AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Higher – Unit 3
1 hour 30 minutes calculator exam
80 marks
– 40% (UMS 120 marks)
20 - 30% Functional Elements
7 marks Number, 25 marks Algebra, 48 marks Geometry
19. Number skills revisited
20. Angles
21. Measurement
1
22. Triangles and constructions
23. Equations, formulae and proof
24. Quadrilaterals and other polygons
25. Perimeter, area and volume
26. 3-D objects
27. Reflection, translation and
3
6
5
5
6
4
4
2
6
Working with numbers and the number system: N1.3, N1.4,
N1.14
Fractions, decimals and Percentages: N2.1, N2.5, N2.6, N2.7
Ratio and Proportion: N3.1, N3.3
Properties of angles and shapes: G1.1, G1.2
Measures and Construction: G3.1, G3.6
Working with numbers and the number system: N1.3
Measures and Construction: G3.1, G3.3, G3.4, G3.5
Properties of angles and shapes: G1.1, G1.2, G1.8
Measures and Construction: G3.9, G3.10
The Language of Algebra: N4.1, N4.2
Expressions and Equations: N5.1, N5.4, N5.6, N5.8
Geometrical reasoning and calculation: G2.3, G2.3h
Expressions and Equations: N5.4
Sequences, Functions and Graphs: N6.3
Properties of angles and shapes: G1.2, G1.3, G1.4
Mensuration: G4.1, G4.4
Geometrical reasoning and calculation: G2.4
Properties of angles and shapes: G1.6, G1.7
Vectors: G5.1

rotation
28. Circles and cylinders
6
29. Measurement
2
30. Enlargement and similarity
31. Non-linear graphs
3
3
6
32. Constructions and loci
33
. Pythagoras’ theorem
3
4
34. Trigonometry 8
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Properties of angles and shapes: G1.5
Geometrical reasoning and calculation: G2.4
Mensuration: G4.1, G4.3, G4.4
Measures and Construction: G3.4, G3.7
Properties of angles and shapes: G1.7, G1.7h G1.8
Measures and Construction: G3.2
Expressions and Equations: N5.2h N5.5h
Sequences, Functions and Graphs: N6.7h, N6.8h, N6.11h,
N6.12, N6.13
Measures and Construction: G3.8, G3.10, G3.11
Geometrical reasoning and calculation: G2.1
Working with numbers and the number system: N1.14h
Geometrical reasoning and calculation: G2.2h
Measures and Construction: G3.6

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 19 Number skills revisited
SEE FOUNDATION SCHEME OF WORK
Time: 3 hours
The number work will not be tested in isolation, but will be in contexts that tie in the other areas of the unit content.
N1.3
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
N1.4
Approximate to a given power of 10, up to three decimal places and one significant figure.
N1.14
Use calculators effectively and efficiently.
N2.1
Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
N2.5
Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.6 Interpret fractions, decimals, percentages as operators
N2.7
Calculate with fractions, decimals and percentages.
N3.1
Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
N3.3 Solve problems involving ratio and proportion, including the unitary method of solution
ADDITIONAL HIGHER CONTENT
N1.4h approximate to specified or appropriate degrees of accuracy including a given number of decimal places and significant figures
N3.3h Direct and indirect proportion and exponential growth
AQA
Spec ref
Learning objectives Grade Common mistakes and misconceptions
B N1.4h
N2.1 round to a given number of significant figures round to a suitable degree of accuracy compare fractions in geometry questions
Not reading the question and therefore understanding the suitability of the rounding required.
N1.14
h
B – A* enter complex calculations and use function keys for reciprocals, squares, cubes and other powers enter a range of calculations including those involving money, time and other measures understand and use functions including trigonometrical functions use a calculator to input numbers in standard form use a calculator to explore exponential growth and decay using a multiplier and the power key
Trying to input all figures in a calculation without checking by doing the calculation in steps.
Not checking if the calculator is in degree or radian mode. understand the calculator display, knowing how to interpret the display, when the display has been rounded by the calculator and not to round during the intermediate steps of calculation understand how to use a calculator to simplify fractions and to convert between decimals and fractions and vice versa
N3.3h use ratio and proportion to solve word problems using informal strategies or using the unitary method of solution
B – A* Not checking whether the question asks for direct or inverse proportion. Not

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification solve best buy problems using informal strategies or using the unitary method of solution use direct proportion to solve geometrical problems use ratios to solve geometrical problems reading the ‘square’ or ‘cube’ element of the question calculate an unknown quantity from quantities that vary in direct proportion or inverse proportion set up and use equations to solve word and other problems involving direct proportion or inverse proportion relate algebraic solutions to graphical representation of the equations
Resources: AQA GCSE Maths Middle sets Book Sections 20
AQA Modular GCSE Mathematics Higher Tier

