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Programme Of Study For Key Stage 4 Mathematics

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A printable version of these cards can be found here.

...apply systematic listing strategies, {including use of the product rule for counting}

...{estimate powers and roots of any given positive number}

...calculate with roots, and with integer {and fractional} indices

...calculate exactly with fractions, {surds} and multiples of π ; {simplify surd ex

...calculate with numbers in standard form A × 10^{n}, where 1≤A<10 and n is an integer

...{change recurring decimals into their corresponding fractions and vice versa}

...identify and work with fractions in ratio problems

...apply and interpret limits of accuracy when rounding or truncating, {including upper and lower bounds}

...simplify and manipulate algebraic ex^{2} + bx + c, including the difference of 2 squares; {factorising quadratic ex^{2} + bx + c} and by simplifying ex

...know the difference between an equation and an identity; argue mathematically to show algebraic ex

...where appropriate, interpret simple ex

...use the form y = mx + c to identify parallel {and perpendicular} lines; find the equation of the line through 2 given points, or through 1 point with a given gradient

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

...recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = with x not equal to 0, {the exponential function y = k^{x} 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}

...{sketch translations and reflections of the graph of a given function}

...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

...{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}

...{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}

...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

...solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph

...{find approximate solutions to equations numerically using iteration}

...translate simple situations or procedures into algebraic ex

...solve linear inequalities in 1 {or 2} variable {s}, {and quadratic inequalities in 1 variable}; represent the solution set on a number line, {using set notation and on a graph}

...recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r^{n} where n is an integer, and r is a positive rational number {or a surd}) {and other sequences}

...deduce ex

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

...convert between related compound units (speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

...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

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

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

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

...interpret and use fractional {and negative} scale factors for enlargements

...{describe the changes and invariance achieved by combinations of rotations, reflections and translations}

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

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

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

...interpret and use bearings

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

...calculate surface areas and volumes of spheres, pyramids, cones and composite solids

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

...apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures

...know the exact values of the sine and cosine of 30, 45, 60 and 90 degrees; know the exact value of the tangent of 30, 45, and 60 degrees

...{know and apply the sine and cosine rules to find unknown lengths and angles}

...{know and apply Area = ½ ab sin C to calculate the area, sides or angles of any triangle}

...describe translations as 2D vectors

...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}

...apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to 1

...use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size

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

...{calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams}

...infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling

...interpret and construct tables and line graphs for time series data

...{construct and interpret diagrams for grouped discrete data and continuous data, ie, histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use}

...interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data, {including box plots} and appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}

...apply statistics to describe a population

...use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing.

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