1) Fractions, Decimals and Percentages
Ref
Description
1.1
Order fractions and decimals
1.2
Recognise equivalence and convert between fractions, decimals and percentages
1.3
+ - x  fractions and decimals, applying rules of BIDMAS where appropriate (including dividing by decimals (up to 2dp) by
transforming it to a problem involving division by an integer.
1.4
Understand ‘reciprocal’ as multiplicative inverse
1.5
Calculate fractions and percentages of a quantity
1.6
Express one quantity as a percentage of another
1.7
Calculate percentage increase and decrease, profit and loss
1.8
Solve problems involving simple/compound interest and depreciation.
1.9
Convert recurring decimals to fractions
1.10 Carry out calculations involving reverse percentages e.g. finding the cost price given the selling price and the percentage profit
2) Algebra
Ref
Description
2.1
Add, subtract, multiply and divide directed numbers
2.2
Use letters to express generalised numbers and express basic arithmetic processes algebraically
2.3
Substitute numbers for words and letters in formulae (involving powers)
2.4
Solve problems by substituting values into simple formulae
2.5
Simplifying expressions (+ - x ) including expanding brackets and collecting like terms
2.6
Solve linear equations in one unknown (unknown on either or both sides, equations involving brackets and where solutions are
negative / fractions)
2.7
Generate formulae and solve problems by writing and solving an equation
2.8
Change the subject of simple formula
2.9
Change the subject of a formula (including where the subject appears twice or where powers of the subject appear.
2.10 Manipulate algebraic fractions
3) Angle
Ref
3.1
3.2
3.3
Description
Use and interpret the geometrical terms: point, line, parallel, perpendicular, acute, right, obtuse and reflex angles
Use and interpret vocabulary of triangles, quadrilaterals, circles, polygons (up to decagon) and simple solid figures (including prism,
pyramid, cylinder and cone)
Calculate unknown angles using the following geometrical properties:
(a) Using angles in a straight line and angles at a point
(b) Using parallel lines to identify alternate and corresponding angles
(c) Calculating unknown angles in triangles and quadrilaterals (equilateral, isosceles, right angles)
(d) Calculating interior and exterior angles in polygons
3.4
Understanding a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices
3.5
Use angle properties of quadrilaterals (Square, Rectangle, Parallelogram, Trapezium and Rhombus)
3.6
Angle properties of irregular polygons
4) Limits of Accuracy
Ref
Description
4.1
Order quantities by magnitude and demonstrate familiarity with the symbols =  < > 
4.2
Rounding to specified numbers of decimal places and significant figures, rounding answers to reasonable accuracy in the context
of a given problem
4.3
Estimate and check answers
4.4
Recognising that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction
4.5
Obtain appropriate upper and lower bounds to solutions of simple problems (e.g. the calculation of the perimeter or area of a
rectangle) given data to a specified accuracy
5) Collecting Data
Ref
Description
5.1
Select suitable method to collect/summarise primary data including grouped data, considering appropriate equal class intervals
5.2
Select and justify a sampling scheme and a method to investigate a population
5.3
Questionnaires and surveys, understand bias etc
5.4
Design and use data collection sheets
5.5
Gather data from secondary sources
5.6
Design and use two-way tables
5.7
Dealing with practical problems such as non-response and missing / inaccurate data
6) Statistics
Ref
6.1
6.2
Description
Read, interpret and draw simple inferences from tables and statistical diagrams
Construct and use:
o Bar charts
o Pie charts
o Pictograms
o Simple frequency distributions
o Histograms with equal intervals (+ Frequency polygons)
o Scatter diagrams, including line of best fit (interpolate and extrapolate)
o Stem and leaf diagrams
6.3
Understand what is meant by positive, negative and zero correlation
6.4
Calculate the mean, median and mode for discrete data, and distinguish between the purposes for which they are used
6.5
6.7
Calculate the range
Construct and read histograms with equal and unequal intervals (areas proportional to frequencies and vertical axis labelled
‘frequency density’) Estimate of the median using group frequency tables and histograms
Construct and use cumulative frequency diagrams
6.8
Find the median, quartiles and inter-quartile range from data and CF diagram
6.9
Construct and interpret box plots for grouped continuous data
6.6
6.10 Calculate an estimate of the mean for grouped and continuous data
6.11 Identify the modal class from a grouped frequency distribution
6.12 Use statistical measures / graphs to compare sets of data
7) Probability
Ref
Description
7.1
List all the outcomes for single events, and for successive events, in a systematic way
7.2
Identify mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1
7.3
Know when to add or multiply two probabilities i.e. p(A or B) = p(A) + p(B) and p(A and B) = p(A) x p(B)
7.4
Use tree diagrams to represent outcomes of compound events, recognising when events are independent and understanding the
concept of conditional probability
7.5
Use Venn diagrams to represent solutions to probability problems and to calculate probabilities from a given data set.