Chapter 1 Whole numbers P1

Chapter 2 Decimals and fractions P8

Chapter 3 Approximation and estimation P20

Chapter 4 Percentages and money P28

Chapter 5 Ratio P43

Chapter 9 Extending the number system P74

Chapter 13 Direct and inverse proportion P114; other forms of proportion P118; Proportion and graphs P121
Resources
Higher Practice Book sections 10.3, 10.4, 11.1 – 11.4, 13.1 – 13.2, 14.1, 19.1 – 19.3, 20.1 – 20.3 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Number, fraction, decimals/Teaching
Lesson plans/resource sheets/homework sheets/powerpoints/worksheets
Functional skills activities Chapters 1, 3, 4, 12, 14, 15
Notes: Candidates should know not to round off values during the intermediate steps of a calculation.
Candidates should be able to use a calculator to apply the four rules to fractions and decimals in problems.
This is part of the core number work required across all units. The core number work will be assessed so that it is linked to other specification references within this unit. In this unit candidates will be expected to use a calculator when solving problems. Questions requiring these number skills could be set, for example, as a numerical part of a question testing fractions, decimals, percentages, ratio or proportion, interpreting graphs, using a formula in words or substitution into an algebraic expression, using a calculator where appropriate.
Candidates should know that some answers are inappropriate without some form of rounding, for example 4.2 buses.
Candidates will not be required to calculate repeated percentage change, reverse percentage or compound interest in this unit. These are assessed in Unit 1 only . Candidates should note that division in a given ratio is assessed in Unit 2 only .
Direct and inverse proportion questions will be restricted to the following proportiona lities: y to x, y to x², y to x³, y to √x, y to 1/x, y to 1/x², 1/x³, 1/³√x
The expected approach would be to set up an equation using a constant of proportionality. Find this and then use the equation to find a value of y given x, or x given y. Other methods may be used and can be given full credit.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 20 Angles
SEE FOUNDATION SCHEME OF WORK
Time: 6 hours
G1.1
Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex.
G1.2
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G3.1
Use and interpret maps and scale drawings.
G3.6
Understand and use bearings.
ADDITIONAL HIGHER CONTENT
None
Resources: AQA GCSE Maths Middle sets Book Sections 21.1 – 21.3
AQA Modular GCSE Mathematics Higher Tier

Types and names of angles; Lines and angles; Parallel lines P227

Types of triangle; The sum of the angles in a triangle; Exterior angle of a triangle P230

Special triangles; special quadrilaterals P232

Sum of the angles of a quadrilateral P234
Higher Practice Book 23.1 – 23.4 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Angles & shapes/Teaching Resources
Lesson plans and starters/questions/homework sheets/powerpoint www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Measures/Teaching Resources
Lesson plans /worksheets/homework sheets/cards
Functional skills activities 11.2
Notes: Candidates should know the meaning and properties of alternate, corresponding, interior and vertically opposite angles. Colloquial terms such as F or Z angles should not be used. Candidates should know the names and properties of isosceles, equilateral, right angled and scalene triangles.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 21 Measurement 1
SEE FOUNDATION SCHEME OF WORK
Time: 5 hours
N1.3
Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
G3.3
Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements.
G3.4
Convert measurements from one unit to another.
G3.5 Make sensible estimates of a range of measures
ADDITIONAL HIGHER CONTENT
None
Resources: AQA GCSE Maths Middle sets Book Sections 22.1 – 22.4
AQA Modular GCSE Mathematics Higher Tier

Units of measurement; metric units; changing from one metric unit to another P326

Estimating with sensible units using suitable degrees of accuracy P327

Imperial units; metric and imperial conversions P329

Discrete and continuous measures P330

A closer look at measures P331

Calculations involving bounds P332
Higher Practice Book 10.3 – 10.4, 14.1 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Number, fractions, decimals/Teaching Resources lesson plans/worksheets/homework sheet/powerpoints/resource sheets www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Measures/Teaching Resources lesson plans/worksheets/homework sheets/cards
Functional skills activities 8.1, 8.2, 8.3, 19.1, 19.3
Notes: Metric conversions should be known. Imperial to metric conversions will be limited to 5 miles ~ 8 kilometres, 4.5 litres ~ 1 gallon, 2.2 pounds ~ 1 kilogram, 1 inch ~ 2.5 centimetres. Any imperial to metric conversions, other than those listed above, will be stated in the question.
Candidates will not be expected to recall conversions between capacity and volume.
For example 1ml = 1cm ³

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 22 Triangles and constructions
SEE FOUNDATION SCHEME OF WORK
Time: 5 hours
G1.1
Recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex.
G1.2
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.8
Understand congruence and similarity.
G3.9
Draw triangles and other 2D shapes using a ruler and protractor.
G3.10
Use straight edge and a pair of compasses to do constructions.
ADDITIONAL HIGHER CONTENT
None
AQA
Mod spec ref
Learning objectives Grade Common mistakes and misconceptions
G1.8
G3.10 understand and use conditions for congruent triangles understand and use SSS, SAS, ASA and RHS to verify standard ruler and compass constructions understand similarity of triangles and of other plane figures, and use this to make geometric inferences use straight edge and a pair of compasses to do standard constructions construct a triangle construct an equilateral triangle with a given side construct a perpendicular bisector of a given line construct the perpendicular from a point to a line construct the perpendicular from a point on a line construct an angle bisector construct angles of 60 º, 90º, 30º and 45º construct a regular hexagon inside a circle construct diagrams of 2D shapes from given information
B/A
B
Mixing the terms congruent and similar.
Not using a compass. Rubbing out construction lines.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources: AQA GCSE Maths Middle sets Book Sections 23.1 -23.3
AQA Modular GCSE Mathematics Higher Tier


