Here you can find example questions covering the Edexcel International GCSE Mathematics Syllabus. You can also try a demo test to get a better understanding of how BOFA works. The syllabus has been taken from the Pearson Edexcel International GCSE in Mathematics specification document.

Content	Strand	Sub-strand	Foundation Tier Curriculum Ref / Description	Higher Tier Curriculum Ref / Description
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	A Understand and use integers (positive, negative and zero)	A Understand and use integers (positive, negative and zero)
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	B Understand place value
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	C Use directed numbers in practical situations	C Use directed numbers in practical situations
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	D Order integers	D Order integers
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	E Use the four rules of addition, subtraction, multiplication and division	E Use the four rules of addition, subtraction, multiplication and division
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	F Use brackets and the hierarchy of operations	F Use brackets and the hierarchy of operations
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	G Use the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’
AO1 Numbers and Algebra	1 Numbers and the number system	1.1 Integers	H Identify prime factors, common factors and common multiples
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	A Understand and use equivalent fractions, simplifying a fraction by cancelling common factors.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	B Understand and use mixed numbers and vulgar fractions.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	C Identify common denominators.	C Identify common denominators.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	D Order fractions and calculate a given fraction of a given quantity.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	E Express a given number as a fraction of another number.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	F Use common denominators to add and subtract fractions and mixed numbers.	F Use common denominators to add and subtract fractions and mixed numbers.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	G Convert a fraction to a decimal or a percentage.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	H Understand and use unit fractions as multiplicative inverses.	H Understand and use unit fractions as multiplicative inverses.
AO1 Numbers and Algebra	1 Numbers and the number system	1.2 Fractions	I Multiply and divide fractions and mixed numbers.	I Multiply and divide fractions and mixed numbers.
AO1 Numbers and Algebra	1 Numbers and the number system	1.3 Decimals	A Use decimal notation	A Convert recurring decimals into fractions
AO1 Numbers and Algebra	1 Numbers and the number system	1.3 Decimals	B Understand place value
AO1 Numbers and Algebra	1 Numbers and the number system	1.3 Decimals	C Order decimals
AO1 Numbers and Algebra	1 Numbers and the number system	1.3 Decimals	D Convert a decimal to a fraction or a percentage	D Convert a decimal to a fraction or a percentage
AO1 Numbers and Algebra	1 Numbers and the number system	1.3 Decimals	E Recognise that a terminating decimal is a fraction
AO1 Numbers and Algebra	1 Numbers and the number system	1.4 Powers and roots	A Identify square numbers and cube numbers	A Understand the meaning of surds
AO1 Numbers and Algebra	1 Numbers and the number system	1.4 Powers and roots	B Calculate squares, square roots, cubes and cube roots	B Manipulate surds, including rationalising a denominator
AO1 Numbers and Algebra	1 Numbers and the number system	1.4 Powers and roots	C Use index notation and index laws for multiplication and division of positive and negative integer powers including zero	C Use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers
AO1 Numbers and Algebra	1 Numbers and the number system	1.4 Powers and roots	D Express integers as a product of powers of prime factors	D Express integers as a product of powers of prime factors
AO1 Numbers and Algebra	1 Numbers and the number system	1.4 Powers and roots		E Find highest common factors (HCF) and lowest common multiples (LCM)
AO1 Numbers and Algebra	1 Numbers and the number system	1.5 Set language and notation		A Understand sets defined in algebraic terms, and understand and use subsets
AO1 Numbers and Algebra	1 Numbers and the number system	1.5 Set language and notation	B Use the set notation $uu$, $nn$ and $in$ and $notin$	B Use Venn diagrams to represent sets and the number of elements in sets
AO1 Numbers and Algebra	1 Numbers and the number system	1.5 Set language and notation	C Understand the concept of the universal set and the empty set and the symbols for these sets	C Use the notation $n(A)$ for the number of elements in the set A
AO1 Numbers and Algebra	1 Numbers and the number system	1.5 Set language and notation	D Understand and use the complement of a set	D Use sets in practical situations
AO1 Numbers and Algebra	1 Numbers and the number system	1.5 Set language and notation	E Use Venn diagrams to represent sets	E Use Venn diagrams to represent sets
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	A Understand that ‘percentage’ means ‘number of parts per 100’	A Use repeated percentage change
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	B Express a given number as a percentage of another number	B Solve compound interest problems
