GCSE Mathematics 3 year Foundation Tier Routemap (2015 specification)
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- Dwain Chase
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1 GCSE Mathematics 3 year Foundation Tier Routemap (2015 specification) GCSE Mathematics Linear Route Map Foundation Tier This Route Map already links to some supporting resources on AQA All About Maths. Further resources will be published along the following timeline Number Algebra Geometry & Measures Statistics Topic Number Topic Topic Algebra Topic Ratio, proportion and rates of change Geometry and Measures Probability Statistics
2 GCSE Mathematics 3 year Foundation Tier Routemap (2015 specification) Year 9 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Basic Number Factors and Multiples Angles Scale diagrams and bearings Basic Algebra Review and Revision 1 Holiday Basic Fractions NOVEMBER DECEMBER JANUARY Coordinates and Linear Graphs Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Basic Decimals Rounding Collecting and Representing Data Year 9 Examinations and Revision Holiday Holiday Sequences Basic Percentages JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Introduction to Perimeter and Area Review and Revision 2 Holiday Introduction to Circumference and Area Ratio and Proportion Basic Probability Review and Revision 3 APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Holiday Equations Scatter Graphs Review and Revision 4 Holiday Transformations JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 Summer Examinations and Revision Summer Examinations and Revision Pythagoras Theorem 2D Representations of 3D Shapes Year 10
3 GCSE Mathematics 3 year Foundation Tier Routemap (2015 specification) Year 10 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Review and Revision 5 Standard Form Calculating with Percentages Measures Review and Revision 6 Holiday Statistical Measures NOVEMBER DECEMBER JANUARY Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Indices Constructions and Loci Year 10 Examinations and Revision Year 10 Examinations and Revision Holiday Holiday Algebra Recap and Extension Congruence and Similarity JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Introduction to Trigonometry Review and Revision 7 Holiday Further Perimeter and Area Graphs recap and extension Further Circumference and Area Review and Revision 8 APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Holiday Simultaneous Equations Properties of Polygons Review and Revision 9 Holiday Real Life Graphs JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 Summer Examinations and Revision Summer Examinations and Revision Review of basic Probability Probability Year 9 Year 11
4 GCSE Mathematics 3 year Foundation Tier Routemap (2015 specification) Year 11 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Review and Revision 10 Volume Algebra: Quadratics, rearranging formulae and Identities Review and Revision 11 Holiday Inequalities Algebra and Graphs NOVEMBER DECEMBER JANUARY Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Algebra and Graphs (continued) Sketching graphs Mock Examinations and Revision Mock Examinations and Revision Holiday Holiday Direct and Inverse proportion Trigonometry JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Trigonometry (continued) Review and Revision 12 Holiday Solving quadratic equations Quadratic Graphs Growth and decay Review and Revision 13 Holiday APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Vectors REVISION Holiday REVISION JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 June Examinations June Examinations Year 10
5 Basic Number Specification content: Specification notes: N1 Order positive and negative integers Use the symbols =,, <, >,, including use on a number line. Students should know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary N2 Apply the four operations, including formal written methods, to integers both positive and negative Understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals) including questions set in context (knowledge of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit and balance, income tax, VAT, interest rate) N3 Recognise and use relationships between operations including inverse operations (e.g. cancellation to simplify calculations and expressions) N14 Estimate answers Check calculations using approximation and estimation, including answers obtained using technology including evaluation of results obtained
6 Factors and Multiples Specification content: Specification notes: N4 Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique factorisation theorem prime factor decomposition including product of prime factors written in index form Apply systematic listing strategies including using lists, tables and diagrams N5 Resources
7 Angles Specification content: Specification notes: Use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries G1 Use the standard conventions for labelling and referring to the sides and angles of triangles Draw diagrams from written descriptions Apply the properties of: angles at a point angles at a point on a straight line vertically opposite angles G3 Understand and use alternate and corresponding angles on parallel lines colloquial terms such as Z angles are not acceptable and should not be used
8 Scale diagrams and bearings Specification content: Specification Notes: Use scale factors, scale diagrams and maps including geometrical problems R2 Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings including the eight compass point bearings and threefigure bearings G15
9 Basic Algebra Specification content: Specification notes: A1 Use and interpret algebraic notation, including: ab in place of a b 3y in place of y + y + y and 3 y a 2 in place of a a, a 3 in place of a a a, a 2 b in place of a a b a in place of a b b it is expected that answers are given in simplest form without an explicit instruction given in the question coefficients written as fractions rather than decimals brackets Use conventional notation for priority of operations, including powers, roots and reciprocals N3 A3 understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors this will be implicitly and explicitly assessed A4 Simplify and manipulate algebraic expressions by: collecting like terms multiplying a single term over a bracket taking out common factors
10 Review and Revision 1 Specification content: Specification notes:
