Transcript Key Stage 4
This version of the GCSE Maths 8300 Route Map does not offer the full functionality of the web based interactive Route Map The web based interactive Route Map will be regularly updated and links directly to supporting resources for each topic Supporting resources for each topic are on All About Maths Return to Routemap GCSE Mathematics Linear Route Map – Foundation TierRoute GCSE Mathematics 2 year Foundation Tier Map (First assessment in 2017 specification) Number Topic Number Geometry and measures Algebra Topic Geometry & Measures Topic Algebra Probability Statistics Topic Ratio, proportion and rates of change Statistics Year 10 GCSE Mathematics 2 year Foundation Tier Routemap (2015 specification) Year 10 OCTOBER SEPTEMBER Wk1 Angles Wk2 Wk3 Scale Diagrams and Bearings Basic Number Wk4 Wk5 Factors and Multiples Wk12 Wk13 Sequences JANUARY Wk22 Wk23 Real Life Graphs Circumference and Area Wk31 Holiday Wk14 Wk15 Year 10 Examinations and Revision Year 10 Examinations and Revision Wk32 Holiday Wk9 Wk10 Basic Decimals Rounding JANUARY Wk16 Wk17 Holiday Wk18 Basic Percentages Holiday Wk19 Perimeter and Area Wk24 Wk25 Wk26 Ratio and Proportion Holiday Wk27 Properties of Polygons Wk28 Wk29 Basic Probability Wk34 Wk35 Transformations JUNE Summer Examinations and Revision Wk43 Wk44 Statistical Measures Standard Form JUNE Wk36 Wk37 Congruence and Similarity 2D Representations of 3D Shapes Wk38 Holiday Wk39 Calculating with Percentages JULY Wk42 Wk30 Indices Equations MAY Wk33 Wk20 MARCH APRIL Summer Examinations and Revision Coordinates and Linear Graphs FEBRUARY Wk21 Wk41 Wk8 DECEMBER Collecting and Representing Data Holiday Wk7 Basic Fractions Basic Algebra NOVEMBER Wk11 Wk6 NOVEMBER Wk45 Constructions and Loci Year 11 Wk40 Measures GCSE Mathematics 2 year Foundation Tier Routemap (2015 specification) Year 11 OCTOBER SEPTEMBER Wk1 Wk2 Wk3 Wk4 Volume Probability Wk6 Wk12 Wk13 Wk14 Wk15 Algebra and Graphs Mock Examinations and Revision Mock Examinations and Revision JANUARY Wk22 Direct and Inverse Proportion Wk23 Holiday Wk24 Wk16 Wk32 Growth and Decay Wk33 Vectors Wk25 Holiday Wk26 Wk27 Solving Quadratic Equations Wk35 REVISION JULY Wk42 Wk43 June Examinations Year 10 Wk44 Pythagoras’ Theorem Wk18 Algebra and Graphs (continued) Wk19 Wk20 Sketching graphs MARCH Trigonometry Wk34 Wk10 Inequalities Holiday Wk28 Wk29 Quadratic Graphs MAY JUNE June Examinations Wk17 Holiday APRIL Wk31 Wk9 JANUARY FEBRUARY Wk21 Wk41 Scatter Graphs Wk8 DECEMBER Simultaneous Equations Holiday Wk7 Algebra: Quadratics, Rearranging Formulae and Identities NOVEMBER Wk11 Wk5 NOVEMBER Wk45 Wk36 Wk30 Holiday JUNE Wk37 Wk38 Holiday Wk39 REVISION Wk40 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 G1 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 G3 angles at a point on a straight line vertically opposite angles Understand and use alternate and corresponding angles on parallel lines Return to Routemap colloquial terms such as Z angles are not acceptable and should not be used Scale diagrams and bearings Specification Notes Use scale factors, scale diagrams and maps including geometrical problems Measure line segments and angles in geometric figures, including interpreting including the eight compass point bearings and three- R2 Specification content: G15 maps and scale drawings and use of bearings Return to Routemap figure bearings Basic Number N1 Specification content: Specification notes: Order positive and negative integers including use of a number line. Use the symbols =, ≠, <, >, ≤, ≥ know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary Apply the four operations, including formal written methods, to integers – both positive and negative N2 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 and understanding of terms used in household finance, for example profit, loss, cost price, selling price, debit, credit, balance, income tax, VAT and interest rate N3 Recognise and use relationships between operations including inverse operations (e.g. cancellation to simplify calculations and expressions) Estimate answers N14 Check calculations using approximation and estimation, including answers obtained using technology Return to Routemap including evaluation of results obtained Factors and Multiples Specification content: Specification notes: Use the concepts and vocabulary of prime numbers, factors (divisors), multiples, prime factor decomposition including product of common factors, common multiples, highest common factor, lowest common prime factors written in index form N4 multiple, prime factorisation, including using product notation, and the unique factorisation theorem Apply systematic listing strategies N5 Return to Routemap including using lists, tables and diagrams Basic Algebra Specification content: Specification notes: Use and interpret algebraic notation, including: it is expected that answers will be given in their - ab in place of a x b simplest form without an explicit instruction given - 3y in place of y + y + y and 3 x y in the question A1 - a2 in place of a x a , a3 in place of a x a x a, a2b in place of a x a x b 𝑎 - 𝑏 in place of a ÷ b - coefficients written as fractions rather than decimals -brackets N3 Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals Understand and use the concepts and vocabulary of expressions, equations, formulae, A3 identities, inequalities, terms and factors Simplify and manipulate algebraic expressions by: A4 collecting like terms multiplying a single term over a bracket taking out common factors Return to Routemap this will be implicitly and explicitly assessed Basic Fractions Specification content: N1 Order positive and negative fractions Apply the four operations, including formal written methods, to simple fractions N2 (proper and improper) and mixed numbers - both positive and negative N8 Calculate exactly with fractions Return to Routemap Specification notes: Coordinates and Linear Graphs Specification content: A8 Work with coordinates in all four quadrants G11 Solve geometrical problems on coordinate axes Plot graphs of equations that correspond to straight-line graphs in the coodinate plane. 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 A10 Identify and interpret gradients and intercepts of linear functions graphically and algebraically Return to Routemap Specification notes: Basic Decimals Specification content: Specification notes N1 Order positive and negative decimals Apply the four operations, including formal written methods, to decimals – both N2 positive and negative Understand and use place value (e.g. when calculating with decimals) Work interchangeably with terminating decimals and their corresponding fractions N10 7 2 3 8 (such as 3.5 and or 0.375 and ) Return to Routemap including ordering Rounding Specification content: Specification notes: Round numbers and measures to an appropriate degree of accuracy (eg to a including appropriate rounding for questions set in specified number of decimal places or significant figures) context N15 students should know not to round values during Use inequality notation to specify simple error intervals due to truncation or rounding Apply and interpret limits of accuracy N16 Return to Routemap intermediate steps of a calculation Collecting and Representing Data Specification content: Specification notes: Interpret and construct tables, charts and diagrams, including: including choosing suitable statistical diagrams frequency tables, bar charts, pie charts and pictograms for categorical data S2 vertical line charts for ungrouped discrete numerical data tables and line graphs for time series data know their appropriate use Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, S4 continuous and grouped data Return to Routemap know and understand the terms primary data, secondary data, discrete data and continuous data Sequences A23 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 Recognise and use: other recursive sequences will be defined in the sequences of triangular, square and cube numbers A24 simple arithmetic progression, Fibonacci-type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer and r is a rational number > 0) A25 Deduce expressions to calculate the nth term of a linear sequence Return to Routemap question Basic Percentages Specification content: Specification notes: Define percentage as ‘number of parts per hundred’ Interpret percentages and percentage changes as a fraction or a decimal and R9 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 Return to Routemap including interpreting percentage problems using a multiplier Perimeter and Area Specification content: G12 Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres Calculate the perimeters of 2D shapes and composite shapes G17 Calculate the area of composite shapes Find the surface area of pyramids and composite solids Know and apply formulae to calculate area of: G16 triangles parallelograms trapezia Return to Routemap Specification notes: 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 and use the formulae including frustums Circumference of a circle = 2𝜋r = 𝜋d Solutions in terms of 𝜋 may be asked for G17 Area of a circle = 𝜋r2 Calculate perimeters of 2D shapes including circles and composite shapes Calculate areas of circles and composite shapes Calculate surface area of spheres, cones and composite solids G18 Calculate arc lengths, angles and areas of sectors of circles N8 Calculate exactly with multiples of 𝜋 Return to Routemap Real Life Graphs Specification content: Specification notes: Plot and interpret graphs (including reciprocal graphs) and graphs of non-standard including problems requiring a graphical solution A14 functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration Interpret the gradient of a straight-line graph as a rate of change R14 Return to Routemap Ratio and Proportion Specification content: N11 R3 Identify and work with fractions in ratio problems R4 Use ratio notation, including reduction to simplest form Specification notes: Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 Divide a given quantity into two parts in a given part : part or part : whole ratio R5 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) R6 R7 R8 Express a multiplicative relationship between