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Edexcel International GCSE Syllabus

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’