Chapter 23 Angles, parallel lines and polygons P227
Accurate constructions P269

More constructions P272

Congruent shapes; congruent triangles P326

Similar figures P342

Similar triangles P344

Showing that two triangles are similar P346
Higher Practice Book 23.1 – 23.4, 30.1 – 30.2, 33.1 – 33.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/2D/3D shapes & loci/Teaching Resources lesson plans/homework sheets/worksheet www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 3/Angles & shapes/Teaching Resources
Lesson plans and starters/questions/homework sheets/powerpoint
Functional skills activities 11.2, 11.3
Notes: Candidates will be expected to show clear evidence that a straight edge and compasses have been used to do constructions.
When constructing triangles, compasses should be used to measure lengths rather than rulers. Construction arcs should be shown.
Candidates will be expected to know the connection between the linear, area and volume scale factors of similar shapes and solids.
Questions may be asked that exploit the relationship between weight and volume, area and cost of paint, etc.
Candidates can justify congruence by a variety of methods but their justifications must be complete. The use of SSS notation, etc. is not expected but will make the justification of congruence easier.
Scales will be given as, for example, 1cm represents 10km, or 1 : 100.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 23 Equations, formulae and proof
SEE FOUNDATION SCHEME OF WORK
Time: 6 hours
N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation
N4.2
Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.1
Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
N5.4
Set up and solve simple linear equations.
N5.6
Derive a formula, substitute numbers into a formula.
N5.8
Use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them.
G2.3
Justify simple geometrical properties.
ADDITIONAL HIGHER CONTENT
N4.2h Higher tier candidates should understand the term ‘identity’ and its symbol
N5.1h Multiply two linear expression including (x + a)(x + b) and (cx + a)(dx + b)
N5.4h Including simultaneous equations in two unknowns.
N5.5h Solve quadratic equations – using the quadratic formula, and factorising. Use of trial and improvement to solve a quadratic equation is not an acceptable method.
G2.3h Simple geometric proofs – may involve congruent triangles (and circle theorems)
AQA
Mod spec ref
Learning objectives Grade Common mistakes and misconceptions
G2.3h
N4.2h
N5.1h
N5.4h apply mathematical reasoning, explaining and justifying inferences and deductions show step-by-step deduction in solving a geometrical problem state constraints and give starting points when making deductions understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments
This is part of the core algebra work required across all units and will be assessed so that it is linked to other specification references within this unit whenever possible.
For example, the angles in a triangle are x° , ( x + 30)° and 2 x °.
a. Form an equation in terms of x .
b. Solve your equation and use it to work out the size of the largest angle in the triangle.
A rectangle has dimensions 2x and 3x -1
Write down an expression in terms of x for the perimeter and the area
Questions in this topic will include geometrical problems, problems set in a functional context and questions requiring a graphical solution.
The expected method for solving simultaneous equations, where one is linear and
A/A*
B/A
Not explaining in words as well as with number work. Using a numerical example rather than generalising.
Working out the value for x without using algebra. Not finishing the question e.g. working out x but not the largest angle.
Example
Jo and Sam each have a piece of wood.
Jo's piece of wood measures 3 cm

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
N5.5h one is non-linear equation will be to substitute a variable from the linear equation into the non-linear equation.
For example, solve the simultaneous equations y = 11x – 2 and y = 5x².
The non-linear equation will be of the form y = ax ² + bx + c, where a, b and c are integers (including zero).
On Unit 3 these will generally lead to a quadratic equation that can be solved graphically to find approximate solutions, or by using the quadratic formula.
Choose or interpret answers to a geometrical problem, for example rejecting a negative solution as a length. solve geometrical problems that lead to a quadratic equation that can be solved by factorisation solve geometrical problems that lead to a quadratic equation that can be solved by using the quadratic formula
Candidates should be aware that use of trial and improvement is not an acceptable method. more than twice the length of Sam's piece of wood.
The sum of the lengths is 33cm.
How long is Jo's piece of wood?
Example
Expressions for the sides of a rectangle are 2x² cm and 9x cm.
The perimeter is 10 cm.
Work out the area of the rectangle.
Give your answer to a suitable degree of accuracy.
Resources: AQA GCSE Maths Middle sets Book Sections 24.1 -24.3
AQA Modular GCSE Mathematics Higher Tier

Iteration P207

Trial and improvement P208

Chapter 10 Introduction to algebra P86

Chapter 11 Solving equations P95

Chapter 12 Formulae P105

Chapter 19 Quadratic Equations P174

Chapter 20 Simultaneous Equations P189

Chapter 21 Algebraic methods P201
Higher Practice Book 12.1 -12.2, 18.1 – 18.3, 22.1, 24.1 – 24.5, 26.1, 26.4, 34.1 -34.2, 40.1 – 40.3 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Transformations/Teaching Resources lesson plans/homework sheets/powerpoints/pdfs www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Algebraic manipulation /Teaching Resources lesson plans/worksheets/homework sheets/powerpoints www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Trial and improvement/Teaching Resources lesson plans/resource sheets/homework sheets/powerpoints