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	C Express a percentage as a fraction and as a decimal
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	D Understand the multiplicative nature of percentages as operators	D Understand the multiplicative nature of percentages as operators
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	E Solve simple percentage problems, including percentage increase and decrease	E Solve simple percentage problems, including percentage increase and decrease
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	F Use reverse percentages	F Use reverse percentages
AO1 Numbers and Algebra	1 Numbers and the number system	1.6 Percentages	G Use compound interest and depreciation	G Use compound interest and depreciation
AO1 Numbers and Algebra	1 Numbers and the number system	1.7 Ratio and proportion	A Use ratio notation, including reduction to its simplest form and its various links to fraction notation
AO1 Numbers and Algebra	1 Numbers and the number system	1.7 Ratio and proportion	B Divide a quantity in a given ratio or ratios	B Divide a quantity in a given ratio or ratios
AO1 Numbers and Algebra	1 Numbers and the number system	1.7 Ratio and proportion	C Use the process of proportionality to evaluate unknown quantities
AO1 Numbers and Algebra	1 Numbers and the number system	1.7 Ratio and proportion	D Calculate an unknown quantity from quantities that vary in direct proportion
AO1 Numbers and Algebra	1 Numbers and the number system	1.7 Ratio and proportion	E Solve word problems about ratio and proportion	E Solve word problems about ratio and proportion
AO1 Numbers and Algebra	1 Numbers and the number system	1.8 Degree of accuracy	A Round integers to a given power of 10	A Solve problems using upper and lower bounds where values are given to a degree of accuracy
AO1 Numbers and Algebra	1 Numbers and the number system	1.8 Degree of accuracy	B Round to a given number of significant figures or decimal places
AO1 Numbers and Algebra	1 Numbers and the number system	1.8 Degree of accuracy	C Identify upper and lower bounds where values are given to a degree of accuracy
AO1 Numbers and Algebra	1 Numbers and the number system	1.8 Degree of accuracy	D Use estimation to evaluate approximations to numerical calculations
AO1 Numbers and Algebra	1 Numbers and the number system	1.9 Standard form	A Calculate with and interpret numbers in the form $a xx 10^n$ where $n$ is an integer and $1 le a < 10$	A Solve problems involving standard form
AO1 Numbers and Algebra	1 Numbers and the number system	1.10 Applying number	A Use and apply number in everyday personal, domestic or community life
AO1 Numbers and Algebra	1 Numbers and the number system	1.10 Applying number	B Carry out calculations using standard units of mass, length, area, volume and capacity	B Carry out calculations using standard units of mass, length, area, volume and capacity
AO1 Numbers and Algebra	1 Numbers and the number system	1.10 Applying number	C Understand and carry out calculations using time, and carry out calculations using money, including converting between currencies
AO1 Numbers and Algebra	1 Numbers and the number system	1.11 Electronic calculators	A Use a scientific electronic calculator to determine numerical results
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.1 Use of symbols		A Use index notation involving fractional, negative and zero powers
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.1 Use of symbols	B Understand that algebraic expressions follow the generalised rules of arithmetic	B Understand that algebraic expressions follow the generalised rules of arithmetic
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.1 Use of symbols	C Use index notation for positive and negative integer powers (including zero)	C Use index notation for positive and negative integer powers (including zero)
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.1 Use of symbols	D Use index laws in simple cases	D Use index laws in simple cases
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation	A Evaluate expressions by substituting numerical values for letters	A Expand the product of two or more linear expressions
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation	B Collect like terms	B Understand the concept of a quadratic expression and be able to factorise such expressions
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation	C Multiply a single term over a bracket	C Manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation	D Take out common factors	D Complete the square for a given quadratic expression
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation	E Expand the product of two simple linear expressions	E Use algebra to support and construct proofs
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.2 Algebraic manipulation		F Understand the concept of a quadratic expression and be able to factorise such expressions (limited to $x^2+bx+c$)
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 Expressions and formulae	A Understand that a letter may represent an unknown number or a variable	A 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
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 Expressions and formulae	B Use correct notational conventions for algebraic expressions and formulae	B Use correct notational conventions for algebraic expressions and formulae
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 Expressions and formulae	C Substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae	C Substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 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	D Use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 Expressions and formulae	E Derive a formula or expression	E Derive a formula or expression
