• convert between numbers and words, e.g.
six billion is 6000000000
10007 is ten thousand and seven
• express 72 as a product of its prime factors
• find the highest common factor (HCF) of two
numbers
• find the lowest common multiple (LCM) of two
numbers.

Venn diagrams are limited to two sets.
The following set notation will be used:
• n(A) Number of elements in set A
• A′ Complement of set A
• Universal set
• A ∪ B Union of A and B
• A ∩ B Intersection of A and B.
Example definition of sets:
A = {x: x is a natural number}
B = {a, b, c, …}
C = {x: a ⩽ x ⩽ b}

Includes recall of squares and their corresponding
roots from 1 to 15, and recall of cubes and their
corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.:
• Write down the value of 169 .
• Work out 58 2 3 # .

Candidates are expected to be able to write
fractions in their simplest form.
Candidates are not expected to use recurring
decimal notation.

• negative numbers
• improper fractions
• mixed numbers
• practical situations, e.g. temperature changes.

find the value of 7 –2.
find the value of 2–3 × 24
, (23
)
2
, 23
÷ 24

Includes decimal places and significant figures.
e.g. write 5764 correct to the nearest thousand.
e.g. by writing each number correct to 1 significant
figure, estimate the value of ..
.
9790 765
41 3

.

e.g. write down the upper bound of a length
measured correct to the nearest metre.
Candidates are not expected to find the bounds
of the results of calculations which have used data
rounded to a specified accuracy

e.g. 20:30:40 in its simplest form is 2:3:4.
e.g. adapt recipes; use map scales; determine best
value.

e.g. calculate with:
• hourly rates of pay
• exchange rates between currencies
• flow rates
• fuel consumption.
e.g. calculate with:
• pressure
• density
• population density.
Required formulas will be given in the question.
Knowledge of speed/distance/time formula is
required.
e.g. A cyclist travels 45km in 3 hours 45 minutes.
What is their average speed?
Notation used will be, e.g. m/s (metres per second),
g/cm3
(grams per cubic centimetre)

Problems may include repeated percentage
change.
Formulas are not given.
e.g. find the cost price given the selling price and
the percentage profit.
Percentage calculations may include:
• deposit
• discount
• profit and loss (as an amount or a percentage)
• earnings
• percentages over 100%.

e.g. know not to round values within a calculation
and to only round the final answer.
e.g. enter 2 hours 30 minutes as 2.5 hours or
2° 30’ 0’’.
e.g. in money 4.8 means $4.80; in time 3.25 means
3 hours 15 minutes.

1 year = 365 days.
In the 24-hour clock, for example, 3.15 a.m. will be
denoted by 0315 and 3.15 p.m. by 1515.
Includes problems involving time zones, local times
and time differences.

e.g. depreciation, population change.
Knowledge of e is not required.

Examples include:
• 20 = 25
200 − 32 = 62 .
Examples include:
• 5
10 = 25
13
1
2
13
− + = + .

Simplify means give the answer in its simplest form,
e.g. 2a
2

• 3ab – 1 + 5a
  2
  – 9ab + 4 = 7a
  2
  – 6ab + 3.
  e.g. expand 3x(2x – 4y), (3x + y)(x – 4y).
  Includes products of more than two brackets,
  e.g. expand (x – 2)(x + 3)(2x + 1).
  Factorise means factorise fully,
  e.g. 9x
  2
• 15xy = 3x(3x + 5y)

Examples include:
• x
3

• x – 4
  2
  • 2x
  3 – 3(x –5)
  2
  • 3a
  4 × 9a
  10
  • 3a
  4 ÷ 9a
  10
  • 1
  x – 2
• x + 1
  x – 3
  .
  e.g. x
  2
  – 2x
  x
  2
  – 5x + 6

e.g. solve:
• 32x = 2
• 5x + 1 = 25x
.
e.g. simplify:
• 3xx 3
4 2 2
1

−

xx 5
2 2 2 2
1
' −
• x
3
2 5 J 3
L
K
K
N
P
O
O .
Knowledge of logarithms is not required.