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Equations/Teaching Resources lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 10.1 -10.4
Notes: Candidates should also know the meaning of the word term.
Questions will include geometrical problems, problems set in a functional context and questions requiring a graphical solution.
Trial & improvement answers will be expected to 1 d.p. Candidates will be expected to test the mid-value of the 1 d.p. interval to establish which
1 d.p. value is nearest to the solution.
Candidates should be able to explain reasons using words or diagrams.
Candidates should realise when an answer is inappropriate.
On Higher tier, proofs involving congruent triangles and circle theorems may be set.
Questions assessing quality of written communication will be set that require clear and logical steps to be shown, with reasons given.
Mini-investigations will not be set but candidates will be expected to make decisions and use the appropriate techniques to solve a problem drawing on well-known facts, such as the sum of angles in a triangle.
Multi-step problems will be set.
Redundant information may sometimes be used, for example the slant height of a parallelogram. Candidates should be able to identify which information given is needed to solve the given problem.
Candidates need not know that b 2 – 4 ac is the discriminant but should be aware that some quadratic equations have no solution.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
24 Quadrilaterals and other polygons Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
N5.4
Set up and solve simple linear equations.
N6.3
Use the conventions for coordinates in the plane and plot points in all four quadrants, including geometric information.
G1.2
Understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals.
G1.3
Calculate and use the sums of the interior and exterior angles of polygons.
G1.4
Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus.
ADDITIONAL HIGHER CONTENT
N6.3h 3D coordinate systems
AQA Mod spec ref
Learning objectives Grade Common mistakes and misconceptions
N6.3h
Resources: AQA GCSE Maths Middle sets Book Sections 25.1 – 25.4 use axes and coordinates to specify points in 3D find the coordinates of points identified by geometrical information in 3D
A Mixing up x, y and z
AQA Modular GCSE Mathematics Higher Tier

Polygons; interior and exterior angles of a polygon; sum of the interior angles of a polygon P237

Sum of the exterior angles of a polygon P238

Regular polygons; exterior angles of a regular polygon P239

Tesselations P240
Higher Practice Book 23.2 – 23.4, 30.1 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Coordinates and graphs/Teaching Resources lesson plans/homework sheets/problem sheets/spreadsheets www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Angles and shapes/Teaching Resources lesson plans & starters/homework sheets/questions/powerpoints
Functional skills activities
Notes Candidates should be able to calculate the values of the interior angle, exterior angle and angle at the centre of regular polygons.
Candidates should know the side, angle and diagonal properties of quadrilaterals.
Questions involving tessellations will be clearly defined and could relate to real-life situations, for example tiling patterns. Candidates should know how to work out the angle sum of polygons up to a hexagon. It will not be assumed that candidates know the names heptagon or nonagon.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 25 Perimeter, area and volume
SEE FOUNDATION SCHEME OF WORK
G4.1 Calculate perimeters and areas of shapes made from triangles and rectangles.
G4.4
Calculate volumes of right prisms and of shapes made from cubes and cuboids.
ADDITIONAL HIGHER CONTENT
G4.2h Calculate the area of a triangle using ½ ab sin C
AQA Mod spec ref
Learning objectives Grade
Time: 4 hours
Common mistakes and misconceptions
G4.1 calculate the area of shapes made from compound shapes made from two or more rectangles, for example an L shape or T shape work out the surface area of nets made up of rectangles and triangles calculate the area of a trapezium
B calculate the area of a triangle given the length of two sides and the included angle. A
Trying to split a trapezium into rectangles and triangles rather than using the formula.
G4.2h Trying to treat the triangle as a right angled triangle
Resources: AQA GCSE Maths Middle sets Book Sections 26.1 -26.3
AQA Modular GCSE Mathematics Higher Tier

3D shapes; volume; volume of a cuboid; surface area of a cuboid P315

Prisms; volume of a prism P316

Area of a triangle P377
Higher Practice Book 25.1, 25.4, 27.1 – 27.2, 38.1, 41.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Perimeter, area and volume/Teaching Resources lesson plans/problem sheets/powerpoints/homework sheets/spreadsheets
Functional skills activities 10.1 -10.4, 21.3

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 26 3-D objects
G2.4
Use 2D representations of 3D shapes.
SEE FOUNDATION SCHEME OF WORK
ADDITIONAL HIGHER CONTENT
None
Resources: AQA GCSE Maths Middle sets Book Sections 27.1
AQA Modular GCSE Mathematics Higher Tier
Higher Practice Book
Time: 2 hours www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/2D/3D, shapes & loci/Teaching Resources lesson plans/worksheets/homework sheets
Functional skills activities 22.1, 22.2

