INTERNATIONAL GCSE MATHEMATICS 2 year Core Tier Route Map (First assessment in 2018 specification)

Year 10 NumberAlgebra Geometry and measures Probability and Statistics International GCSE Mathematics 2 year Core Tier Route Map (First assessment in 2018 specification) Centres are encouraged to integrate problem solving approaches /questions in all topic coverage of both the Core and Extension.

SEPTEMBER OCTOBERNOVEMBER DECEMBERJANUARY FEBRUARYMARCH APRILMAYJUNE JULY Holiday Basic Fractions Basic Fractions Basic Number Basic Number Basic Percentages Basic Percentages Factors and Multiples Factors and Multiples Year 10 International GCSE Mathematics 2 year Core Tier Routemap (2016 specification) Measures Coordinates and Linear Graphs and Linear Graphs Sequences Year 11 Summer Examinations and Revision Summer Examinations and Revision Transformations Formulae and Equations Basic Decimals and Rounding Basic Decimals and Rounding Basic Algebr a Basic Algebr a Angles Year 10 Examinations and Revision Year 10 Examinations and Revision Indices (number and algebra) Indices (number and algebra) Real Life Graphs Real Life Graphs Properties of Polygons Properties of Polygons Scale Diagrams and Bearings Scale Diagrams and Bearings Collecting and Representing Data Collecting and Representing Data Statistical Measures Statistical Measures Perimeter and Area Ratio and Proportion Ratio and Proportion 2D Representations of 3D Shapes 2D Representations of 3D Shapes Calculating with Percentages Calculating with Percentages Basic Probability Basic Probability Constructions and Loci Constructions and Loci Set Notation and Venn diagrams Set Notation and Venn diagrams Pythagoras’ Theorem Pythagoras’ Theorem Simple Reflection and Rotation Simple Reflection and Rotation

SEPTEMBER OCTOBERNOVEMBER DECEMBERJANUARY FEBRUARYMARCH APRILMAYJUNE JULY Holiday Year 11 International GCSE Mathematics 2 year Core Tier Routemap (2016 specification) Correlation, Interpretation and comparison of data, diagrams and distributions Correlation, Interpretation and comparison of data, diagrams and distributions Year 10 June Examinations June Examinations Quadratic Functions REVISION Solving Quadratic Equations Solving Quadratic Equations Mock Examinations and Revision Mock Examinations and Revision Inequalities Solving problems algebraically and graphically REVISION VolumeAlgebra: Simple Functions, Quadratics and Algebraic argument Sketching graphs Sketching graphs Trigonometry Probability Congruence and Similarity Congruence and Similarity Reasoning and Proof Reasoning and Proof Simultaneous Equations Simultaneous Equations Standard Form Standard Form Algebraic Fractions Algebraic Fractions

Specification content: Specification notes: G1  use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons including regular polygons  Use the standard conventions for labelling and referring to the sides and angles of triangles G2  recall and use properties of angles at a point, angles at a point on a straight line including right angles and perpendicular lines; vertically opposite angles G3  understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals  students should know the meaning and properties of ‘alternate’, ‘corresponding’, and ‘interior’ angles  colloquial terms such as ‘Z angles’ should not be used. Students should know the names and properties of isosceles, equilateral and scalene triangles, and also right-angled, acute-angled and obtuse-angled triangles Angles

Specification content: Specification Notes G12  measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of scale factors and bearings  including the eight compass point bearings and three- figure bearings Scale diagrams and bearings

Specification content: Specification notes: N1  including use of a number line 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 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) Basic Number

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 Factors and Multiples

Simple Reflection and Rotation Specification content: Specification notes: G6  recognise reflection and rotation symmetry of 2D shapes

Specification content: Specification notes: A1  it is expected that answers will be given in their simplest form without an explicit instruction given in the question N3  Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals A3  understand and use the concepts of expressions, equations, formulae, identities, inequalities, terms and factors Basic Algebra

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  including questions set in context N7  Calculate exactly with fractions Basic Fractions

Specification content: Specification notes: A10  Work with coordinates in all four quadrants A11  plot graphs of equations that correspond to straight-line graphs in the coordinate plane  use the form y = mx + c  Identify and interpret gradients and intercepts of linear functions graphically and algebraically understand the gradients of parallel lines Coordinates and Linear Graphs

Specification content: Specification notes: S1  understand and use qualitative, discrete and continuous data, including grouped and ungrouped data S4  produce charts and diagrams for various data types; scatter graphs, stem-and- leaf, tally charts, pictograms, bar charts, dual and composite bar charts, pie charts, line graphs, frequency polygons, histograms with equal class intervals Collecting and Representing Data

Specification content: Specification notes N1  Order positive and negative decimals N2  Apply the four operations, including formal written methods, to decimals – both positive and negative  Understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals)  including questions set in context N10  use calculators effectively and efficiently including trigonometrical functions N11  round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures)  use estimation to work out approximate answers to calculations Basic Decimals and Rounding

Specification content: Specification notes: N12  understand and use equivalent fractions, understand and use percentages, convert between fractions, terminating decimals and percentages N13  interpret fractions, decimals and percentages as operators N14  Work with percentages greater than 100%  express one quantity as a percentage of another, where the percentage is less than 100 or greater than 100 Basic Percentages

Specification content: Specification notes: G15  know and apply formulae to calculate: area of triangles, parallelograms, trapezia G10  Identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres G8  Identify and apply circle definitions and properties, including centre, radius, chord, diameter, circumference, tangent, arc, sector and segment G16  know and use the formulae: circumference of a circle = 2 π r = π d  area of a circle = π r 2  calculate perimeters and areas of 2D shapes, including composite shapes  solutions in terms of π may be asked for Perimeter and Area