11 Basic Fractions Specification content: Specification notes: N1 Order positive and negative fractions Apply the four operations, including formal written methods, to simple fractions (proper and improper) and mixed numbers - both positive and negative N2 Calculate exactly with fractions N8
12 Coordinates and Linear Graphs Specification content: Specification notes: Work with co-ordinates in all four quadrants A8 Solve geometrical problems on co-ordinate axes G11 Plot graphs of equations that correspond to straight line graphs in the coordinate plane A9
13 Basic Decimals Specification content: Specification notes Order positive and negative decimals N1 N2 Apply the four operations, including formal written methods, to decimals both positive and negative Understand and use place value (e.g. when calculating with decimals) Work interchangeably with terminating decimals and their corresponding fractions (such as including ordering 3.5 and 7 2 or and 3 8 ) N10
14 Rounding Specification content: Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures) Specification notes: including appropriate rounding for questions set in context N15 Use inequality notation to specify simple error intervals due to truncation or rounding students should know not to round values during intermediate steps of a calculation Apply and interpret limits of accuracy N16
15 Collecting and Representing Data Specification content: Specification notes: S2 Interpret and construct tables, charts and diagrams including, for categorical data: frequency tables bar charts pie charts pictograms vertical line charts for ungrouped discrete numerical data tables and line graphs for time series data know their appropriate use including choosing suitable statistical diagrams S4 Interpret, analyse and compare distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data know and understand the terms primary data, secondary data, discrete data and continuous data
16 Sequences Specification content: Specification notes: Generate terms of a sequence from either a term-to-term or a position-toterm rule including from patterns and diagrams A23 A24 Recognise and use: sequences of triangular, square and cube numbers simple arithmetic progression Fibonacci type sequences quadratic sequences and simple geometric progressions (r n where n is an integer and r is a rational number > 0) other recursive sequences will be defined in the question
17 Basic Percentages Specification content: Specification notes: R9 Define percentage as number of parts per hundred Interpret percentages and percentage changes as a fraction or decimal and interpret these multiplicatively Express one quantity as a percentage of another Compare two quantities using percentages Work with percentages greater than 100% N12 Interpret fractions and percentages as operators including interpreting percentage problems using a multiplier
18 Introduction to Perimeter and Area Specification content: Specification notes: G12 Identify properties of the faces, surfaces, edges and vertices of: cube, cuboids, prisms, cylinders, pyramids, cones and spheres G17 Calculate the perimeter of a 2D shape and composite shapes G16 Know and apply formulae to calculate area of: triangles parallelograms trapezia Calculate the area of composite shapes G17
19 Review and Revision 2 Specification content: Specification notes:
20 Introduction to Circumference and Area Specification content: Specification notes: G9 Identify and apply circle definitions and properties, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment Know the formulae circumference of a circle = 2πr = πd area of a circle = πr 2 G17 Calculate: perimeters of 2D shapes, including circles and composite shapes Calculate areas of circles and composite shapes Resources
21 Ratio and Proportion (Slide 1 of 2) Specification content: Specification notes: N11 Identify and work with fractions in ratio problems R3 Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 R4 Use ratio notation, including reduction to simplest form R5 Divide a given quantity into two parts in a given part:part or part:whole ratio Express the division of a quantity into two parts as a ratio Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing and concentrations) including better value or best buy problems
22 Ratio and Proportion (Slide 2 of 2) Specification content: Specification notes: Express a multiplicative relationship between two quantities as a ratio or fraction R6 Understand and use proportion as equality of ratios R7 Relate ratios to fractions and to linear functions R8
23 Basic Probability Specification content: Specification notes: P1 Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees probabilities should be written as fractions, decimals or percentages Apply the property that the probabilities of an exhaustive set of outcomes sum to one P4 Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one P7 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
24 Review and Revision 3 Specification content: Specification notes:
25 Equations Specification content: Specification notes: Substitute numerical values into formulae and expressions, including scientific formulae unfamiliar formulae will be given in the question A2 Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation including use of brackets A17
26 Scatter Graphs Specification content: Specification notes: Use and interpret scatter graphs of bivariate data Recognise correlation and know that it does not indicate causation know and understand the terms positive correlation, negative correlation, no correlation, weak correlation and strong correlation S6 Draw estimated lines of best fit Make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of doing so
27 Review and Revision 4 Specification content: Specification notes:
28 Transformations Specification content: Specification notes: G7 Identify, describe and construct congruent and similar shapes, on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional scale factors) Describe translations as 2D vectors G24
29 Pythagoras Theorem Specification content: Specification notes: Know the formula for Pythagoras' Theorem a 2 + b 2 = c 2 Apply it to find length in right angled triangles in two dimensional figures G20
30 2D Representations of 3D Shapes Specification content: Specification notes: Construct and interpret plans and elevations of 3D shapes G13
31 Review and Revision 5 Specification content: Specification notes:
32 Standard Form Specification content: Specification notes: Understand and use place value (e.g. when working with very large or very small numbers) N2 Calculate with and interpret standard form A 10 n where 1 A < 10 and n is an integer with and without a calculator interpret calculator displays N9
