1.1 Integers
A understand and use integers (positive, negative and zero)
B understand place value
C use directed numbers in practical situations
D order integers
E use the four rules of addition, subtraction, multiplication and division
F use brackets and the hierarchy of operations
G use the terms ‘odd’, ‘even’, ’prime numbers’,
‘factors’ and ‘multiples’
H identify prime factors, common factors and common multiples

1.2 Fractions
A understand and use equivalent fractions, simplifying a fraction by cancelling common factors
B understand and use mixed numbers and vulgar fractions
C identify common denominators
D order fractions and calculate a given fraction of a given quantity
E express a given number as a fraction of another number
F use common denominators to add and subtract fractions and mixed numbers
G convert a fraction to a decimal or a percentage
H understand and use unit fractions as multiplicative inverses
I multiply and divide fractions and mixed numbers

1.3 Decimals
A use decimal notation
B understand place value
C order decimals
D convert a decimal to a fraction or a percentage
E recognise that a terminating decimal is a fraction
F convert recurring decimals into fractions

1.4 Powers and roots
A identify square numbers and cube numbers
B calculate squares, square roots, cubes and cube roots
C use index notation and index laws for multiplication and division of positive and negative integer powers including zero
D express integers as a product of powers of prime factors
E find highest common factors (HCF) and lowest common multiples (LCM)
F understand the meaning of surds
G manipulate surds, including rationalising a denominator
H use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

1.5 Set language and notation
A understand the definition of a set
B use the set notation ∪,∩ and ∈ and ∉
C understand the concept of the universal set and the empty set and the symbols for these sets
D understand and use the complement of a set
E use Venn diagrams to represent sets
F understand sets defined in algebraic terms, and understand and use subsets
G use Venn diagrams to represent sets and the number of elements in sets
H use the notation n(A) for the number of elements in the set A
I use sets in practical situations

1.6 Percentages
A understand that 'percentage' means 'number of parts per 100'
B express a given number as a percentage of another number
C express a percentage as a fraction and as a decimal
D understand the multiplicative nature of percentages as operators
E solve simple percentage problems, including percentage increase and decrease
F use reverse percentages
G use repeated percentage change

1.7 Ratio and proportion
A use ratio notation, including reduction to its simplest form and its various links to fraction notation
B divide a quantity in a given ratio or ratios
C use the process of proportionality to evaluate unknown quantities
D calculate an unknown quantity from quantities that vary in direct proportion
E solve word problems about ratio and proportion

1.8 Degree of accuracy
A round integers to a given power of 10
B round to a given number of significant figures or decimal places
C identify upper and lower bounds where values are given to a degree of accuracy
D use estimation to evaluate approximations to numerical calculations
E solve problems using upper and lower bounds where values are given to a degree of accuracy

1.9 Standard form
A calculate with and interpret numbers in the form a * 10” where n is an integer and 1 < a < 10

B solve problems involving standard form

1.10 Applying number
A use and apply number in everyday personal, domestic or community life
B carry out calculations using standard units of mass, length, area, volume and capacity
C understand and carry out calculations using time, and carry out calculations using money, including converting between currencies

1.11 Electronic calculators
A use a scientific electronic calculator to determine numerical results

2.1 Use of symbols
A understand that symbols may be used to represent numbers in equations or variables in expressions and formulae
B understand that algebraic expressions follow the generalised rules of arithmetic
C use index notation for positive and negative integer powers (including zero)
D use index laws in simple cases
E use index notation involving fractional, negative and zero powers

2.2 Algebraic manipulation
A evaluate expressions by substituting numerical values for letters
B collect like terms
C multiply a single term over a bracket
D take out common factors
E expand the product of two simple linear expressions
F understand the concept of a quadratic expression and be able to factorise such expressions (limited to x2 + bx + c)
G expand the product of two or more linear expressions
H understand the concept of a quadratic expression and be able to factorise such expressions
I manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic
J complete the square for a given quadratic expression
K use algebra to support and construct proofs

2.3 Expressions and formulae
A understand that a letter may represent an unknown number or a variable
B use correct notational conventions for algebraic expressions and formulae
C substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae
D use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols
E derive a formula or expression
F change the subject of a formula where the subject appears once
G 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

2.4 Linear equations
A solve linear equations, with integer or fractional coefficients, in one unknown in which the unknown appears on either side or both sides of the equation
B set up simple linear equations from given data