Set Notation and Venn diagrams Specification content: Specification notes: N9  use language and notation of sets including n(A),, A B, A B, ξ  understand and use Venn diagrams to solve problems

Specification content: Specification notes: A17  plot and interpret graphs, and graphs of non-standard 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 Real Life Graphs

Specification content: Specification notes: A24  generate terms of a sequence from either a term-to-term or a position-to-term rule A25  recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions A26  deduce expressions to calculate the n th term of a linear sequence Sequences

Specification content: Specification notes: N16  use ratio notation, including reduction to simplest form and links to fraction notation N14 express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 N17  Divide a given quantity in a given ratio N18  apply ratio to solve problems N19  use common measures of rate, including calculating rates of pay and best-buy problems  including making comparisons N20  solve problems involving direct and inverse proportion including repeated proportional change Ratio and Proportion

Specification content: Specification notes G4  calculate and use the sums of the interior and exterior angles of polygons  students should be able to calculate the values of the interior angle, exterior angle and angle at the centre of regular polygons G5  recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus Properties of Polygons

Specification content: Specification notes: A2  substitute numbers for words and letters in formulae and transform simple formulae A19  solve linear equations in one unknown algebraically  including use of brackets and those with the unknown on both sides of the equation Formulae and Equations View next page

Specification content: Specification notes: N5  Use positive integer powers and associated real roots (square, cube and higher)  Recognise powers of 2, 3, 4, 5 N6  index laws for multiplication and division using integer powers A6  index laws for multiplication and division using integer powers Indices

Specification content: Specification notes: S9  understand and use the vocabulary of probability and the probability scale S10  understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency  understand and use expected frequency S14  understand and use sample spaces for situations where outcomes are single events Basic Probability

Specification content: Specification notes: G21  describe and transform 2D shapes using single rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations  translations will be specified by a vector G22  understand and use vector notation for translations Transformations

Specification content: Specification notes: G19 Pythagoras’ Theorem

Specification content: Specification notes: G11  interpret plans and elevations of 3D shapes construct and interpret plans and elevations of 3D shapes 2D Representations of 3D Shapes

Specification content: Specification notes: N15  solve problems involving percentage change, including increase/decrease, simple interest and compound interest Calculating with Percentages

Specification content: Specification notes: G14  use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.); change freely between related standard units (eg time, length, area, volume/capacity, mass) and compound units (eg speed and density)  24 and 12 hour clock for times N11  apply and interpret limits of accuracy Measures

Specification content: Specification notes: S3  design and use two-way tables for grouped and ungrouped data S5  calculate median, mean, range, mode and modal class Statistical Measures

Specification content: Specification notes: G13  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 an angle of 60 ° )  use these to construct given figures and solve loci problems  know that the perpendicular distance from a point to a line is the shortest distance to the line Constructions and Loci

Specification content: Specification notes: S11  compare experimental data and theoretical probabilities S12  understand that if an experiment is repeated, this may - and usually will - result in different outcomes S13  understand that increasing sample size generally leads to better estimates of probability and population characteristics S14  understand and use sample spaces for situations where outcomes are single events and for situations where outcomes are two successive events S15 identify different mutually exclusive and exhaustive outcomes and know that the sum of the probabilities of all these outcomes is 1 know and use that for mutually exclusive events A and B P(A  B) = P(A) + P(B) S16  understand and use Venn diagrams to work out probabilities Probability

Specification content: Specification notes: G15  volume of 3D shapes using V = Ah where A is the constant cross sectional area and h is the height/length Volume

Specification content: Specification notes: A9  interpret simple expressions as functions with inputs and outputs A4  collecting like terms and expanding brackets up to expanding products of two linear expressions A5 A8  argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments Algebra: Simple functions, Quadratics and Algebraic argument

Reasoning and Proof Specification content: Specification notes: G9  geometrical reasoning and proof: use standard theorems to justify results in geometric contexts

Specification content: Specification notes: A21  Solve two linear simultaneous equations in two variables algebraically  Find approximate solutions using a graph Simultaneous Equations

Specification content: Specification notes: A7  manipulation of rational expressions: use of +  × ÷ for algebraic fractions with denominators being numeric Algebraic Fractions

Specification content: Specification notes: A19  solve linear equations in one unknown algebraically  find approximate solutions using a graph  including use of brackets and those with the unknown on both sides of the equation A22  translate simple situations or procedures into algebraic expressions or formulae  derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution  including the solution of geometrical problems and problems set in context Solving problems algebraically and graphically

Sketching Graphs Specification content: Specification notes: A12

Specification content: Specification notes: N2  understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals)  including questions set in context N8  interpret calculator displays Standard Form

Specification content: Specification notes: S8  recognise correlation and draw and/or use lines of best fit by eye, understanding what these represent  students should know and understand the terms: positive correlation, negative correlation, no correlation, weak correlation and strong correlation S2  extract data from printed tables and lists S6  read and interpret a wide range of graphs and diagrams and draw conclusions S7  compare distributions and make inferences Correlation, Interpretation and comparison of data, diagrams and distributions

Specification content: Specification notes: G19 Trigonometry

Specification content: Specification notes: A20  solve quadratic equations algebraically by factorising  find approximate solutions using a graph Solving Quadratic Equations

Specification content: Specification notes: A16  identify and interpret roots, intercepts and turning points of quadratic functions graphically  deduce roots algebraically  including the symmetrical property of a quadratic Quadratic Functions

Congruence and Similarity Specification content: Specification notes: G7  understand congruence and similarity  calculate lengths of similar figures

Specification content: Specification notes: A23  solve linear inequalities in one variable  represent the solution set on a number line Inequalities