33 Calculating with Percentages Specification content: Specification notes: R9 Solve problems involving percentage change, including: percentage increase / decrease problems original value problems simple interest, including in financial mathematics problems set in context using a multiplier
34 Measures (Slide 1 of 2) Continued on next page Specification content: Specification notes: Apply and interpret limits of accuracy N16 G14 Use standard units of measure and related concepts (length, area, volume / capacity, mass, time, money etc) Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate know and use metric conversion factors for length, area, volume and capacity. Imperial / metric conversions will be given in the question N13 View next page
35 Measures (Slide 2 of 2) Specification content: Specification notes: Change freely between related standard units (e.g. time, length, area, volume / capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts R1 Use compound units such as speed, rates of pay, unit pricing, density and pressure including making comparisons R11 Return to previous page
36 Review and Revision 6 Specification content: Specification notes:
37 Statistical Measures Specification content: Specification notes: S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through : appropriate measures of central tendency (median, mean, mode and modal class) spread (range, including consideration of outliers) Apply statistics to describe a population S5 S1 Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
38 Indices Specification content: Specification notes: N6 Use positive integer powers and associated real roots (square, cube and higher) Recognise powers of 2, 3, 4, 5 including square numbers up to 15x15 know that 1000=10 3 and 1 million = 10 6 Calculate with roots and with integer indices N7
39 Constructions and Loci Specification content: Specification notes: Use the standard ruler and compass constructions: perpendicular bisector of a line segment constructing a perpendicular to a given line from / at a given point bisecting a given angle constructing a 60 angle G2 Know that the perpendicular distance from a point to a line is the shortest distance to the line Use these to construct given figures and solve loci problems
40 Algebra Recap and Extension Specification content: Specification notes: A3 Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors (review of Year 9) this will be implicitly and explicitly assessed A4 Simplify and manipulate algebraic expressions (including those involving surds) by: collecting like terms multiplying a single term over a bracket taking out common factors A25 A17 Deduce expressions to calculate the nth term of a linear sequence Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation (review of Year 9) including use of brackets
41 Congruence and Similarity Specification content: Specification notes: Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) G5 G6 Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides including Pythagoras Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs G19 Apply and use the concepts of congruence and similarity, including the relationships between lengths in similar figures Resources
42 Introduction to trigonometry Specification content: Specification notes: Know and use the trigonometric ratios G20 sinθ = opposite, cosθ = adjacent opposite and tanθ = hypotenuse hypotenuse adjacent Apply them to find angles and lengths in right-angled triangles in two dimensional figures Compare lengths using ratio notation R12
43 Review and Revision 7 Specification content: Specification notes:
44 Further Perimeter and Area Specification content: Specification notes: G12 Identify properties of the faces, surfaces, edges and vertices of: cube, cuboids, prisms, cylinders, pyramids, cones and spheres (review of Year 9) G17 Calculate the perimeter of a 2D shape and composite shapes (review of Year 9) G16 G17 Know and apply formulae to calculate area of: triangles parallelograms trapezia (review of Year 9) Calculate the area of composite shapes (review of Year 9) Find the surface area of pyramids and composite solids
45 Graphs Recap and Extension Specification content: Specification notes: Solve geometrical problems on co-ordinate axes G11 A9 Use the form y = mx + c to identify parallel lines Find the equation of the line through two given points, or through one point with a given gradient Identify and interpret gradients and intercepts of linear functions graphically and algebraically A10
46 Further Circumference and Area Specification content: Specification notes: G9 Identify and apply circle definitions and properties, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment (review of Year 9) Know and use the formulae Circumference =2πr = πd Area = πr 2 including frustums G17 G18 N8 Calculate the perimeter of 2D shapes including circles and composite shapes Calculate areas of circles and composite shapes (review of Year 9) Calculate surface area of spheres, cones and composite solids Calculate arc lengths, angles and areas of sectors of circles Calculate exactly with multiples of π
47 Review and Revision 8 Specification content: Specification notes:
48 Simultaneous Equations Specification content: Specification notes: A19 Solve two simultaneous equations in two variables (linear / linear) algebraically Find approximate solutions using a graph including the approximate solution of a quadratic equation by drawing a straight line to intersect with another quadratic equation A21 Translate simple situations or procedures into algebraic expressions or formulae; derive two simultaneous equations Solve the equations and interpret the solution
49 Properties of Polygons Specification content: Specification notes Derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) G3 G4 Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus and triangles and other plane figures using appropriate language including knowing names and properties of isosceles, equilateral, scalene, right-angled, acuteangled, obtuse-angled triangles including knowing names and using the polygons: pentagon, hexagon, octagon and decagon Resources
50 Review and Revision 9 Specification content: Specification notes:
51 Real Life Graphs Specification content: Specification notes: A14 Plot and interpret graphs (including reciprocal graphs) and graphs of nonstandard functions in real contexts, to find approximate solutions to problems such as simple kinematics problems involving distance, speed and acceleration including problems requiring a graphical solution Interpret the gradient of a straight line as a rate of change R14
52 Review of basic probability Specification content: Specification notes: P1 Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees (review of Year 9) probabilities should be written as fractions, decimals or percentages Apply the property that the probabilities of an exhaustive set of outcomes sum to one (review of Year 9) P4 Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one (review of Year 9) P7 Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities (review of Year 9)
53 Probability Specification content: Specification notes: P2 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future experiments P3 Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 1 probability scale P5 Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing sample size P6 P8 Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions know when to add and when to multiply two or more probabilities Resources
54 Review and Revision 10 Specification content: Specification notes:
55 Volume Specification content: Specification notes: Compare lengths, areas and volumes using ratio notation Make links to similarity and scale factors R12 G16 Know and apply the formulae to calculate the volume of cuboids and other right prisms (including cylinders) G17 N8 Calculate the volume of spheres, pyramids, cones and composite solids Calculate exactly with multiples of π
56 Algebra: Quadratics, Rearranging Formulae and Identities Specification content: Specification notes: A4 A5 Simplify and manipulate algebraic expressions (including those involving surds) by: expanding products of two binomials factorising quadratic expressions of the form x 2 + bx + c including the difference of two squares simplifying expressions involving sums, products and powers, including the laws of indices Understand and use standard mathematical formulae Rearrange formulae to change the subject including use of formulae from other subjects in words and using symbols A6 Know the difference between an equation and an identity Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments Where appropriate, interpret simple expressions as functions with inputs and outputs A7
57 Review and Revision 11 Specification content: Specification notes:
58 Inequalities Specification content: Specification notes: Solve linear inequalities in one variable Represent the solution set on a number line know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary A22
59 Algebra and graphs Specification content: Specification notes: A17 Solve linear equations in one unknown algebraically Including those with the unknown on both sides of the equation Find approximate solutions using a graph including use of brackets A21 Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations) and the solve the equation(s) and interpret the solution including solution of geometrical problems and problems set in context
60 Sketching Graphs Specification content: Specification notes: Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions and the reciprocal function including using the symmetry of functions y = 1 with x 0 x A12
61 Direct and Inverse Proportion Specification content: Specification notes: R10 Solve problems involving direct and inverse proportion, including graphical and algebraic representations R13 Understand that X is inversely proportional to Y is equivalent to X is proportional to 1 Y Interpret equations that describe direct and inverse proportion Recognise and interpret graphs that illustrate direct and inverse proportion R14
62 Trigonometry Specification content: Specification notes: Know and use the trigonometric ratios G20 G21 sinθ = opposite, cosθ = adjacent hypotenuse hypotenuse opposite and tanθ = adjacent Apply them to find angles and lengths in right-angled triangles in two dimensional figures (Review of year 10) Know the exact values of sinθ and cosθ for θ = 0, 30 45, 60 and 90 Know the exact value of tanθ for θ = 0, 30, 45 and 60 R12 Compare lengths using ratio notation (Review of Year 10) Make links to trigonometric ratios
63 Review and Revision 12 Specification content: Specification notes:
64 Solving Quadratic Equations Specification content: Specification notes: Solve quadratic equations algebraically by factorising Find approximate solutions using a graph A18 Resources
65 Quadratic Graphs Specification content: Specification notes: Recognise, sketch and interpret graphs of quadratic functions A12 Identify and interpret roots, intercepts and turning points of quadratic functions graphically Deduce roots algebraically including the symmetrical property of a quadratic A11
66 Growth and Decay Specification content: Specification notes: Set up, solve and interpret the answers in growth and decay problems, including compound interest R16
67 Review and Revision 13 Specification content: Specification notes:
68 Vectors Specification content: Specification notes: Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representation of vectors G25
69 GCSE Mathematics Linear Route Map Higher Tier GCSE Mathematics (8300) 3 year higher tier Route Map Number Algebra Geometry & Measures Statistics Topic Number Topic Topic Algebra Topic Ratio, proportion and rates of change Geometry and Measures Probability Statistics Year 10
70 GCSE Mathematics (8300) 3 year higher tier Route Map Year 9 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Basic number Factors & multiples Angles Scale diagrams and bearings Basic algebra review Basic fractions Review and revision 1 Holiday Basic decimals NOVEMBER DECEMBER JANUARY Coordinates and linear graphs Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Rounding Collecting and representing Sequences Year 9 data examinations and revision Holiday Holiday Basic percentages Perimeter and area JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Real life graphs Review and revision 2 Holiday Circumference and area Ratio and proportion Equations Review and revision 3 APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Holiday Basic probability Scatter graphs Standard form Review and revision 4 Holiday Transformations JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 Summer examinations and revision Summer examinations and revision Constructions and loci 2D representat ions of 3D shapes Year 10
