New GCSE Maths

Annotations:

1.3.4 apply and interpret limits of accuracy, including upper and lower bounds

1.3.3 round numbers and measures to an appropriate degree of accuracy ; use inequality notation to specify simple error intervals

1.3.1 use standard units of mass, length, time, money and other measures

1.2.2 identify and work with fractions in ratio problems

1.2.1 work interchangeably with terminating decimals and their corresponding fractions, change recurring decimals into their corresponding fractions and vice versa

1.1.9 calculate with and interpret standard form A x 10n , where 1 ≤ A < 10 and n is an integer

1.1.8 calculate exactly with fractions, surds and multiples of π; simplify surd expressions involving squares and rationalise denominators

1.1.7 calculate with roots, and with integer and fractional indices

1.1.5 use positive integer powers and associated real roots (square, cube ...)

1.1.4 use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation,

1.1.3 Recognise and use relationships between operations, including inverse operations, use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

1.1.2 Add, Subtract, Multiply and Divide integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value

2.4.3 deduce expressions to calculate the nth term of linear and quadratic sequences.

2.4.2 recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions

2.4.1 generate terms of a sequence from either a term-to-term or a position-to-term rule

2.3.6 solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

2.3.5 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

2.3.3 solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically

2.3.2 solve quadratic equations algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph

2.3.1 solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

2.2.9 calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts

2.2.8 sketch translations and reflections of a given function

2.2.7 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.

2.2.6 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 kinematic problems involving distance, speed and acceleration

2.2.5 work with coordinates in all four quadrants

2.2.4 recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1 x with x ≠ 0, exponential functions =xyk for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x , y = cos x and y = tan x for angles of any size

2.2.3 identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square

2.2.2 identify and interpret gradients and intercepts of linear functions graphically and algebraically

2.2.1 plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradient

2.1.7 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’.

2.1.6 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

2.1.5 understand and use standard mathematical formulae; rearrange formulae to change the subject

2.1.4 understand and use the concepts and vocabulary of expressions, equations, formulae, identities inequalities, terms and factors

2.1.3.6 simplifying expressions involving sums, products and powers, including the laws of indices

2.1.3.5 factorising quadratic expressions, including the difference of two squares;

2.1.3.4 expanding products of two or more binomials

2.1.3 simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:

3.16 understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y; construct and interpret equations that describe direct and inverse proportion

3.15 set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes

3.14 interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

3.13 compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors

3.12 interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

3.11 relate ratios to fractions and to linear functions

3.10 use compound units such as speed, rates of pay, unit pricing, density and pressure

3.8 understand and use proportion as equality of ratios

3.7 define percentage ; interpret percentages and percentage changes as a fraction or a decimal, express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change

3.5 express a multiplicative relationship between two quantities as a ratio or a fraction

3.4 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

3.3 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

3.2 express one quantity as a fraction of another,

4.3.2 apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs

4.2.10 know and apply Area = 1/2 ab SinC to calculate the area, sides or angles of any triangle.

4.2.9 know and apply the sine rule and cosine rule, to find unknown lengths and angles

4.2.8 know the exact values of sinθ and cosθ for given values of θ (see attached)

4.2.7 know the formulae for: Pythagoras’ theorem and the trigonometric ratios, sinθ = opposite hypotenuse , cosθ = adjacent hypotenuse and tanθ = opposite adjacent ; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

4.2.6 apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures

4.2.5 calculate arc lengths, angles and areas of sectors of circles

4.2.4 know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids

4.2.3 know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders)

4.2.2 measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

4.2.1 use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

4.1.13 construct and interpret plans and elevations of 3D shapes.

4.1.11 identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres

4.1.10 apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

4.1.9 describe the changes and invariance achieved by combinations of rotations, reflections and translations

4.1.8 identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

4.1.7 identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)

4.1.6 use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

4.1.5 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

4.1.4 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

4.1.3 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; derive and use the sum of angles in a triangle

4.1.2 use the standard ruler and compass constructions ; use these to construct given figures and solve loci problems

4.1.1 use conventional terms and notations; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description

5 Probability

5.1 record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

5.2 apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments

5.3 relate relative expected frequencies to theoretical probability, using appropriate language and the 0 - 1 probability scale

5.4 apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one

5.5 understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

5.6 enumerate sets and combinations of sets, using tables, grids, Venn diagrams and tree diagrams

5.7 construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

5.8 calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions