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# KS4

KEY COURSE INFORMATION

The course studied in KS4 is the Pearson Edexcel Linear Examination. This is 100% examination taken at the end of the course which consists of three papers, two calculator and one non-calculator. Students will be entered for Higher or Foundation, depending upon their target grade.

Throughout the course topics will be studied to enrich students’ thinking skills and further the application and functionality of Mathematics.

 Year 9 Topics Skills Autumn 1 Number. Calculations, checking and rounding. Indices and roots. Factors, multiples, primes. Standard form and surds. Work confidently with positive, negative and decimal numbers, including formal written methods. Use concepts and vocabulary of prime numbers, factors, multiples and use prime factor decomposition. Use BODMAS. Use positive, negative and fractional indices. Calculate with and interpret standard form. Round numbers to a specified number of decimal places or significant figures. Autumn 2 Algebra. Algebra; the basics. Setting up, rearranging and solving equations. Sequences. Use and interpret algebraic notion. Substitute numerical values. Expand and factorise single and double brackets. Change the subject of an equation. Solve liner equations. Form an equation from information given. Generate terms of a sequence. Find the general expression for linear and quadratic sequences. Spring 1 Interpreting & Representing Data. Averages and range. Representing and interpreting data. Scatter-graphs. Understand different methods of sampling. Interpret and construct charts and diagrams. Interpret and construct histograms. Analyse distributions. Spring 2 Fractions, ratio and percentages. Fractions. Percentages. Ratios and percentages. Apply the four operations to fractions. Change recurring decimals to fractions and vice-versa. Use ratio notation. Divide a quantity using a ratio, relate ratio to fractions and proportion. Find percentage change. Summer 1 Angles and trigonometry. Polygons, angles and parallel lines. Pythagoras and trigonometry. Understand and use alternate angles and corresponding angles on parallel lines. Deduce and use angle sum of angles in a polygon. Use Pythagoras' Theorem and trigonometry to find missing sides and angles in right-angled triangles. Know the exact values for particular values of tan θ, sin θ and cos θ. Summer 2 Graphs. Graphs, the basics and real life graphs. Linear graphs and coordinate geometry. Quadratic, cubic and other graphs. Work with coordinates in all four quadrants. Plot straight line graphs and use y = mx + c to identify parallel and perpendicular lines. Find roots, intercepts and turning points of quadratic functions, cubic functions and the reciprocal function. Calculate or estimate the area under a graph and interpret this in a context. Recognise and use the equation of a circle. Year 10 Topics Skills Autumn 1 Area and volume. Perimeter, area and circles. 3d forms and volume. Accuracy and bounds. Know and apply formulae to calculate: area of triangles, parallelograms, trapezia, volume of cuboid and other right prisms. Know and use formulae to calculate: area and circumference of a circle, surface area and volume of spheres, cones and pyramids. Calculate arc lengths and areas of sectors. Apply and interpret limits of accuracy. Autumn 2 Transformations and constructions. Transformations. Constructions, loci and bearings. Equations and inequalities. Solving quadratic and simultaneous equations. Inequalities. Use scale factors, scale diagrams and maps. Use standard ruler and compass constructions. Use basic congruence criteria for triangles. Use rotation, reflection, translation and enlargement to transform a shape. Construct plans and elevations of 3D shapes. Solve quadratics equations by factorising, completing the square and by using quadratic formula. Solve simultaneous equations in two variables. Solve linear inequalities in one or two variables. Solve quadratic inequalities in one variable. Spring 1 Probability. Multiplicative reasoning. Apply systematic listing strategies. Calculate and interpret probability through the use of tree diagrams, two-way tables and Venn diagrams. Use union and intersect notation. Use compound units such as speed and density. Calculate percentage increase and decrease using a multiplier e.g. with compound interest. Express the multiplicative relationship between two quantities as a ratio or fraction. Spring 2 Similarity and congruence in 2D and 3D. More trigonometry. Graphs of trigonometry. Further trigonometry. Understand and use congruency conditions to construct proofs and formal arguments. Understand similarity. Prove that two shapes are similar. Identify scale factors of similar shapes. Find missing area, volume and length in similar shapes. Be able to sketch graphs of y = cos x, y = sin x and y = tan x. Apply translations and reflections to the graph of a trigonometric function. Use the sine rule and cosine rule to find missing lengths and angles. Find the area of triangles using formula. Summer 1 Further Statistics. Collecting data. Cumulative frequency, box plots and histograms. Quadratics. Quadratics. Expanding more than two brackets. Sketching graphs. Write questions to eliminate bias. Understand how to ensure that a sample is representative. Construct and interpret cumulative frequency curves and box plots: read medians and quartiles. Understand and use frequency density. Identify turning points by completing the square. Recognise and sketch quadratic and cubic functions. Solve simultaneous equations (one linear/one quadratic). Expand the product of more than two linear functions. Solve quadratic inequalities. Summer 2 Circle theorems and circle geometry. Circle theorems. Find missing angles using properties of radii, tangents and chords. Prove the circle theorems. Year 11 Topic Skills Autumn 1 Algebra. Surds. Algebraic fractions. Changing the subject of an equation. Functions. Simplify algebraic expressions involving surds. Multiply and divide algebraic fractions. Rearrange equations and formulae, including where the variable is on the denominator. Expand products of two or more binomials. Use function notation and be able to find the inverse of a function. Autumn 2 Geometry. Vectors. Geometric proof. Preparation for mock assessment. Use Pythagoras' Theorem to find the length of a vector. Show that two vectors are parallel. Produce geometrical proofs to show that points are collinear and lines are parallel. Spring 1 Graphs. Reciprocal and exponential graphs. Transformation of curves. Gradient. Area under a curve. Sketch graphs of reciprocal and exponential functions. Interpret and analyse transformations of graphs of functions. Find and interpret gradient of linear and non-linear graphs. Estimate area under a quadratic by dividing it into trapezia. Spring 2 Review. Practise examination style questions. Re-cap topics. Summer 1 Review. Practise examination style questions. Re-cap topics. Summer 2 Exams