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.3 Expressions and formulae	F Change the subject of a formula where the subject appears once	F Change the subject of a formula where the subject appears once
AO1 Numbers and Algebra	2 Equations, formulae and identities	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	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
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.4 Linear equations	B Set up simple linear equations from given data	B Set up simple linear equations from given data
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.5 Proportion		A Set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.6 Simultaneous linear equations	A Calculate the exact solution of two simultaneous equations in two unknowns	A Calculate the exact solution of two simultaneous equations in two unknowns
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.6 Simultaneous linear equations		B Interpret the equations as lines and the common solution as the point of intersection
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.7 Quadratic equations	A Solve quadratic equations by factorisation (limited to $x^2+bx+c$)	A Solve quadratic equations by factorisation
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.7 Quadratic equations		B Solve quadratic equations by using the quadratic formula or completing the square
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.7 Quadratic equations		C Form and solve quadratic equations from data given in a context
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.7 Quadratic equations		D Solve simultaneous equations in two unknowns, one equation being linear and the other being quadratic
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.8 Inequalities	A Understand and use the symbols >, <, ≥ and ≤	A Solve quadratic inequalities in one unknown and represent the solution set on a number line
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.8 Inequalities	B Understand and use the convention for open and closed intervals on a number line	B Identify harder examples of regions defined by linear inequalities
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.8 Inequalities	C Solve simple linear inequalities in one variable and represent the solution set on a number line	C Solve simple linear inequalities in one variable and represent the solution set on a number line
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.8 Inequalities	D Represent simple linear inequalities on rectangular Cartesian graphs	D Represent simple linear inequalities on rectangular Cartesian graphs
AO1 Numbers and Algebra	2 Equations, formulae and identities	2.8 Inequalities	E Identify regions on rectangular Cartesian graphs defined by simple linear inequalities	E Identify regions on rectangular Cartesian graphs defined by simple linear inequalities
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.1 Sequences	A Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence	A Understand and use common difference ($d$) and first term ($a$) in an arithmetic sequence
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.1 Sequences	B Find subsequent terms of an integer sequence and the rule for generating it	B Know and use $n^"th"$ term = $a+(n-1)d$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.1 Sequences	C Use linear expressions to describe the $n^"th"$ term of arithmetic sequences	C Find the sum of the first $n$ terms of an arithmetic series ($S_n$)
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.2 Function notation		A Understand the concept that a function is a mapping between elements of two sets
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.2 Function notation		B Use function notations of the form $f(x)$ and $f:x mapsto ...$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.2 Function notation		C Understand the terms ‘domain’ and ‘range’ and which values may need to be excluded from a domain
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.2 Function notation		D Understand and find the composite function $fg$ and the inverse function $f^-1$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	A Interpret information presented in a range of linear and non-linear graphs	A Recognise, plot and draw graphs with equation: $y=Ax^3+Bx^2+Cx+D$ in which: (i) the constants are integers and some could be zero (ii) the letters xand ycan be replaced with any other two letters or: $y=Ax^3+Bx^2+Cx+D+E/x+F/(x^2)$ in which: (i) the constants are numerical and at least three of them are zero (ii) the letters xand ycan be replaced with any other two letters or: $y= sinx, y=cosx, y=tanx$ for angles of any size (in degrees)
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	B Understand and use conventions for rectangular Cartesian coordinates	B Apply to the graph of $y=f(x)$ the transformations $y=f(x)+a, y=f(ax), y=f(x+a), y=af(x)$ for linear, quadratic, sine and cosine functions
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	C Plot points $(x,y)$ in any of the four quadrants or locate points with given coordinates	C Interpret and analyse transformations of functions and write the functions algebraically
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	D Determine the coordinates of points identified by geometrical information	D Find the gradients of non-linear graphs