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 27 Reflection, translation and rotation
SEE FOUNDATION SCHEME OF WORK
Time: 6 hours
G1.6
Recognise reflection and rotation symmetry of 2D shapes.
G1.7
Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations.
G5.1
Understand and use vector notation for translations.
ADDITIONAL HIGHER CONTENT
G1.7h
Use positive fractional and negative scale factors. Translations will be specified by a vector
G5.1h Vector algebra
AQA Mod spec ref
G1.7h
Learning objectives
Transform shapes using more than one transformation
Grade
C
Describe combined transformations of shapes on a grid use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations
Common mistakes and misconceptions
Not appreciating that two transformations, one followed by another, may be equivalent to a single transformation.
Not understanding that for ‘general’ questions where no shape is given, transformations can be carried out on different shapes to investigate what happens.
G5.1h Calculate and represent graphically the sum of two vectors, the difference of two vectors and a scalar multiple of a vector. Calculate the resultant of two vectors.
Understand and use the commutative and associative properties of vector addition.
Solve simple geometric problems in 2D using vector methods understand and use vector notation apply vector methods for simple geometric proofs recognise when lines are parallel using vectors recognise when three or more points are collinear using vectors
A/A* Mixing up coordinates with column vectors.
Trying to use a diagram when algebra is required.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources: AQA GCSE Maths Middle sets Book Sections 28.1 -28.3
AQA Modular GCSE Mathematics Higher Tier


Lines of symmetry; rotational symmetry; symmetry of quadrilaterals P233
Reflection P276

Rotation P278

Translation P279

Describing transformations P284

Combinations of transformations P287

Vectors and scalars; vector notation P353

Equal vectors P354

Vectors in opposite directions; Multiplying a vector by a scalar P355

Vector addition P356

Vector diagrams P357

Vectors and geometry P360
Higher Practice Book 31.1 – 31.3, 42.1 -42.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Transformations /Teaching Resources lesson plans /pdfs/homework sheets/worksheets/powerpoints www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Vectors/Teaching Resources lesson plans /homework sheets/worksheets
Functional skills activities 11.1
Translations will be specified by a vector.
Lines of symmetry on a Cartesian grid will be restricted to x = a, y = a, y = x, y = –x
The direction of rotation will always be given.
Enlargements may be drawn on a grid, or on a Cartesian grid, where the centre of enlargement will always be at the intersection of two grid lines.
When describing transformations, the minimum requirement is:
Rotations described by centre, direction (unless half a turn) and an amount of turn (as a fraction of a whole or in degrees)
Reflection by a mirror line
Translations described by a vector or a clear description such as three squares to the right, five squares down.
Column vectors may be used to describe translations.
Use of bold type and arrows will be used to represent vectors in geometrical problems.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 28 Circles and cylinders
SEE FOUNDATION SCHEME OF WORK
G1.5
Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment.
G2.4
Use 2D representations of 3D shapes.
G4.1
Calculate perimeters and areas of shapes made from triangles and rectangles.
G4.3
Calculate circumferences and areas of circles.
G4.4
Calculate volumes of right prisms and of shapes made from cubes and cuboids.
ADDITIONAL HIGHER CONTENT
G1.5h
Know and use circle theorems
G4.1h Extend to other compound shapes e.g shapes made from circles or part circles with other known shapes.
G2.3h Simple geometric proofs – may involve congruent triangles and circle theorems
G4.3h Calculate lengths of arcs and areas of sectors
Time: 6 hours
G4.5h Solve mensuration problems involving more complex shapes and solids including cones, spheres, compound shapes and frustrums.
AQA Mod spec ref
G1.5h
Learning objectives
Use chord and tangent properties to solve problems
Grade
B
Common mistakes and misconceptions
Giving answers but not explaining the understand that the tangent at any point on a circle is perpendicular to the radius at that point understand and use the fact that tangents from an external point are equal in l ength explain why the perpendicular from the centre to a chord bisects the chord understand that inscribed regular polygons can be constructed by equal division of a circle properties used.
Not appreciating that listing the unknown facts can help progress the solution to the problem.
G1.5h B Mistaking chords for diameters and therefore incorrectly identifying the subtended angle as 90°.
G2.4
G4.1h
G4.3h
Use circle theorems to solve geometrical problems
Cyclic quadrilaterals – opposite angles = 180º
Angle at centre = twice angle at circumference
Angle in a semicircle = 90º
Angles in the same segment are equal
Alternate segment theorem identify and name common solids, for example cylinder, sphere and cone
Calculate area and perimeter from shapes made from circles or part circles with other known shapes calculate the length of arcs of circles calculate the area of sectors of circles calculate the area of segments of circles calculate the length of arcs of circles
B
B/A/A*
A/A*
Calling a sphere a ball
Squaring after multiplying by π
Giving an answer to a number of decimal

G4.5h
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification calculate the area of sectors of circles calculate the area of segments of circles places when asked to leave in terms of π
A/A* Not breaking the problem down work out perimeters of complex shapes work out the area of complex shapes made from a combination of known shapes work out the area of segments of circles work out volumes of frustums of cones work out volumes of frustums of pyramids calculate the surface area of compound solids constructed from cubes, cuboids, cones, pyramids, cylinders, spheres and hemispheres solve real life problems using known solid shapes

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources: AQA GCSE Maths Middle sets Book Sections 29.1 -29.3, 36.1 – 36.2
AQA Modular GCSE Mathematics Higher Tier


Circles P245
Circle properties P246

Tangents P249

Alternate segment theorems P250

Geometric proofs P252
 The greek letter π; circumference of a circle; area of a circle P257