7.6
Compare experimental data (Relative frequency) and theoretical probabilities
7.6
Understand that if an experiment is repeated different outcomes may (and usually) occur, and that increasing sample size generally
leads to better estimates of probability and population parameters
8) Indices and Surds
Ref
8.1
8.2
Description
Calculate squares, square roots, cubes and cube roots of numbers, including the use of trial and improvement
Use and interpret positive, negative and zero indices (including index laws)
x a  x b  x a b
(a)
x a  x b  x a b
(b)
(c)
( x a )b  x ab
x0  1
(d)
1
xa  a
(e)
x
(f)
a
x b  ( b x )a  b ( x a )
8.3
Use the standard form A  10n to convert between numerical and standard form and in calculations
8.4
Use and interpret (fractional) indices e.g. solve 32x = 2
8.5
Simplify and use surds using laws
8.6
Rationalise the denominator of surds
ab  a  b and
a
a

b
b
9) Numbers and Sequences
Ref
Description
9.1
Understanding even, odd and prime numbers
9.2
Finding factors and multiples of numbers
9.3
Finding HCF, LCM and prime factor decomposition
9.4
Generate and Extend common integer sequences (including: sequences of odd or even integers; squared integers; powers of 2;
powers of 10; triangle numbers)
9.5
Use the term to term rule to generate or fill in missing terms in a sequence
9.6
Describe the nth term of a sequence using words and algebra and use the nth rule term to find the value of a particular term
9.7
Deduce expressions to calculate the nth term of quadratic sequences
9.8
Recognise and use simple geometric progressions
10) Coordinates and Graphs of Linear Functions
Ref
Description
10.1 Using axes and coordinates to specify points in all four quadrants and locate points with given coordinates
10.2 Finding the coordinates of points identified by geometrical information
10.3 Finding the coordinates of the midpoint of the a line segment
10.4 Construct tables of values and draw graphs for functions in which y is given explicitly in terms of x, or implicitly
10.5
Understanding that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the yintercept. Find the gradient and y-intercept when values for m and c are given
10.6
Finding the gradient of a line. Exploring the gradients of parallel lines and lines perpendicular to each other. Finding the equation of
a line.
10.7 Constructing linear functions and plot the corresponding graphs arising from real-life problems. Discuss and interpret the results
11) Compound Measures
Ref
Description
11.1 Read clocks, dials and timetables; calculate times and time differences in terms of the 12- and 24-hour clocks
11.2 Know and use decimal equivalents of times given in hours and minutes
11.3 Use the relationship between density, mass and volume to solve problems and convert between units of density (kg/m3 to g/cm3)
11.4 Converting between area measures, including square centimetres and square metres
11.5 Converting between volume measures, including cubic centimetres and cubic metres
11.6 Use the relationship between distance, speed and time to solve problems
11.7 Convert between metric units of speed e.g. km/h to m/s
12) Simultaneous Equations (Linear)
Ref
Description
12.1 Solve simultaneous linear equations in two unknowns by graphical methods
12.2 Solve simultaneous linear equations in two unknowns by algebraic methods (e.g. elimination of one variable)
12.3 Solve problems involving simultaneous linear equations by the most appropriate method (e.g. elimination or substitution)
13) Factorising
Ref
Description
13.1 Extract common factors
13.2 Expanding the product of two linear expressions
13.3 Factorise quadratic expressions, including the difference of two squares
14) Quadratic Equations
Ref
Description
14.1 Generating points and plotting graphs of quadratic functions
14.2 Finding approximate solutions of a quadratic equation from the graph of the corresponding quadratic function
14.3 Solving simple quadratic equations by factorising
14.4 Solve quadratic equations using the quadratic formula giving answers to 1dp and in surd form
14.5 Solve quadratic equations by completing the square
14.6 Complete the square of a quadratic function and use this to determine the min / max value of the function
15) Simultaneous Equations
Ref
Description
14.4 Estimate solutions to simultaneous equations (linear and quadratic) using graphical methods
14.5 Constructing the graph of x 2  y 2  r 2 for a circle of radius r centred at the origin of coordinates
14.6
Finding graphically the intersection points of a given straight line with this circle and knowing that this corresponds to solving the
two simultaneous equations representing the line and the circle
Solving exactly, by elimination of an unknown, two simultaneous equations in two unknowns, one of which is linear in each
14.7 unknown, and the other is linear in one unknown and quadratic in the other, of where the second is of the form x 2  y 2  r 2 (Also
graphical solutions)
16) Mensuration
Ref
Description
15.1 Understand and use Pythagoras’ theorem in 2-D and 3D
15.2 Pythagoras on a coordinate grid: given the points A and B, calculate the length AB
15.3 Calculating perimeters and areas of shapes made from triangles and rectangles (including area of parallelogram / trapezium)
15.4
Finding circumferences of circles and areas enclosed by circles, recalling relevant formulae (using surds and pi in exact
calculations without a calculator)
15.5 Calculating the lengths of arcs and sectors / segments of circles (using surds and pi in exact calculations without a calculator)
15.6 Solve problems involving the surface area of cuboids and prisms (including cylinders)
15.7 Solve problems involving the volume of cuboids and prisms (including cylinders) and given the formulae cones and pyramids.