2.5 Proportion
A set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations

2.6 Simultaneous linear equations
A calculate the exact solution of two simultaneous equations in two unknowns
B calculate the exact solution of two simultaneous equations in two unknowns
C interpret the equations as lines and the common solution as the point of intersection

2.7 Quadratic equations
A solve quadratic equations by factorisation (limited to x2 + bx + c = 0)
B solve quadratic equations by factorisation
C solve quadratic equations by using the quadratic formula or completing the square
D form and solve quadratic equations from data given in a context
E solve simultaneous equations in two unknowns, one equation being linear and the other being quadratic

2.8 Inequalities
A understand and use the symbols >,<, and <
B understand and use the convention for open and closed intervals on a number line
C solve simple linear inequalities in one variable and represent the solution set on a number line
D represent simple linear inequalities on rectangular Cartesian graphs
E identify regions on rectangular Cartesian graphs defined by simple linear inequalities
F solve quadratic inequalities in one unknown and represent the solution set on a number line
G identify harder examples of regions defined by linear inequalities

3.1 Sequences
A generate terms of a sequence using term-to-term and position-to-term definitions of the sequence
B find subsequent terms of an integer sequence and the rule for generating it
C use linear expressions to describe the /th term of arithmetic sequences
D understand and use common difference (d) and first term (a) in an arithmetic sequence
E know and use nth term = a + (n - 1)d
F find the sum of the first n terms of an arithmetic series (Sn)

3.2 Function notation
A understand the concept that a function is a mapping between elements of two sets
B use function notations of the form f(x) = ... and f : x ^ ...
C understand the terms 'domain' and 'range' and which values may need to be excluded from a domain
D understand and find the composite function fg and the inverse function f^-1

3.3 Graphs
A interpret information presented in a range of linear and non-linear graphs
B understand and use conventions for rectangular Cartesian coordinates
C plot points (x, y) in any of the four quadrants or locate points with given coordinates
D determine the coordinates of points identified by geometrical information
E determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points
F draw and interpret straight line conversion graphs
G find the gradient of a straight line
H recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c)
I recognise, generate points and plot graphs of linear and quadratic functions
J recognise, plot and draw graphs with equation:
y = Ax3 + Bx2+ Cx + D in which:
(i)  the constants are integers and some could be zero
(ii)the letters x and y can be replaced with any other two letters or:
in which:
(i)  the constants are numerical and at least three of them are zero
(ii)the letters x and y can be replaced with any other two letters or:

y = sin x, y = cos x, y = tan x for angles of any size (in degrees)
K apply to the graph ofy = 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
L interpret and analyse transformations of functions and write the functions algebraically
M find the gradients of non-linear graphs
N find the intersection points of two graphs, one linear (y1) and one non-linear (y2), and and recognise that the solutions correspond to the solutions of (y 2 - yd = o
O calculate the gradient of a straight line given the coordinates of two points
P find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line

3.4 Calculus
A understand the concept of a variable rate of change
B differentiate integer powers of x
C determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs
D distinguish between maxima and minima by considering the general shape of the graph only

E apply calculus to linear kinematics and to other simple practical problems

4.1 Angles, lines and triangles
A distinguish between acute, obtuse, reflex and right angles
B use angle properties of intersecting lines, parallel lines and angles on a straight line
C understand the exterior angle of a triangle property and the angle sum of a triangle property
D understand the terms 'isosceles', 'equilateral' and 'right-angled triangles' and the angle properties of these triangles

4.2 Polygons
A recognise and give the names of polygons
B understand and use the term 'quadrilateral' and the angle sum property of quadrilaterals
C understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
D understand the term 'regular polygon' and calculate interior and exterior angles of regular polygons
E understand and use the angle sum of polygons
F understand congruence as meaning the same shape and size
G understand that two or more polygons with the same shape and size are said to be congruent to each other

4.3 Symmetry
A identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure

4.4 Measures
A interpret scales on a range of measuring instruments
B calculate time intervals in terms of the 24-hour and the 12-hour clock
C make sensible estimates of a range of measures
D understand angle measure including three-figure bearings
E measure an angle to the nearest degree
F understand and use the relationship between average speed, distance and time
G use compound measure such as speed, density and pressure