71 GCSE Mathematics (8300) 3 year higher tier Route Map Year 10 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Review and revision 5 Calculating with percentages Measures Surds Review and revision 6 Holiday Statistical measures NOVEMBER DECEMBER JANUARY Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Indices Properties of polygons Examinations and revision Examinations and revision Holiday Holiday Number recap and review Congruence and similarity JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Pythagoras theorem and basic trigonometry Review and revision 7 Holiday Simultaneous equations Probability Statistics recap and review Review and revision 8 APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Holiday Algebra: introduction to quadratics and rearranging formulae Volume Review and revision 9 Holiday Algebra recap and review Sketching graphs JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 Summer examinations and revision Summer examinations and revision Linear and quadratic equations and their graphs Geometry and measures recap and review Year 11
72 GCSE Mathematics (8300) 3 year higher tier Route Map Year 11 SEPTEMBER OCTOBER NOVEMBER Wk1 Wk2 Wk3 Wk4 Wk5 Wk6 Wk7 Wk8 Wk9 Wk10 Review and revision 10 Algebra: further quadratics, rearranging formulae and identities Trigonometry recap and extension Growth and decay Review and revision 11 Holiday Equation of a circle Further equations and graphs NOVEMBER DECEMBER JANUARY Wk11 Wk12 Wk13 Wk14 Wk15 Wk16 Wk17 Wk18 Wk19 Wk20 Further equations and graphs Direct and inverse proportion Mock examinations and revision Mock examinations and revision Holiday Holiday Inequalities Vectors JANUARY FEBRUARY MARCH Wk21 Wk22 Wk23 Wk24 Wk25 Wk26 Wk27 Wk28 Wk29 Wk30 Further sketching graphs Review and revision 12 Holiday Sine and cosine rules Transforming functions Numerical methods Circle theorems Review and revision 13 Holiday APRIL MAY JUNE Wk31 Wk32 Wk33 Wk34 Wk35 Wk36 Wk37 Wk38 Wk39 Wk40 Holiday Gradients and rate of change Pre-calculus and area under a curve Algebraic fractions Revision Holiday Revision JUNE JULY Wk41 Wk42 Wk43 Wk44 Wk45 June examinations June examinations Year 10
73 Basic number Specification content Specification notes N1 N2 N3 N14 Order positive and negative integers Use the symbols =,, <, >,, Apply the four operations, including formal written methods, to integers both positive and negative Understand and use place value (e.g. when working with very large or very small number, and when calculating with decimals) Recognise and use relationships between operations including inverse operations (e.g. cancellation to simplify calculations and expressions) Estimate answers Check calculations using approximation and estimation, including answers obtained using technology including use of a number line including questions set in context (knowledge of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit and balance, income tax, VAT, interest rate) including evaluation of results obtained
74 Factors and multiples Specification content Specification notes N4 N5 Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation, and the unique factorisation theorem Apply systematic listing strategies and the use of the product rule for counting prime factor decomposition including product of prime factors written in index form including using lists, tables and diagrams
75 Angles Specification content Specification notes G1 G3 Use conventional terms and notations: -points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries Use the standard conventions for labelling and referring to the sides and angles of triangles Draw diagrams from written descriptions Apply the properties of: - angles at a point - angles at a point on a straight line - vertically opposite angles Understand and use alternate and corresponding angles on parallel lines colloquial terms such as Z angles are not acceptable and should not be used
76 Scale diagrams and bearings Specification content Use scale factors, scale diagrams and maps Specification notes Including geometrical problems R2 Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings including the eight compass point bearings and three-figure bearings G15
77 Basic algebra review Specification content Specification notes A1 Use and interpret algebraic notation, including: -ab in place of a x b -3y in place of y + y + y and 3 x y - a 2 in place of a x a, a 3 in place of a x a x a, a 2 b in place of a x a x b - a b in place of a b it is expected that answers are given in simplest form without an explicit instruction given in the question - coefficients written as fractions rather than decimals -brackets N3 A3 Use conventional notation for priority of operations, including powers, roots and reciprocals Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors this will be implicitly and explicitly assessed A4 Simplify and manipulate algebraic expressions (including those involving surds) by: - collecting like terms - multiplying a single term over a bracket - taking out common factors
78 Basic fractions Specification content Specification notes N1 Order positive and negative fractions N2 Apply the four operations, including formal written methods, to simple fractions (proper and improper) and mixed numbers - both positive and negative Calculate exactly with fractions N8
79 Review and revision 1 Specification content Specification notes
80 Basic decimals Continued on next page Specification content Specification notes Order positive and negative decimals N1 N2 Apply the four operations, including formal written methods, to decimals both positive and negative Understand and use place value (e.g. when working calculating with decimals) including questions set in context (knowledge of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit and balance, income tax, VAT, interest rate) Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7 and and 3 ) including ordering 2 8 N10 Change recurring decimals into their corresponding fractions and vice versa
81 Coordinates and linear graphs Specification content Specification notes Work with co-ordinates in all four quadrants A8 G11 Solve geometrical problems on co-ordinate axes A9 A10 Plot graphs of equations that correspond to straight line graphs in the co-ordinate plane. Use the form y = mx + c to identify parallel lines and perpendicular lines Find the equation of the line through two given points, or through one point with a given gradient Identify and interpret gradients and intercepts of linear functions graphically and algebraically
