linear equations in one unknown;
solve
fractional equations with numerical and linear algebraic
denominators;
solve
simultaneous linear equations in two unknowns by:
∗ substitution
and elimination methods
∗ graphical
method

Graphical
representation of inequalities


Congruence
and similarity

Include:
∗ corresponding
angles are equal
∗ corresponding
sides are proportional
enlargement
and reduction of a plane figure by a scale factor
scale
drawings
determining
whether two triangles are
∗
congruent ∗
similar
ratio
of areas of similar plane figures
ratio
of volumes of similar solids
solving
simple problems involving similarity and congruence

Geometrical
constructions

measure
lines and angles;
construct
simple geometrical figures from given data, angle bisectors and
perpendicular bisectors using protractors or set squares as
necessary;
read
and make scale drawings.
(Where it is necessary to
construct a triangle given the three sides, ruler and compasses
only must be used.)

Bearings


Symmetry

recognise
line and rotational symmetry (including order of rotational
symmetry) in two dimensions, and properties of triangles,
quadrilaterals and circles directly related to their symmetries;
recognise
symmetry properties of the prism (including cylinder) and the
pyramid (including cone);

Properties
of circles

Include:
∗ equal
chords are equidistant from the centre
∗ the
perpendicular bisector of a chord passes through the centre
∗ tangents
from an external point are equal in length
∗ the
line joining an external point to the centre of the circle bisects
the
angle between the tangents
∗ angle
in a semicircle is a right angle
∗ angle
between tangent and radius of a circle is a right angle
∗ angle
at the centre is twice the angle at the circumference
∗ angles
in the same segment are equal
∗ angles
in opposite segments are supplementary

Angle,
triangles and polygons

Include:
right,
acute, obtuse and reflex angles, complementary and supplementary
angles, vertically opposite angles, adjacent angles on a straight
line, adjacent angles at a point, interior and exterior angles
angles
formed by two parallel lines and a transversal: corresponding
angles, alternate angles, interior angles
properties
of triangles and special quadrilaterals
classifying
special quadrilaterals on the basis of their properties
angle
sum of interior and exterior angles of any convex polygon
properties
of regular pentagon, hexagon, octagon and decagon
properties
of perpendicular bisectors of line segments and angle bisectors
construction
of simple geometrical figures from given data (including
perpendicular bisectors and angle bisectors) using compasses,
ruler, set square and protractor, where appropriate

Locus

(a)
sets of points in two or three dimensions
(i)
which are at a given distance from a given point,
(ii)
which are at a given distance from a given straight line,
(iii)
which are equidistant from two given points;
(b)
sets of points in two dimensions which are equidistant from
two given intersecting straight lines.

Mensuration

solve
problems involving
(i)
the perimeter and area of a rectangle and triangle,
(ii)
the circumference and area of a circle,
(iii)
the area of a parallelogram and a trapezium,
(iv)
the surface area and volume of a cuboid, cylinder, prism,
sphere, pyramid and cone (formulae will be given for the sphere,
pyramid and cone),
conversion
between cm^{2
}and
m^{2
},
and between cm^{3
}and
m^{3
}
problems
involving volume and surface area of composite solids
arc
length and sector area as fractions of the circumference and area
of a circle
use
of radian measure of angle (including conversion between radians
and
degrees)
problems
involving the arc length, sector area of a circle and area of a
segment

Trigonometry

apply
Pythagoras Theorem and the sine, cosine and tangent ratios for
acute angles to the calculation of a side or of an angle of a
right angled triangle (angles will be quoted in, and answers
required in, degrees and decimals of a degree to one decimal
place);
solve
trigonometrical problems in two dimensions including those
involving angles of elevation and depression and bearings;
extend
sine and cosine functions to angles between 90° and 180°;
solve problems using the sine and cosine rules for any triangle
and the formula for the area of a triangle;
solve
simple trigonometrical problems in three dimensions.
(Calculations of the angle between two planes or of the angle
between a straight line and plane will not be required.)

Statistics

collect,
classify and tabulate statistical data; read, interpret and draw
simple inferences from tables and statistical diagrams;
construct
and use bar charts, pie charts, pictograms, simple frequency
distributions, dot diagram, stem and leaf diagram, and frequency
polygons;
use
frequency density to construct and read histograms with equal and
unequal intervals;
calculate
the mean, median and mode for individual data and distinguish
between the purposes for which they are used;
range,
interquartile, and standard deviation as a measure of spread of
data
construct
and use cumulative frequency diagrams; estimate the median,
percentiles, quartiles and interquartile range;
calculate
the mean for grouped data; identify the modal class from a
grouped frequency distribution.
calculation
of the standard deviation for a set of data (grouped and
ungrouped)
using
the mean and standard deviation to compare two sets of data

Probability

calculate
the probability of a single event as either a fraction or a
decimal (not a ratio);
calculate
the probability of simple combined events using possibility
diagrams and tree diagrams where appropriate. (In possibility
diagrams outcomes will be represented by points on a grid and in
tree diagrams outcomes will be written at the end of branches and
probabilities by the side of the branches.)

Matrices

display
information in the form of a matrix of any order;
solve
problems involving the calculation of the sum and product (where
appropriate) of two matrices, and interpret the results;
calculate
the product of a scalar quantity and a matrix;
use
the algebra of axb matrices including the zero and identity
matrices;
calculate
the determinant and inverse of a nonsingular matrix. (A^{–1
}denotes
the inverse of A.)

Transformations

use
the following transformations of the plane: reflection (M),
rotation (R), translation (T), enlargement (E), shear (H),
stretching (S) and their combinations (If M(a) = b and R(b) = c
the notation RM(a) = c will be used; invariants under these
transformations may be assumed.);
identify
and give precise descriptions of transformations connecting given
figures; describe transformations using coordinates and matrices.
(Singular matrices are excluded.)

Vectors
in two dimensions

describe
a translation by using a vector represented by ,
add
vectors and multiply a vector by a scalar;
calculate
the magnitude of a vector as
(Vectors
will be printed as and their magnitudes denoted
by
modulus signs, e.g.. ln all their answers to questions candidates
are expected to indicate a
in
some definite way, e.g. by an arrow or by underlining, thus
or
a);