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	E Determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points	E Find the intersection points of two graphs, one linear (y1) and one non-linear (y2) and recognise that the solutions correspond to the solutions of $(y_2-y_1)=0$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	F Draw and interpret straight line conversion graphs	F Calculate the gradient of a straight line given the coordinates of two points
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	G Find the gradient of a straight line	G Find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	H Recognise that equations of the form $y=mx+c$ are straight line graphs with gradient mand intercept on the $y$-axis at the point $(0,c)$	H Recognise that equations of the form $y=mx+c$ are straight line graphs with gradient mand intercept on the $y$-axis at the point $(0,c)$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.3 Graphs	I Recognise, generate points and plot graphs of linear and quadratic functions	I Recognise, generate points and plot graphs of linear and quadratic functions
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.4 Calculus		A Understand the concept of a variable rate of change
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.4 Calculus		B Differentiate integer powers of $x$
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.4 Calculus		C Determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.4 Calculus		D Distinguish between maxima and minima by considering the general shape of the graph only
AO1 Numbers and Algebra	3 Sequences, functions and graphs	3.4 Calculus		E Apply calculus to linear kinematics and to other simple practical problems
AO2 Shape, space and measure	4 Geometry	4.1 Angles, lines and triangles	A Distinguish between acute, obtuse, reflex and right angles	A Distinguish between acute, obtuse, reflex and right angles
AO2 Shape, space and measure	4 Geometry	4.1 Angles, lines and triangles	B Use angle properties of intersecting lines, parallel lines and angles on a straight line	B Use angle properties of intersecting lines, parallel lines and angles on a straight line
AO2 Shape, space and measure	4 Geometry	4.1 Angles, lines and triangles	C Understand the exterior angle of a triangle property and the angle sum of a triangle property	C Understand the exterior angle of a triangle property and the angle sum of a triangle property
AO2 Shape, space and measure	4 Geometry	4.1 Angles, lines and triangles	D Understand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties of these triangles	D Understand the terms ‘isosceles’, ‘equilateral’ and ‘right-angled triangles’ and the angle properties of these triangles
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	A Recognise and give the names of polygons	A Recognise and give the names of polygons
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	B Understand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals	B Understand and use the term ‘quadrilateral’ and the angle sum property of quadrilaterals
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	C Understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite	C Understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	D Understand the term ‘regular polygon’ and calculate interior and exterior angles of regular polygons	D Understand the term ‘regular polygon’ and calculate interior and exterior angles of regular polygons
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	E Understand and use the angle sum of polygons	E Understand and use the angle sum of polygons
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	F Understand congruence as meaning the same shape and size	F Understand congruence as meaning the same shape and size
AO2 Shape, space and measure	4 Geometry	4.2 Polygons	G Understand that two or more polygons with the same shape and size are said to be congruent to each other	G Understand that two or more polygons with the same shape and size are said to be congruent to each other
AO2 Shape, space and measure	4 Geometry	4.3 Symmetry	A Identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure	A Identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure
AO2 Shape, space and measure	4 Geometry	4.4 Measures	A Interpret scales on a range of measuring instruments	A Interpret scales on a range of measuring instruments
AO2 Shape, space and measure	4 Geometry	4.4 Measures	B Calculate time intervals in terms of the 24-hour and the 12-hour clock	B Calculate time intervals in terms of the 24-hour and the 12-hour clock
AO2 Shape, space and measure	4 Geometry	4.4 Measures	C Make sensible estimates of a range of measures	C Make sensible estimates of a range of measures
AO2 Shape, space and measure	4 Geometry	4.4 Measures	D Understand angle measure including three-figure bearings	D Understand angle measure including three-figure bearings
AO2 Shape, space and measure	4 Geometry	4.4 Measures	E Measure an angle to the nearest degree	E Measure an angle to the nearest degree
AO2 Shape, space and measure	4 Geometry	4.4 Measures	F Understand and use the relationship between average speed, distance and time	F Understand and use the relationship between average speed, distance and time
AO2 Shape, space and measure	4 Geometry	4.4 Measures	G Use compound measure such as speed, density and pressure	G Use compound measure such as speed, density and pressure
AO2 Shape, space and measure	4 Geometry	4.5 Construction	A Measure and draw lines to the nearest millimetre	A Measure and draw lines to the nearest millimetre
AO2 Shape, space and measure	4 Geometry	4.5 Construction	B Construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses	B Construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses
AO2 Shape, space and measure	4 Geometry	4.5 Construction	C Solve problems using scale drawings	C Solve problems using scale drawings
AO2 Shape, space and measure	4 Geometry	4.5 Construction	D Use straight edge and compasses to: (i) construct the perpendicular bisector of a line segment (ii) construct the bisector of an angle	D Use straight edge and compasses to: (i) construct the perpendicular bisector of a line segment (ii) construct the bisector of an angle
AO2 Shape, space and measure	4 Geometry	4.6 Circle properties	A Recognise the terms ‘centre’, ‘radius’, ‘chord’, ‘diameter’, ‘circumference’, ‘tangent’, ‘arc’, ‘sector’ and ‘segment’ of a circle	A Understand and use the internal and external intersecting chord properties
AO2 Shape, space and measure	4 Geometry	4.6 Circle properties	B Understand chord and tangent properties of circles	B Recognise the term ‘cyclic quadrilateral’
AO2 Shape, space and measure	4 Geometry	4.6 Circle properties		C 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
AO2 Shape, space and measure	4 Geometry	4.7 Geometrical reasoning	A Give informal reasons, where required, when arriving at numerical solutions to geometrical problems	A Provide reasons, using standard geometrical statements, to support numerical values for angles obtained in any geometrical context involving lines, polygons and circles
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem	A Know, understand and use Pythagoras’ theorem in two dimensions	A Understand and use sine, cosine and tangent of obtuse angles
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem	B Know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle	B Understandand use angles of elevation and depression
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem	C Apply trigonometrical methods to solve problems in two dimensions	C Understand and use the sine and cosine rules for any triangle
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem		D Use Pythagoras’ theorem in three dimensions
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem		E Understand and use the formula $1/2 ab sinC$ for the area of a triangle
AO2 Shape, space and measure	4 Geometry	4.8 Trigonometry and Pythagoras' theorem		F Apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane
AO2 Shape, space and measure	4 Geometry	4.9 Mensuration of 2D shapes	A Convert measurements within the metric system to include linear and area units	A Find perimeters and areas of sectors of circles
AO2 Shape, space and measure	4 Geometry	4.9 Mensuration of 2D shapes	B Find the perimeter of shapes made from triangles and rectangles	B Find the perimeter of shapes made from triangles and rectangles
AO2 Shape, space and measure	4 Geometry	4.9 Mensuration of 2D shapes	C Find the area of simple shapes using the formulae for the areas of triangles and rectangles	C Find the area of simple shapes using the formulae for the areas of triangles and rectangles
AO2 Shape, space and measure	4 Geometry	4.9 Mensuration of 2D shapes	D Find the area of parallelograms and trapezia	D Find the area of parallelograms and trapezia
AO2 Shape, space and measure	4 Geometry	4.9 Mensuration of 2D shapes	E Find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles	E Find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	A Recognise and give the names of solids	A Find the surface area and volume of a sphere and a right circular cone using relevant formulae
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	B Understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids	B Understand the terms ‘face’, ‘edge’ and ‘vertex’ in the context of 3D solids
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	C Find the surface area of simple shapes using the area formulae for triangles and rectangles	C Find the surface area of simple shapes using the area formulae for triangles and rectangles
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	D Find the surface area of a cylinder	D Find the surface area of a cylinder
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	E Find the volume of prisms, including cuboids and cylinders, using an appropriate formula	E Find the volume of prisms, including cuboids and cylinders, using an appropriate formula
AO2 Shape, space and measure	4 Geometry	4.10 3D shapes and volumes	F Convert between units of volume within the metric system	F Convert between units of volume within the metric system
AO2 Shape, space and measure	4 Geometry	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	A Understand that areas of similar figures are in the ratio of the square of corresponding sides
AO2 Shape, space and measure	4 Geometry	4.11 Similarity	B Use and interpret maps and scale drawings	B Understand that volumes of similar figures are in the ratio of the cube of corresponding sides
AO2 Shape, space and measure	4 Geometry	4.11 Similarity		C Use areas and volumes of similar figures in solving problems
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		A Understand that a vector has both magnitude and direction
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		B Understand and use vector notation including column vectors
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		C Multiply vectors by scalar quantities
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		D Add and subtract vectors
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		E Calculate the modulus (magnitude) of a vector
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		F Find the resultant of two or more vectors