82 Rounding Continued on next page Specification content Specification notes N15 Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures) Use inequality notation to specify simple error intervals due to truncation or rounding including appropriate rounding for questions set in context know not to round values during intermediate steps of a calculation Apply and interpret limits of accuracy including upper and lower bounds N16
83 Collecting and representing data (slide 1 of 2) Specification content Specification notes Interpret and construct tables, charts and diagrams including, for categorical data: -frequency tables - bar charts - pie charts - pictograms including choosing suitable statistical diagrams S2 - vertical line charts for ungrouped discrete numerical data - tables and line graphs for time series data - know their appropriate use S4 S3 Interpret, analyse and compare distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data, including boxplots Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use know and understand the terms primary data, secondary data, discrete data and continuous data
84 Sequences Specification content Specification notes Generate terms of a sequence from either a term-to-term or a position-to-term rule including from patterns and diagrams A23 A24 A25 Recognise and use: -sequences of triangular, square and cube numbers - simple arithmetic progression, - Fibonacci type sequences, - quadratic sequences, - and simple geometric progressions (r n where n is an integer and r is a rational number > 0, - Other sequences Deduce expressions to calculate the nth term of linear and quadratic sequences other recursive sequences will be defined in the question View next page
85 Basic percentages Specification content Specification notes R9 Define percentage as number of parts per hundred Interpret percentages and percentage changes as a fraction or decimal and interpret these multiplicatively Express one quantity as a percentage of another Compare two quantities using percentages Work with percentages greater than 100% Interpret fractions and percentages as operators including interpreting percentage problems using a multiplier N12
86 Perimeter and area Continued on next page Specification content Specification notes G12 Identify properties of the faces, surfaces, edges and vertices of: cube, cuboids, prisms, cylinders, pyramids, cones and spheres G17 G16 Calculate the perimeter of a 2D shape and composite shapes Know and apply formulae to calculate area of: - triangles - parallelograms - Trapezia G17 Find the surface area of pyramids and composite solids
87 Real life graphs Specification content Plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematics problems involving distance, speed and acceleration Specification notes including problems requiring a graphical solution A14 R14 Interpret the gradient of a straight line as a rate of change
88 Review and revision 2 Specification content Specification notes
89 Circumference and area Continued on next page Specification content Specification notes Identify and apply circle definitions and properties, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment G9 G17 Know and use the formulae -Circumference of a circle = 2πr 2 = πd - Area of a circle = πr 2 Calculate the perimeter of 2D shapes including circles and composite shapes Calculate areas of circles and composite shapes Calculate surface area of spheres, cones and composite solids solutions in terms of π may be asked for Calculate arc lengths, angles and areas of sectors of circles G18
90 Ratio and proportion Specification content Specification notes N11 R3 R4 R5 Identify and work with fractions in ratio problems Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 Use ratio notation, including reduction to simplest form Divide a given quantity into two parts in a given part:part or part:whole ratio Express the division of a quantity into two parts as a ratio Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing and concentrations) Including better value or best buy problems R6 R7 R8 Express a multiplicative relationship between two quantities as a ratio or fraction Understand and use proportion as equality of ratios Relate ratios to fractions and to linear functions
91 Equations Specification content Specification notes Substitute numerical values into formulae and expressions, including scientific formulae unfamiliar formulae will be given in the question A2 Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation including use of brackets A17 View next page
92 Review and revision 3 Specification content Specification notes
93 Basic probability Specification content Specification notes P1 Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees (probabilities should be written as fractions, decimals or percentages) Apply the property that the probabilities of an exhaustive set of outcomes sum to one P4 Apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities P7
94 Scatter graphs Specification content Specification notes S6 Use and interpret scatter graphs of bivariate data Recognise correlation and know that it does not indicate causation know and understand the terms positive correlation, negative correlation, no correlation, weak correlation and strong correlation S6 Draw estimated lines of best fit Make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of doing so
95 Standard form Specification content Understand and use place value (e.g. when working with very large or very small numbers) Specification notes including questions set in context N2 Calculate with and interpret standard form A 10 n where 1 A < 10 and n is an integer with and without a calculator interpret calculator displays N9
96 Review and revision 4 Specification content Specification notes
97 Transformations Specification content Specification notes G7 Identify, describe and construct congruent and similar shapes, including on co-ordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors) G24 Describe translations as 2D vectors G8 Describe the changes and invariance achieved by combinations of rotations, reflections and translations (including using column vector notation for translations)
98 Constructions and loci Specification content Specification notes G2 Use the standard ruler and compass constructions : - perpendicular bisector of a line segment - constructing a perpendicular to a given line from / at a given point - bisecting a given angle including constructing an angle of 60 0 Know that the perpendicular distance from a point to a line is the shortest distance to the line Use these to construct given figures and solve loci problems G2
99 2D representations of 3D Shapes Specification content Specification notes Construct and interpret plans and elevations of 3D shapes G13
100 Review and revision 5 Specification content Specification notes
101 Calculating with percentages Specification content Specification notes R9 Solve problems involving percentage change, including : - percentage increase / decrease problems - original value problems - simple interest, including in financial mathematics - problems set in context - using a multiplier
102 Measures Specification content Specification notes N16 G14 N13 Apply and interpret limits of accuracy including upper and lower bounds Use standard units of measure and related concepts (length, area, volume / capacity, mass, time, money etc) Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate know and use metric conversion factors for length, area, volume and capacity. Imperial / metric conversions will be given in the question R1 Change freely between related standard units (e.g. time, length, area, volume / capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts R11 Use compound units such as speed, rates of pay, unit pricing, density and pressure including making comparisons
103 Surds Specification content Specification notes Calculate exactly with surds Simplify surd expressions involving squares (eg 12 = 4 3 = 4 3 = 2 3) and N8 rationalise denominators Recognise and use simple geometric progressions (r n where n is an integer and r is a surd) A24
104 Review and revision 6 Specification content Specification notes
105 Statistical measures Specification content Specification notes S4 Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through : - appropriate measures of central tendency (median, mean, mode and modal class) -- spread (range, including consideration of outliers, quartiles and inter-quartile range) Apply statistics to describe a population S5 S1 Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
106 Indices Specification content Specification notes N6 Use positive integer powers and associated real roots (square, cube and higher) Recognise powers of 2, 3, 4, 5 5 Estimate powers and roots of any given positive number including square numbers up to 15x15 know that 1000=10 3 and 1 million = 10 6 Calculate with roots and with integer and fractional indices N7
107 Properties of polygons Specification content Specification notes Derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons) G3 G4 Derive and apply the properties and definitions of: - special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus - and triangles and other plane figures using appropriate language (including knowing names and properties of isosceles, equilateral, scalene, right-angled, acute-angled, obtuse-angled triangles. including knowing names and using the polygons: pentagon, hexagon, octagon and decagon
108 Number recap and review Specification content Specification notes N10 N16 A25 A24 Change recurring decimals into their corresponding fractions and vice versa. Apply and interpret limits of accuracy including upper and lower bounds Deduce expressions to calculate the nth term of linear and quadratic sequences Recognise and use simple geometric progressions (r n where n is an integer and r is a surd) including other sequences Calculate exactly with surds N8 Simplify surd expressions involving squares (eg 12 = 4 3 = 4 3 = 2 3) and rationalise denominators Calculate with roots and with integer and fractional indices N7
109 Congruence and similarity Specification content Specification notes Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) G5 G6 Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides including the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs G19 Apply and use the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures
110 Pythagoras theorem and basic trigonometry Specification content Specification notes Know the formula for Pythagoras Theorem a 2 + b 2 = c 2 Apply it to find lengths in right angled triangles in two dimensional figures G20 Know and use the trigonometric ratios sin θ = opposite, cos θ = adjacent opposite, tan θ = hypotenuse hypotenuse adjacent Apply them to find lengths in right angled triangles in two dimensional figures G21 G6 Know the exact values of sinθ and cosθ for θ = 0, 30 45, 60 and 90 Know the exact value of tanθ for θ = 0, 30, 45 and 60 Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras Theorem, and use known results to obtain simple proofs R12 Compare lengths using ratio notation; make links to trigonometric ratios
111 Review and revision 7 Specification content Specification notes
112 Simultaneous equations Specification content Old Wording A19 Solve two simultaneous equations in two variables (linear / linear or quadratic/linear) algebraically Find approximate solutions using a graph including the approximate solution of a quadratic equation by drawing a straight line to intersect with another quadratic equation A21 Translate simple situations or procedures into algebraic expressions or formulae; Derive two simultaneous equations Solve the equations and interpret the solution including the solution of geometrical problems and problems set in context
113 Probability Specification content Specification notes P2 P3 Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes or multiple future experiments Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 1 probability scale P5 Understand that empirical unbiased samples tend towards theoretical probability distributions with increasing sample size P6 Enumerate sets and combinations of sets systematically using tables, grids, Venn diagrams and tree diagrams P8 P9 Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions Know when to add and when to multiply two or more probabilities Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams
114 Statistics recap and review Specification content Specification notes S3 S4 S6 S1 Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use Interpret, analyse and compare distributions of data sets from univariate empirical distributions through box plots interpret, analyse and compare the distributions of data sets from univariate empirical distributions through consideration of outliers, quartiles and inter-quartile range Draw estimated lines of best fit Make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of doing so Infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling.
115 Review and revision 8 Specification content Specification notes
116 Algebra: introduction to quadratics and rearranging formulae Specification content Specification notes A4 A5 Simplify and manipulate algebraic expressions by: - expanding products of two binomials - factorising quadratic expressions of the form x 2 + bx + c including the difference of two squares - simplifying expressions involving sums, products and powers, including the laws of indices Understand and use standard mathematical formulae Rearrange formulae to change the subject including use of formulae from other subjects in words and using symbols
117 Volume Specification content Specification notes R12 Compare lengths, areas and volumes using ratio notation Make links to similarity and scale factors Know and apply the formulae to calculate the volume of cuboids and other right prisms (including cylinders) G16 G17 Calculate the volume of spheres, pyramids, cones and composite solids including frustums N8 Calculate exactly with multiples of π
118 Review and revision 9 Specification content Specification notes
119 Algebra recap and review Specification content Specification notes A9 Use the form y = mx + c to identify parallel lines and perpendicular lines Find the equation of the line through two given points, or through one point with a given gradient A10 A14 Identify and interpret gradients and intercepts of linear functions graphically and algebraically Plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematics problems involving distance, speed and acceleration including problems requiring a graphical solution A17 Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation including use of brackets
120 Sketching graphs Specification content Specification notes Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions and the reciprocal function y = 1 with x 0 x A12 (Including using the symmetry of functions)
121 Linear and quadratic equations and their graphs Specification content Specification notes A17 Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation Find approximate solutions using a graph including use of brackets A18 Solve quadratic equations algebraically by factorising Find approximate solutions using a graph A21 Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and the solve the equation and interpret the solution including solution of geometrical problems and problems set in context
122 Geometry and measures recap and review Specification content Specification notes G11 G7 Solve geometrical problems on co-ordinate axes Identify, describe and construct congruent and similar shapes, including on co-ordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors) G8 Describe the changes and invariance achieved by combinations of rotations, reflections and translations including using column vector notation for translations G17 Find the surface area of pyramids and composite solids Calculate surface area of spheres, cones and composite solids Calculate the volume of spheres, pyramids, cones and composite solids including frustums G18 Calculate arc lengths, angles and areas of sectors of circles
123 Review and revision 10 Specification content Specification notes
124 Algebra: quadratics, rearranging formulae and identities Specification content Specification notes A4 A5 A6 Simplify and manipulate algebraic expressions (including those involving surds) by: - expanding products of two or more binomials - factorising quadratic expressions of the form x 2 + bx + c including the difference of two squares - factorising quadratic expressions of the form ax 2 + bx + c - simplifying expressions involving sums, products and powers, including the laws of indices Understand and use standard mathematical formulae Rearrange formulae to change the subject Know the difference between an equation and an identity Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs including use of formulae from other subjects in words and using symbols. A7 Where appropriate, interpret simple expressions as functions with inputs and outputs Interpret the reverse process as the inverse function Interpret the succession of two functions as a composite function understand and use function notation: f x, fg x, f 1 x is expected at higher tier
125 Trigonometry recap and extension Specification content Specification notes G20 Know the formula for Pythagoras Theorem a 2 + b 2 = c 2 Apply it to find lengths in right angled triangles and, where possible, general triangles in two and three dimensional figures Know and use the trigonometric ratios sin θ = opposite, cos θ = adjacent opposite, tan θ = hypotenuse hypotenuse adjacent Apply them to find lengths in right angled triangles and, where possible, general triangles in two and three dimensional figures G21 G6 Know the exact values of sin and cos for = 0 0, 30 0, 45 0, 60 0 and 90 0 Know the exact value of tan for 0 0, 30 0, 45 0, 60 0 Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras Theorem, and use known results to obtain simple proofs R12 Compare lengths using ratio notation; make links to trigonometric ratios
126 Growth & decay Specification content Specification notes R16 Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes
127 Review and revision 11 Specification content Specification notes
128 Equation of a circle Specification content Specification notes A16 Recognise and use the equation of a circle with centre at the origin Find the equation of a tangent to a circle at a given point.
129 Further equations and graphs Specification content Specification notes A17 Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation Find approximate solutions using a graph including use of brackets A18 Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula Find approximate solutions using a graph Recognise, sketch and interpret graphs of linear and quadratic functions A12 A11 Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square including the symmetrical property of a quadratic A21 Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and the solve the equation and interpret the solution including solution of geometrical problems and problems set in context
130 Direct and inverse proportion Specification content Specification notes R10 Solve problems involving direct and inverse proportion, including graphical and algebraic representations Understand that X is inversely proportional to Y is equivalent to X is proportional to 1 Y R13 Construct and interpret equations that describe direct and inverse proportion R14 Recognise and interpret graphs that illustrate direct and inverse proportion
131 Inequalities Specification content Specification notes A22 Solve linear inequalities in one or two variables and quadratic inequalities in one variable Represent the solution set on a number line, using set notation and on a graph know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary in graphical work the convention of a dashed line for strict inequalities and a solid line for an included inequality will be required
132 Vectors Specification content Specification notes Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representation of vectors G25 Use vectors to construct geometric arguments and proofs
133 Further sketching graphs Specification content Specification notes Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, and the reciprocal function y = 1 x for x 0, exponential functions y = kx for A12 positive values of k, and the trigonometric functions (with arguments in degrees) y = sinx, y = cosx and y = tanx for angles of any size (including using the symmetry of functions)
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