two quantities as a ratio or a fraction Understand and use proportion as equality of ratios Relate ratios to fractions and to linear functions Return to Routemap including better value or best-buy problems Properties of Polygons Specification content: Specification notes Derive and use the sum of angles in a triangle (eg to deduce and use the angle sum G3 in any polygon, and to derive properties of regular polygons) Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, G4 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 Return to Routemap Equations Specification content: Specification notes: Substitute numerical values into formulae and expressions, including scientific unfamiliar formulae will be given in the question A2 formulae A17 Solve linear equations in one unknown algebraically including those with the including use of brackets unknown on both sides of the equation Return to Routemap View next page Indices N6 Specification content: Specification notes: Use positive integer powers and associated real roots (square, cube and higher) including square numbers up to 15 x 15 Recognise powers of 2, 3, 4, 5 know that 1000 = 103 and 1 million = 106 N7 Calculate with roots and with integer indices Return to Routemap Standard Form Specification content: Specification notes: Understand and use place value (eg when working with very large or very small N2 numbers) Calculate with and interpret standard from A x 10n where 1 ≤ A < 10 and n is an N9 integer Return to Routemap with and without a calculator interpret calculator displays Basic Probability Specification content: Specification notes: Record, describe and analyse the frequency of outcomes of probability Probabilities should be written as fractions, decimals P1 experiments using tables and frequency trees Apply the property that the probabilities of an exhaustive set of outcomes sum to 1 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 P7 equally likely outcomes and use these to calculate theoretical probabilities Return to Routemap or percentages Transformations Specification content: Identify, describe and construct congruent and similar shapes, on coordinate axes, G7 by considering rotation, reflection, translation and enlargement (including fractional scale factors) G24 Describe translations as 2D vectors Return to Routemap Specification notes: Congruence and Similarity Specification content: G5 Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS) Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to G6 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 Apply and use the concepts of congruence and similarity, including the relationships G19 between lengths in similar figures Return to Routemap Specification notes: 2D Representations of 3D Shapes Specification content: Construct and interpret plans and elevations of 3D shapes G13 Return to Routemap Specification notes: Calculating with Percentages R9 Specification content: Specification notes: Solve problems involving percentage change, including : problems may be set in context percentage increase/decrease problems using a multiplier original value problems simple interest, including in financial mathematics Return to Routemap Measures Specification content: N16 Apply and interpret limits of accuracy G14 Use standard units of measure and related concepts (length, area, volume/capacity, Specification notes: mass, time, money etc.) Use standard units of mass, length, time, money and other measures (including N13 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 Change freely between related standard units (eg time, length, area, R1 volume/capacity, mass) and compound units (eg 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 Return to Routemap including making comparisons Statistical Measures Specification content: Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through : S4 appropriate measures of central tendency (median, mean, mode and modal class) spread (range, including consideration of outliers) S5 Apply statistics to describe a population Infer properties of populations or distributions from a sample, whilst knowing the S1 limitations of sampling Return to Routemap Specification notes: Constructions and Loci Specification content: Specification notes: Use the standard ruler and compass constructions (perpendicular bisector of a line including constructing an angle of 60o segment, constructing a perpendicular to a given line from/at a given point, bisecting a given 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 Return to Routemap 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 to 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 Calculate the probability of independent and dependent combined events, including P8 using tree diagrams and other representations, and know the underlying assumptions Return to Routemap including knowing when to add and when to multiply two or more probabilities Volume Specification content: Compare lengths, areas and volumes using ratio notation R12 Scale factors G16 G17 N8 Know and apply formulae to calculate the volume of cuboids and other right Make links to similarity prisms (including cylinders) Calculate the volume of spheres, pyramids, cones and composite solids Calculate exactly with multiples of 𝜋 Return to Routemap Specification notes: Algebra: Quadratics, Rearranging Formulae and Identities Specification content: Specification notes: Simplify and manipulate algebraic expressions (including those involving surds) by: A4 simplifying expressions involving sums, products and powers, including the laws of indices expanding products of two binomials factorising quadratic expressions of the form 𝑥2 + 𝑏𝑥 + 𝑐 including the difference of two squares A5 Understand and use standard mathematical formulae Rearrange formulae to change the subject Know the difference between an equation and an identity A6 Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments A7 Where appropriate, interpret simple expressions as functions with inputs and outputs Return to Routemap including use of formulae from other subjects in words and using symbols Scatter Graphs Specification content: Specification notes: Use and interpret scatter graphs of bivariate data know and understand the terms positive correlation, S6 Recognise correlation and know that it does not indicate causation negative correlation, no correlation, weak correlation Draw estimated lines of best fit and strong correlation Make predictions Interpolate and extrapolate apparent trends whilst knowing the dangers of doing so Return to Routemap Inequalities Specification content: Specification notes: Solve linear inequalities in one variable know the conventions of an open circle on a number A22 Represent the solution set on a number line Return to Routemap line for a strict inequality and a closed circle for an included boundary Pythagoras Theorem Specification content: Know the formula for Pythagoras’ Theorem 𝑎2 + 𝑏2 = 𝑐2 G20 Apply it to find lengths in right angled triangles in two dimensional figures Return to Routemap Specification notes: Simultaneous Equations Specification content: Specification notes: Solve two simultaneous equations in two variables (linear/linear) algebraically A19 Find approximate solutions using a graph Translate simple situations or procedures into algebraic expressions or formulae A21 Derive two simultaneous equations, solve the equations and interpret the solution Return to Routemap including the solution of geometrical problems and problems set in context Algebra and graphs Specification content: Specification notes: Solve linear equations in one unknown algebraically including use of brackets A17 Including those with the unknown on both sides of the equation Find approximate solutions using a graph Translate simple situations or procedures into algebraic expressions or formulae A21 Derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution Return to Routemap including the solution of geometrical problems and problems set in context Sketching Graphs Specification content: Specification notes: Recognise, sketch and interpret graphs of linear functions, quadratic functions A12 Simple cubic functions and the reciprocal function y = Return to Routemap 1 𝑥 with 𝑥 ≠ 0 Direct and Inverse Proportion Specification content: Specification notes: R10 Solve problems involving direct and inverse proportion, including graphical and algebraic representations 1 R13 Understand that X is inversely proportional to Y is equivalent to X is proportional to 𝑌 Interpret equations that describe direct and inverse proportion R14 Recognise and interpret graphs that illustrate direct and inverse proportion Return to Routemap Trigonometry Specification content: Specification notes: Know and use the trigonometric ratios 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 G20 sin 𝜃 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 , 𝑐𝑜𝑠 𝜃 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 , 𝑡𝑎𝑛 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝜃= 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 Apply them to find angles and lengths in right-angled triangles in two dimensional figures Know the exact values of sinθ and cosθ for θ = 00, 300, 450, 600 and 900 G21 Know the exact value of tanθ for θ = 00, 300, 450, 600 Compare lengths using ratio notation R12 Make links to trigonometric ratios Return to Routemap Solving Quadratic Equations Specification content: Solve quadratic equations algebraically by factorising A18 Find approximate solutions using a graph Return to Routemap Specification notes: Quadratic Graphs Specification content: Specification notes: A12 Recognise, sketch and interpret graphs of quadratic functions Identify and interpret roots, intercepts and turning points of quadratic functions A11 graphically Deduce roots algebraically Return to Routemap including the symmetrical property of a quadratic Growth and Decay Specification content: Set up, solve and interpret the answers in growth and decay problems, including R16 compound interest Return to Routemap Specification notes: Vectors Specification content: Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and G25 diagrammatic and column representation of vectors Return to Routemap Specification notes: