Autumn

Analysing and Displaying Data

• types of data, two-way tables, averages and range, grouped data, bar charts and line graphs, pie charts, scatter graphs and correlation

Number Skills

• factors, multiples, primes, negative numbers, squares, square roots, powers, estimating

Equations, Functions and Formulae

• writing and simplifying algebraic expressions, expanding brackets, factorising, substitution

Fractions

• forming and simplifying, mixed numbers, fraction arithmetic, fractions of amounts

 Factors and Powers

• products of prime factors, laws of indices, powers of ten, significant figures

Simplifying and Solving

• identities, writing and simplifying algebraic expressions, algebraic laws of indices, expanding brackets, factorising, substitution, forming and solving equations

Ratio, Proportion and Real-life Graphs

• direct proportion, distance-time graphs, real-life graphs

2D Shapes and 3D Solids

• nets, volume of prisms, circles, cylinders, Pythagoras’ Theorem

Interpreting and Representing Data

• stem-and-leaf diagrams, frequency polygons, pie charts, two-way tables, time series graphs, scatter graphs and correlation, averages

Number

• HCF and LCM, laws of indices, standard form, estimation, rounding, surds

Spring

Angles and Shapes

• parallel lines, angles in triangles, line and rotational symmetry, properties of shapes, angles in polygons

Decimals

• ordering, comparing, rounding, decimal arithmetic, converting

Equations

• forming and solving

Multiplicative Reasoning

• forming and simplifying ratios, dividing into ratios, proportion

Fractions, Decimals and Percentages

• recurring decimals, percentages of amounts, percentage change, compound interest

Sequences

• quadratic, Fibonacci and geometric sequences

Statistical Diagrams

• pie charts, cumulative frequency graphs, box plots, time series graphs, averages from grouped frequency tables, bias

Algebra

• algebraic indices, simplifying algebraic expressions, solving linear equations, factorising quadratics, linear and quadratic sequences

Fractions, Ratios and Percentages

• fraction arithmetic, forming and simplifying ratios, direct proportion, percentage change, compound interest

Summer

Perimeter, Area and Volume

• area of standard shapes, perimeters, nets, surface area, volume, converting between metric units

Sequences and Graphs

• nth term, coordinates, midpoints, drawing straight-line graphs

Transformations

• rotations, reflections, translations, enlargements, planes of symmetry

Constructions and Loci

• ruler and compass constructions, loci

Probability

• mutually exclusive events, sample spaces, Venn diagrams, tree diagrams

Graphs

• equation of a straight-line graph, gradient, y-intercept, parallel and perpendicular lines

Scale Drawings

• maps, bearings, similar shapes, congruent shapes

Angles and Trigonometry

• angles in polygons, angles in parallel lines, Pythagoras’ Theorem, trigonometry

Graphs

• equation of a straight-line graph, gradient, y-intercept, midpoints, parallel and perpendicular lines, distance-time graphs, velocity-time graphs, quadratic graphs, cubic graphs, circular graphs, solving graphs simultaneously

Area and Volume

• circles

Autumn

Area and Volume

• cylinders, spheres, cones, pyramids

Equations

• factorising and solving quadratics, completing the square, quadratic formula, simultaneous equations

Transformations and Constructions

• rotations, reflections, translations, enlargements, invariant points, ruler and compass constructions, maps and scale drawings, bearings, loci

 Circle Theorems

• circle theorems, equation of a circle

More Algebra

• changing the subject, algebraic fractions, rationalising the denominator, functions, iteration, algebraic proof

Spring

Probability

• listing outcomes, mutually exclusive events, sample spaces, expectation, relative frequency, tree diagrams, Venn diagrams, set notation

Multiplicative Reasoning

• compound interest, converting between metric units, compound measures, direct and inverse proportion

Similarity and Congruence

• similarity, congruence, scale factors

Vectors and Geometric Proof

• vectors

Proportion and Graphs

• equations of proportion, graphs of proportion, areas under graphs, estimating gradients, transformation of graphs

Summer

More Trigonometry

• sine rule, cosine rule, area of a triangle, 3D Pythagoras’ Theorem, 3D trigonometry

Further Statistics

• sampling techniques, capture-recapture, cumulative frequency graphs, boxplots, histograms, comparing data

Equations and Graphs

• graphical simultaneous equations, inequalities, sketching graphs

Autumn

Algebraic Expressions

• indices, surds and rationalising the denominator

Quadratics

• solving, modelling and the discriminant

Equations and Inequalities

• simultaneous equations, quadratic equations and inequalities

Graphs and Transformations

• cubics, quartics and reciprocal graphs

Polynomials

• algebraic fractions and factor theorem

Coordinate Geometry

• equations of straight-line graphs, equation of a circle, tangent and chord properties

Trigonometry

• trigonometric identities and solving trigonometric equations

Vectors

• solving geometric problems & modelling with vectors

Data Collection

• sampling techniques, types of data and the large data set

Kinematics

• SUVAT equations, displacement-time graphs and velocity-time graphs

Functions

• modulus function, composite and inverse functions

Trigonometry

• double-angle formulae, solving trigonometric equations and proving trigonometric identities

Trigonometric Functions

• reciprocal and inverse trigonometric functions

Differentiation

• differentiation of trigonometric functions and exponentials, the chain, product and quotient rules, and rates of change

Vectors

• solving geometric problems and modelling with vectors

Further Kinematics

• vectors in kinematics, vector methods with projectiles, variable acceleration, differentiating and integrating vectors

Projectile Motion

• horizontal and vertical components, projection at any angle and projectile motion formulae

Probability

• set notation, conditional probability, Venn diagrams, probability formulae and tree diagrams

Spring

Differentiation

• differentiating polynomials, finding tangents and normals, stationary points and sketching gradient graphs.

The Binomial Expansion

• the Binomial expansion

Data Processing, Presentation and Interpretation

• median, IQR, mean and standard deviation

Hypothesis Testing

• Binomial hypothesis testing

Forces and Newton’s Laws of Motion

• force diagrams, forces as vectors, F=ma, connected particles and pulleys

Further Differentiation

• implicit and parametric differentiation

Integration

• integration methods and trapezium rule

Normal Distribution

• finding probabilities, inverse normal, standard normal, mean and variance, approximating a Binomial distribution, and hypothesis testing

Force and Motion

• static particles, modelling with statics, friction and static particles, static rigid bodies, dynamics and inclined planes, connected particles

Friction

• resolving forces and friction on inclined planes

Summer

Integration

• indefinite and definite integrals, area under curves and area between curves and lines

Exponentials and Logarithms

• exponential modelling, laws of logs and solving equations using logarithms

Variable Acceleration

• applying differentiation and integration, maxima and minima problems and constant acceleration formulae

Sequences and Series

• Arithmetic and Geometric sequences, recurrence relations and sigma notation

Radians

• small angle approximations and radian measure

Proof

• proof by deduction, counter example, exhaustion and contradiction

Numerical Methods

• iteration, Newton-Raphson, and applications to modelling

Differential Equations

• solving differential equations and modelling with differential equations

Hypothesis Testing

• testing exponential models, measuring correlation and hypothesis testing using the Normal distribution

Moments

• resultant moments, equilibrium, and centres of mass and tilting