4.5 Construction
A measure and draw lines to the nearest millimetre
B construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses
C solve problems using scale drawings
D use straight edge and compasses to:
(i)  construct the perpendicular bisector of a line segment
(ii) construct the bisector of an angle
E understand and use the internal and external intersecting chord properties
F recognise the term 'cyclic quadrilateral’
G understand and use angle properties of the circle including:
(i)  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
(ii) angle subtended at the circumference by a diameter is a right angle
(iii) angles in the same segment are equal
(iv)the sum of the opposite angles of a cyclic quadrilateral is 180°
(v) the alternate segment theorem

4.6 Circle properties
A recognise the terms 'centre', 'radius', 'chord', 'diameter', 'circumference', 'tangent', 'arc', 'sector' and 'segment' of a circle
B understand chord and tangent properties of circles

4.7 Geometrical reasoning
A give informal reasons, where required, when arriving at numerical solutions to geometrical problems
B provide reasons, using standard geometrical statements, to support numerical values for angles obtained in any geometrical context involving lines, polygons and circles

4.8 Trigonometry and Pythagoras’ theorem
A know, understand and use Pythagoras' theorem in two dimensions
B know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle
C apply trigonometrical methods to solve problems in two dimensions
D understand and use sine, cosine and tangent of obtuse angles
E understand and use angles of elevation and depression
F understand and use the sine and cosine rules for any triangle
G use Pythagoras' theorem in three dimensions
H understand and use the formula 1 ab sin C for the area of a triangle
I apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane

4.9 Mensuration of 2D shapes
A convert measurements within the metric system to include linear and area units
B find the perimeter of shapes made from triangles and rectangles
C find the area of simple shapes using the formulae for the areas of triangles and rectangles
D find the area of parallelograms and trapezia
E find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles
F find perimeters and areas of sectors of circles

4.10 3D shapes and volume
A recognise and give the names of solids
B understand the terms 'face', 'edge' and 'vertex' in the context of 3D solids
C find the surface area of simple shapes using the area formulae for triangles and rectangles
D find the surface area of a cylinder
E find the volume of prisms, including cuboids and cylinders, using an appropriate formula
F convert between units of volume within the metric system
G find the surface area and volume of a sphere and a right circular cone using relevant formulae

4.11 Similarity
A understand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged
B use and interpret maps and scale drawings
C understand that areas of similar figures are in the ratio of the square of corresponding sides
D understand that volumes of similar figures are in the ratio of the cube of corresponding sides
E use areas and volumes of similar figures in solving problems

5.1 Vectors
A understand that a vector has both magnitude and direction
B understand and use vector notation including column vectors
C multiply vectors by scalar quantities
D add and subtract vectors
E calculate the modulus (magnitude) of a vector
F find the resultant of two or more vectors
G apply vector methods for simple geometrical proofs

5.2 Transformation geometry
A understand that rotations are specified by a centre and an angle
B rotate a shape about a point through a given angle
C recognise that an anti-clockwise rotation is a positive angle of rotation and a clockwise rotation is a negative angle of rotation
D understand that reflections are specified by a mirror line
E construct a mirror line given an object and reflect a shape given a mirror line
F understand that translations are specified by a distance and direction
G translate a shape
H understand and use column vectors in translations
I 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
J understand that enlargements are specified by a centre and a scale factor
K understand that enlargements preserve angles and not lengths
L enlarge a shape given the scale factor
M identify and give complete descriptions of transformations

6.1 Graphical representation of data
A use different methods of presenting data
B use appropriate methods of tabulation to enable the construction of statistical diagrams
C interpret statistical diagrams
D construct and interpret histograms
E construct cumulative frequency diagrams from tabulated data
F use cumulative frequency diagrams

6.2 Statistical measures
A understand the concept of average
B calculate the mean, median, mode and range for a discrete data set
C calculate an estimate for the mean for grouped data
D identify the modal class for grouped data
E estimate the median from a cumulative frequency diagram
F understand the concept of a measure of spread
G find the interquartile range from a discrete data set
H estimate the interquartile range from a cumulative frequency diagram

6.3 Probability
A understand the language of probability
B understand and use the probability scale
C understand and use estimates or measures of probability from theoretical models
D find probabilities from a Venn diagram
E understand the concepts of a sample space and an event, and how the probability of an event happening can be determined from the sample space
F list all the outcomes for single events and for two successive events in a systematic way
G estimate probabilities from previously collected data
H calculate the probability of the complement of an event happening
I use the addition rule of probability for mutually exclusive events
J understand and use the term 'expected frequency’
K draw and use tree diagrams
L determine the probability that two or more independent events will occur
M use simple conditional probability when combining events
N apply probability to simple problems