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.1 Vectors		G Apply vector methods for simple geometrical proofs
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	A Understand that rotations are specified by a centre and an angle	A Understand that rotations are specified by a centre and an angle
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	B Rotate a shape about a point through a given angle	B Rotate a shape about a point through a given angle
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	C Recognise that an anti-clockwise rotation is a positive angle of rotation and a clockwise rotation is a negative angle of rotation	C Recognise that an anti-clockwise rotation is a positive angle of rotation and a clockwise rotation is a negative angle of rotation
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	D Understand that reflections are specified by a mirror line	D Understand that reflections are specified by a mirror line
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	E Construct a mirror line given an object and reflect a shape given a mirror line	E Construct a mirror line given an object and reflect a shape given a mirror line
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	F Understand that translations are specified by a distance and direction	F Understand that translations are specified by a distance and direction
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	G Translate a shape	G Translate a shape
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	H Understandand use column vectors in translations	H Understandand use column vectors in translations
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	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	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
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	J Understand that enlargements are specified by a centre and a scale factor	J Understand that enlargements are specified by a centre and a scale factor
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	K Understand that enlargements preserve angles and not lengths	K Understand that enlargements preserve angles and not lengths
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	L Enlarge a shape given the scale factor	L Enlarge a shape given the scale factor
AO2 Shape, space and measure	5 Vectors and transformation geometry	5.2 Transformation geometry	M Identify and give complete descriptions of transformations	M Identify and give complete descriptions of transformations
AO3 Handling Data	6 Statistics and probability	6.1 Graphical representation of data	A Use different methods of presenting data	A Construct and interpret histograms
AO3 Handling Data	6 Statistics and probability	6.1 Graphical representation of data	B Use appropriate methods of tabulation to enable the construction of statistical diagrams	B Construct cumulative frequency diagrams from tabulated data
AO3 Handling Data	6 Statistics and probability	6.1 Graphical representation of data	C Interpret statistical diagrams	C Use cumulative frequency diagrams
AO3 Handling Data	6 Statistics and probability	6.2 Statistical measures	A Understand the concept of average	A Estimate the median from a cumulative frequency diagram
AO3 Handling Data	6 Statistics and probability	6.2 Statistical measures	B Calculate the mean, median, mode and range for a discrete data set	B Understand the concept of a measure of spread
AO3 Handling Data	6 Statistics and probability	6.2 Statistical measures	C Calculate an estimate for the mean for grouped data	C Find the interquartile range from a discrete data set
AO3 Handling Data	6 Statistics and probability	6.2 Statistical measures	D Identify the modal class for grouped data	D Estimate the interquartile range from a cumulative frequency diagram
AO3 Handling Data	6 Statistics and probability	6.3 Probability	A Understand the language of probability	A Draw and use tree diagrams
AO3 Handling Data	6 Statistics and probability	6.3 Probability	B Understand and use the probability scale	B Determine the probability that two or more independent events will occur
AO3 Handling Data	6 Statistics and probability	6.3 Probability	C Understand and use estimates or measures of probability from theoretical models	C Use simple conditional probability when combining events
AO3 Handling Data	6 Statistics and probability	6.3 Probability	D Find probabilities from a Venn diagram	D Apply probability to simple problems
AO3 Handling Data	6 Statistics and probability	6.3 Probability	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	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
AO3 Handling Data	6 Statistics and probability	6.3 Probability	F List all the outcomes for single events and for two successive events in a systematic way	F List all the outcomes for single events and for two successive events in a systematic way
AO3 Handling Data	6 Statistics and probability	6.3 Probability	G Estimate probabilities from previously collected data	G Estimate probabilities from previously collected data
AO3 Handling Data	6 Statistics and probability	6.3 Probability	H Calculate the probability of the complement of an event happening	H Calculate the probability of the complement of an event happening
AO3 Handling Data	6 Statistics and probability	6.3 Probability	I Use the addition rule of probability for mutually exclusive events	I Use the addition rule of probability for mutually exclusive events
AO3 Handling Data	6 Statistics and probability	6.3 Probability	J Understandand use the term ‘expected frequency’	J Understandand use the term ‘expected frequency’