.g. write an expression for the product of two
consecutive even numbers.
Includes constructing simultaneous equations.
Examples include:
• 3x + 4 = 10
• 5 – 2x = 3(x + 7).
Examples include:
• x
2x + 1
= 4
• 2
x + 2 + 3
2x – 1 = 1
• x
x + 2 = 3
x – 6 .
With powers no higher than two.
Includes writing a quadratic expression in
completed square form.
Candidates may be expected to give solutions in
surd form.
The quadratic formula is given in the List of
formulas.
e.g. change the subject of a formula where:
• the subject appears twice
• there is a power or root of the subject.

When representing and interpreting inequalities on
a number line:
• open circles should be used to represent strict
inequalities (<, >)
• closed circles should be used to represent
inclusive inequalities (⩽, ⩾).
e.g. – 3 ⩽ x < 1
–3–2–10 1
x
Examples include:
• 3x < 2x + 4
• –3 ⩽ 3x – 2 < 7 .
The following conventions should be used:
• broken lines should be used to represent strict
inequalities (<, >)
• solid lines should be used to represent inclusive
inequalities (⩽, ⩾)
• shading should be used to represent unwanted
regions (unless otherwise directed in the
question).
e.g.
0 12 0 12
x x
yy
1
2
1
2
x < 1
y ⩾ 1
Linear programming problems are not included.

Subscript notation may be used, e.g. Tn is the nth
term of sequence T.
Includes linear, quadratic, cubic and exponential
sequences and simple combinations of these.

Includes linear, square, square root, cube and cube
root proportion.
Knowledge of proportional symbol (∝) is required.

Includes estimation and interpretation of the
gradient of a tangent at a point.
Areas will involve linear sections of the graph only.

find the intersection of a line and a curve

Knowledge of symmetry and roots is required.
Knowledge of turning points is not required

Equations will be given in the form y = mx + c
(e.g. y = –2x + 5), unless a table of values is given.

From a grid only.

Questions may:

• use and request lines in the forms
y = mx + c
x = k

• involve fnding the equation when the graph is
given

• ask for the gradient or y-intercept of a graph
from an equation, e.g. fnd the gradient and
y-intercept of the graph with the equation
y = 6x + 3.

e.g. fnd the equation of the line parallel to
y = 4x – 1 that passes through (1, –3).

Candidates are not expected to show that two
shapes are congruent.

• cube

• cuboid

• prism

• cylinder

• pyramid

• cone

• sphere (term ‘hemisphere’ not required)

• face

• surface

• edg

A ruler should be used for all straight edges.
Constructions of perpendicular bisectors and angle
bisectors are not required.
e.g. construct a rhombus by drawing two triangles.
Construction arcs must be shown.
Examples include:

• draw nets of cubes, cuboids, prisms and
pyramids

• use measurements from nets to calculate
volumes and surface areas.

A ruler must be used for all straight edges.
Bearings are measured clockwise from north
(000° to 360°).
e.g. fnd the bearing of A from B if the bearing of B
from A is 025°.
Includes an understanding of the terms north, east,
south and west.
e.g. point D is due east of point C.

Includes properties of triangles, quadrilaterals and
polygons directly related to their symmetries.

Knowledge of three-letter notation for angles is
required, e.g. angle ABC. Candidates are expected
to use the correct geometrical terminology when
giving reasons for answers.

Units include:

• mm, cm, m, km

• mm
2
, cm
2
, m
2
, km
2

• mm
3
, cm
3
, m
3

• ml, l

• g, kg.
Conversion between units includes:

• between diferent units of area, e.g. cm
2
↔ m
2

• between units of volume and capacity,
e.g. m
3
↔ litres.

Questions will not involve combinations of
transformations. A ruler must be used for all straight
edges.

Probability notation is not required.
Probabilities should be given as a fraction, decimal
or percentage. Problems may require using
information from tables, graphs or Venn diagrams
(limited to two sets).
e.g. The probability that a counter is blue is 0.8.
What is the probability that it is not blue

. tally tables, two-way tables.