15.8 Solving problems involving volumes of compound shapes made from cones, pyramids, etc (including frustums)
17) Trigonometry
Ref
Description
16.1 Interpret and use 3 figure bearings measured clockwise from north
16.2
Apply the sine, cosine and tangent ratios for acute angles to the calculation of a side or angle of a right-angled triangle (angles will
be quoted in, and answers required in, degrees and decimals to one decimal place)
16.3 Solve problems using the sine and cosine rules for any triangle
16.4 Calculate the area of triangle using Area 
1
ab sin C
2
16.5 Solve problems using Pythagoras and trigonometry in 3 dimensions
16.6 Finding the angles between a line and a plane
18) Ratio and Proportion
Ref
Description
17.1 Using ratio notation, including reduction to its simplest form and it various links to fractions notation
17.2 Dividing a quantity in a given ratio
17.3 Solving word problems about ratio, including using informal strategies and the unitary method of solution
17.4 Using and interpreting maps and scale drawings
17.5 Interpret direct and inverse proportions as algebraic functions ( y  x  y  kx , y 
1
k
1
k
 y  , y  x 2  y  kx 2 , y  2  y  2 )
x
x
x
x
17.6 Use algebraic functions for direct and inverse proportionality, with their value of k, to find unknown values
19) Constructions and Loci
Ref
18.1
Description
Drawing approximate constructions of triangles and other 2-D shapes, using a ruler and protractor, given information about side
lengths and angles
Similar Triangles - Understand from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are
unique, but SSA are not
Construct:
 Triangles, given three sides (using compasses and straightedge only)
 Simple geometric figures (e.g. a regular hexagon inside a circle)
18.3
 Perpendicular bisector of a line segment (using compasses and straightedge only)
 Bisector of an angle (using compasses and straightedge only)
 30º, 45º, 60º, 90º angles
Use the following loci and the method of intersecting loci for sets of points in 2D which
 are at a given distance from a given point
18.4
 are at a given distance from a given straight line
 are equidistant from two given points
 are equidistant from two given intersecting straight lines
18.2
20) Drawing and Constructing 2-D / 3-D Shapes
Ref
Description
19.1
Recognise and represent 3-D shapes through 2-D projections and cross-sections, including plan and elevation
19.2
Recognise 3-D shapes from their nets
19.3
Draw / Construct accurate nets of solids
21) Graphs of Functions
Ref
Description
Plotting graphs of
 simple cubic functions
1
with x  0
x
20.1
 exponential function y  k x for integer values of x and simple positive values of k
 the functions y = sin x and y = cos x,
using a spreadsheet or graph plotter as well as pencil and paper

reciprocal function y 
20.2 Recognising the characteristic shapes of all these functions
20.3
Starting with the graph of y = f(x) perform the following transformations y = f(x) + a, y = f(ax), y=f(x+ a), y = af(x) for linear,
quadratic, sine and cosine functions f(x)
20.4
Drawing, sketching and describing the graphs of trigonometric functions for angles of any size, including transformations involving
scalings in either or both the x and y directions
22) Circle Theorem
Ref
Description
21.1 Understanding that the tangent at any point on a circle is perpendicular to the radius at that point
21.2 Understanding and using the fact that tangents from an external point are equal in length
21.3 Explaining why the perpendicular from the centre to a chord bisect the chord
21.4
Proving and using the fact that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on
the circumference
21.5 Proving and using the fact that the angle subtended at the circumference by a semicircle is a right angle
21.6 Proving and using the fact that angles in the same segments are equal
21.7 Proving and using the fact that opposite angles of a cyclic quadrilateral sum to 180 degrees
21.8 Proving and using the alternate segment theorem
23) Inequalities
Ref
Description
22.1 Solving linear inequalities in one variable
22.2 Represent the solution set on a number line
22.3 Represent inequalities graphically
22.4 Solving several linear inequalities in two variables and finding the solution set on a graph using appropriate shading
24) Symmetry and Transformations
Ref
Description
23.1
Recognise symmetry properties (e.g. plane symmetry and order of rotational symmetry about an axis) for prisms and pyramids,
including cylinders and cones
23.2
Reflect simple plane figures in horizontal, vertical and diagonal lines
23.3
Rotate simple plane figures about the origin, vertices or mid-points of edges of the figures, through multiples of 90°
23.4
Construct given translations and enlargements of simple plane figures
23.5
Recognise and fully describe reflections, rotations, translations and enlargements
23.6
Understand that shapes produced by translation, rotation and reflection are congruent to its image and use this to make geometric
inferences
23.7
Recognising that enlargements preserve angle but not length, and find the length of missing sides on similar shapes
23.8
Understanding the implications of enlargement for perimeter
23.9
Understand and use the effect of enlargement on areas and volumes of shapes and solids
23.10
Understanding and using SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and
to verify standard ruler and compass constructions
25) Vectors
Ref
Description
24.1 Understanding and using vector notation
24.2 Calculating, and representing graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector
24.3 Calculating the resultant of two vectors
24.4 Understanding and using the commutative and associative properties of vector addition
24.5 Solving simple geometrical problems in 2-D using vector methods