Segments and sectors; Lengths of arcs and areas of sectors P259

Area of shapes P262

Compound shapes P263

Volume of a cylinder P316

Surface area of a cylinder P318

Cones; pyramids; spheres P320
Higher Practice Book 25.2, 25.3, 27.3, 36.1, 38.2, 38.3, 39.1, 39.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Angle & shape/Teaching Resources lesson plans & starters/questions/homework sheets/powerpoints www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/2D/3D shapes & loci/Teaching Resources lesson plans/worksheets/homework sheets www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Perimeter, area, volume/Teaching Resources lesson plans/problem sheets/homework sheets/powerpoints/spreadsheets www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Circle theorems/Teaching Resources lesson plans/question sheets/homework sheets/teacher sheets
Functional skills activities 21.1 – 21.3
Notes: Questions asking for the angle at the centre of a regular polygon may be set.
When asked to give reasons for angles any clear indication that the correct theorem is being referred to is acceptable. For example, angles on the same chord (are equal), angle at centre is equal to twice angle at circumference angle on diameter is 90 º, opposite angle in cyclic quadrilateral add up to 180 º, Alternate segment theorem. Questions assessing quality of written communication will be set that require clear and logical steps to be shown, with reasons given.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 29 Measurement 2
SEE FOUNDATION SCHEME OF WORK
G3.4
Convert measurements from one unit to another.
G3.7
Understand and use compound measures
ADDITIONAL HIGHER CONTENT
G3.7
Including density at Higher Tier. Other measures will be defined in the question.
AQA Mod spec ref
Learning objectives Grade
Time: 3 hours
Common mistakes and misconceptions
G3.7
G3.7
Make calculations using density
Recognise formulae for length, area or volume by considering dimensions
C
B
Not remembering the formulae.
Using the wrong formula.
Not appreciating that for an expression to represent a quantity every term must have the same dimension.
Resources: AQA GCSE Maths Middle sets Book Sections 30.3 – 30.4
AQA Modular GCSE Mathematics Higher Tier

Speed and average speed P68

Other compound measures; density; population density P71

Dimensions and formulae P335
Higher Practice Book 14.2, 36.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Measures/Teaching Resources lesson plans/worksheets/homework sheets/cards
Functional skills activities
Notes: Calculations involving distance and time will be restricted to ¼ hour, ⅓ hour, ½ hour, ⅔ hour or a whole number of hours.
Speed may be expressed in the form metres per second, (m/s). Candidates would be expected to understand these, and also units in common usage such as miles per hour (mph) or kilometres per hour (km/h) or metres per second, m/s m s¹. Candidates who express speed in alternative units such as metres per minute will not be penalised providing the units are clearly stated.
Density will be given as gm/cm ³ or kg/m³. Candidates who express density in alternative units such as grams per cubic metre will not be penalised providing the units are clearly stated.
Compound measures may be expressed in the form metres per second, m/s, m s¹.
Other compound measures that are non-standard would be defined in the question, e.g. population density is population/km ².

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 30 Enlargement and similarity
SEE FOUNDATION SCHEME OF WORK
Time: 3 hours
G1.7
Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations.
G1.8
Understand congruence and similarity.
G3.2
Understand the effect of enlargement for perimeter, area and volume of shapes and solids.
ADDITIONAL HIGHER CONTENT
G1.7h Use positive fractional and negative scale factors.
G3.2h Use the effect of enlargement for perimeter, area and volume calculations
AQA Mod spec ref
Learning objectives Grade Common mistakes and misconceptions
G1.7h,
G3.2
Enlarge a shape using a fractional or negative scale factor recognise that enlargements preserve angle but not length understand the effect of enlargement on perimeter understand the effect of enlargement on areas of shapes understand the effect of enlargement on volumes of shapes and solids
C/B Not using the centre of enlargement.
G1.7h,
G1.8
Understand similarity and the link with enlargement
Use similarity. Understand and use conditions for congruent triangles.
B Incorrectly simplifying the ratio.
Not using corresponding sides when making a ratio.
Resources: AQA GCSE Maths Middle sets Book Sections 31.2 – 31.3
AQA Modular GCSE Mathematics Higher Tier

Enlargement; using a centre of enlargement P281

Enlargement with a negative scale factor P282

Lengths, areas and volumes of similar figures; scale factors for length, area and volume P348
Higher Practice Book 31.4, 33.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Transformations/Teaching Resources lesson plans/pdfs/homework sheets/powerpoints www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Measures/Teaching Resources lesson plans/work sheets/homework sheets/cards
Functional skills activities

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 31 Non-linear graphs
SEE FOUNDATION SCHEME OF WORK
.
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations
N6.13
Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.
ADDITIONAL HIGHER CONTENT
Time: 6 hours
N5.5h
Solve quadratic equations.
N6.7h
Find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the corresponding simultaneous equations representing the linear and quadratic functions.
N6.8h
Draw, sketch, recognise graphs of simple cubic functions, the reciprocal function y = 1/ x with x ≠ 0, the function y = k x for integer values of x and simple positive values of k , the circular functions y = sin x and y = cos x .
N6.9h Transformations of functions
N6.11h
Construct quadratic and other functions from real life problems and plot their corresponding graphs
.
AQA Mod spec ref
N6.8h
Learning objectives
Draw cubic graphs
Use a graph to solve cubic equations
Grade
B
Common mistakes and misconceptions
Incorrectly finding the cube of a negative number. Forgetting to write down all the solutions.
N6.7h
Draw, sketch, recognise graphs of simple cubic functions, the reciprocal function 1/x, graphs of the form y = k/x, exponential functions y = kx for integer values of x and simple positive values of k, the circular functions y = sin x and y = cos x
Draw, sketch and recognise graphs of the form y = x³ + k where k is an integer
Find the approximate solution of a quadratic equation by drawing a straight line to A/A* Working in the wrong direction from the equation of the graph to the given equation
N6.9h intersect with another quadratic equation (graph)
Draw the graph of a linear function of the form y = mx + c on a grid to intersect the given graph of a quadratic function
Read off the solutions to the common roots of the two functions to the appropriate degree of accuracy
Appreciate that the points of intersection of the graphs of y = x² + 3x – 10 and y = 2x + 1 are the solutions to the equation x² + 3x – 10 = 2x + 1
Transform the graph of any function f(x) including: f(x) + k, f(ax), f(-x) + b, f(x + c) where a, b, c, and k are integers.
A/A* Using non-geometric language e.g. move or shift rather than translate. Using general language e.g. transform instead of translate.
N6.11h
Recognise transformations of functions and be able to write down the function of a transformation given the original function.
Transformations of the graphs of trigonometric functions based on y= sin x and y = cos x for 0 < x < 360 will also be assessed calculate values for a quadratic and draw the graph Not forming a smooth curve recognise a quadratic graph

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
N6.12 sketch a quadratic graph sketch an appropriately shaped graph (partly or entirely non-linear) to represent a real-life situation choose a correct sketch graph from a selection of alternatives interpret line graphs from real-life situations; for example conversion graphs interpret graphs showing real-life situations in geometry, such as the depth of water in containers as they are filled at a steady rate interpret non-linear graphs showing real-life situations, such as the height of a ball plotted against time
Resources: AQA GCSE Maths Middle sets Book Sections 32.1 -32.2
AQA Modular GCSE Mathematics Higher Tier

Further graphs P165

Using graphs to solve equations P166

Solving equations graphically; Cubic graphs P167

The graph of the reciprocal function; the graph of the exponential function P17

The graph of the circle P171

Simultaneous equations in which one equation is linear and one is quadratic P197

Translating a graph P211

Stretching a graph P212

Function notation P214

Reflecting a graph P215

Using graphs to find relationships; linear functions P218

Non-linear functions P219

Trigonometric functions and their graphs P365

Another look at the graphs of trigonometric functions P369
Higher Practice Book 16.1, 37.1 – 37.4
Not drawing a line on the graph and therefore introducing inaccuracies. www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Quadratic graphs/Teaching Resources lesson plans/homework sheets www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Equations/Teaching Resources lesson plans/homework sheets/worksheets/powerpoints www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Coordinates and graphs/Teaching Resources lesson plans/homework sheets/problem sheets/spreadsheets

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Functional skills activities 19.2
Notes: Distance-time graphs will be assessed in Unit 2. Everyday graphs representing financial situations (e.g. gas, electric, water, mobile phone bills, council tax) with or without fixed charges will be assessed in Unit 2. Linear graphs with or without a table of values will be assessed in Unit 2.
For non-linear graphs, a table may be given in which some y values may have to be calculated.
Quadratic graphs are expected to be drawn as a smooth curve. f(x) will be restricted to a simple quadratic, y = ax ² + bx + c, where one of b or c will be zero, y = sin(x) or y = cos(x)
Candidates will be expected to know that the roots of an equation f(x) = 0 can be found where the graph of the function intersects the x-axis and that the solution of f(x) = a is found where y = a intersects with f(x).
Candidates would be expected to recognise a sketch of the cubic, for example, y = x ³, and reciprocal graphs (including negative values of x). They would also be expected to sketch a graph of y = sin x, and y = cos x between - and 360 º, and know that the maximum and minimum values for sin and cos are 1 and –1.
They would also be expected to know that the graphs of sin and cos are periodic.
If candidates are required to draw an exponential graph, then a table will be given in which some y values may have to be calculated. Graphs are expected to be drawn as a curve. Joining points with straight lines will not get full credit.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 32 Constructions and loci
SEE FOUNDATION SCHEME OF WORK
G3.8
Measure and draw lines and angles.
G3.10
Use straight edge and a pair of compasses to do constructions.
G3.11
Construct loci.
ADDITIONAL HIGHER CONTENT
Time: 3 hours
N6.10h Construct the graphs of simple loci
G3.10 Higher tier will also include perpendicular from a point to a line, perpendicular at a point on a line and an angle of 60 °.
AQA Mod spec ref
G3.8,
G3.10
Learning objectives
May have been covered in Topic 22 Triangles and constructions
Construct perpendiculars
Construct the perpendicular bisector of a line segment
Construct angles of 90° and 60°
Construct the bisector of an angle
Grade
C?B
Common mistakes and misconceptions
Failing to keep the settings of compasses constant.
Rubbing out construction lines.
Not using compasses.
N6.10h Recognise, sketch and draw the graphs of functions defined by spatial conditions
Understand and use terms such as locus, parallel and equidistant in this context
Candidates will be expected to recognise that the locus of all points meeting certain conditions can be represented by a graph and they should be able to write down or work out the equation of that graph.
Although the equation of a circle is not required, candidates should know that the
Forgetting a circular motion is required at the vertex of straight line shapes. locus of all points that are a given distance from a single point is a circle and may be asked to sketch or draw this.
In questions, a grid will be provided.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources: AQA GCSE Maths Middle sets Book Sections 33.1 -33.2
AQA Modular GCSE Mathematics Higher Tier


Following rules and locus P267
Accurate constructions P269

More constructions P272
Higher Practice Book 30.1, 30.2 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/2D/3D, shapes & loci /Teaching Resources lesson plans/homework sheets/worksheets
Functional skills activities
Notes: Loci questions will be restricted to 2D only.
Loci problems may be set in practical contexts such as finding the position of a radio transmitter.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 33 Pythagoras’ theorem
SEE FOUNDATION SCHEME OF WORK
G2.1
Use Pythagoras’ theorem
ADDITIONAL HIGHER CONTENT
G2.1h Extend to use in 3D
AQA Mod spec ref
G2.1h
Learning objectives understand, recall and use Pythagoras' theorem in 2D, then 3D problems investigate the geometry of cuboids including cubes, and shapes made from cuboids, including the use of Pythagoras' theorem to calculate lengths in three dimensions
In three dimensions candidates should identify a right-angled triangle that contains the required information and then use Pythagoras' theorem (or trigonometry) to solve the problem. The use of the rule d² = √(a² + b² + c²) is not required as problems will always be solvable using a combination of triangles.
Grade
Time: 4 hours
Common mistakes and misconceptions
Not recognising Pythagoras theorem is required.
Resources: AQA GCSE Maths Middle sets Book Sections 34.1 -34.4
AQA Modular GCSE Mathematics Higher Tier

Checking the theorem of Pythagoras P292

Finding the hypotenuse P293

Finding one of the shorter sides P294

Problems involving the use of Pythagoras Theorem P295

Solving problems in three dimensions P297
Higher Practice Book 23.5 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Pythagoras theorem/Teaching Resources lesson plans/worksheets/powerpoints/homework sheets
Functional skills activities
Notes: Questions may be set in context, for example, a ladder against a wall, but questions will always include a diagram of a right angled triangle with two sides marked and the third side to be found. Quoting the formula will not gain credit.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 34 Trigonometry
SEE FOUNDATION SCHEME OF WORK
G3.6
Understand and use bearings.
ADDITIONAL HIGHER CONTENT
N1.14h
Including trigonometrical functions.
G2.2h
Use the trigonometrical ratios and the sine and cosine rules to solve 2D and 3D problems.
AQA Mod spec ref
Learning objectives Grade
Time: 8 hours
Common mistakes and misconceptions
G2.2h,
N1.14h
G2.2h
G2.2h
Understand and recall trigonometric ratios in right-angled triangles
Know how to enter the trigonometric functions on a calculator
Use trigonometric ratios to find lengths in right-angled triangles use these relationships in 3D contexts, including finding the angles between a line and a plane (but not the angle between two planes or between two skew lines); calculate the area of a triangle using ½ absinc use the sine and cosine rules to solve 2D and 3D problems
Use trigonometric ratios to find the angles in right-angled triangles
B Forgetting that the sine, cosine and tangent ratios only apply to right-angled triangles.
Incorrectly using the trigonometric function keys on a calculator.
B – A* Not using sine and cosine rules with nonright angled triangles
G2.2h,
G3.6
G2.2h
Use trigonometric ratios and Pythagoras’ theorem to solve problems, including the use of bearings
Solve problems using an angle of elevation or an angle of depression
B/A NOTE: Although sin -1 has been introduced, it is not required at GCSE; therefore, it can be simply said that the inverse is being found.
Incorrectly using the trigonometric function keys on a calculator.
B – A* Not identifying the appropriate information when problems are set in context.
Rounding off values during the intermediate steps of a calculation.
B/A Drawing a diagram that incorrectly represents the problem.

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources: AQA GCSE Maths Middle sets Book Sections 35.1 -35.5
AQA Modular GCSE Mathematics Higher Tier


The sine ratio; finding the length of the opposite side P301
Finding an angle P303

Finding the hypotenuse P304

The cosine and tangent ratios; how to select and use the correct ratio P305

Angles of elevation and depression P308

Three figure bearings P309

Solving problems in three dimensions; the angle between a line and a plane P311

Sines, cosines and tangents of angles between 0 and 360 P366

Finding angles P368

Triangles which are not right angled P370

The sine rule: finding sides P371

The sine rule: finding angles P372

The ambiguous case P373

Deriving the cosine rule P374

The cosine rule: finding sides P375

The cosine rule: finding angles P376

Solving problems involving triangles P379
Higher Practice Book 35.1 – 35.3, 41.1 – 41.3 www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/ Higher Tier/Unit 3/Trigonometry/Teaching Resources lesson plans/worksheet/powerpoints/homework sheets
Functional skills activities
Notes: In three dimensions candidates should identify a right angled triangle that contains the required information and then use trigonometry (or
Pythagoras' theorem) to solve the problem. Although the sine and cosine rule can sometimes be used to solve 3D problems they will always be solvable by a combination of right angled triangles.