# Mathematics

## Year 7

Year 7 covers the following topics:

Number:  4 main operations, negative numbers, types of numbers (e.g. factors and multiples), order of operations, adding, subtracting and multiplying fractions, equivalence of percentages, fractions and decimals and recurring decimals

Algebra:  coordinates in all four quadrants, collecting like terms; multiply a single term over a bracket, substitute positive integers into linear expressions and formulae, construct and solve simple linear equations (unknown on only one side)

Ratio, proportion and rates of change:  scale drawing

Geometry and measures:  construction (straight lines and simple triangles), area of triangle, rectangle, parallelogram and compound shapes, angles (at a point, on a straight line in a triangle, vertically opposite), classify triangles and quadrilaterals by their geometrical properties and 2-D representations of 3-D objects

Probability:  experimental and theoretical probabilities in simple contexts and if the probability of an event occurring is p then the probability of it not occurring is 1 – p

Statistics:  frequency tables for discrete data, pie-charts, stem and leaf diagrams and averages from rawraw data

## Year 8

Year 8 covers the following topics:

Number:  use index laws for multiplication and division of integer powers, significant figures, trial and improvement method and dividing fractions

Algebra:  construct and solve linear equations (unknown on either or both sides), change the subject of a formula (in simple cases), substitute positive and negative integers into formulae, nth term of an arithmetic sequence, term-to-term and position-to-term rules, midpoint of a line segment, straight-line graphs parallel to the x or y-axis,  conversion graphs, distance–time graph

Ratio, proportion and rates of change:  percentage increase or decrease, decimal multipliers, divide a quantity in a given ratio, unitary method for direct proportion, rates of change in everyday contexts (e.g. km per hour, pence per metre), compound measures in real-life contexts (value for money) and convert one metric unit to another

Geometry and measures: angles in parallel lines, interior and exterior angles of regular polygons, area of a trapezium and a circle, 4 main transformations ( including enlargements with a positive scale factor), congruent shapes, nets of 3-D shapes, plans and elevations, volumes and surface areas of cuboids and of right prisms

Statistics:  frequency tables for continuous data and two-way tables, mean from frequency tables and scatter graphs

## Year 9

Year 9 covers the following topics:

Number: negative and fractional powers, upper and lower bounds, compound interest, reverse percentages and standard form

Algebra: straight line graphs, double brackets, factorising, simultaneous equations, inequalities and function notation

Geometry and measures: Pythagoras' theorem, construct triangles given RHS, SAS, ASA & SSS (S = side, A = angle, R = right angle, H = hypotenuse), loci, trigonometry, enlargement with fractional and negative scale factors and higher order graphs (quadratic, cubic, reciprocal and square root)

Probability:  sample space diagrams and dependent and independent events with tree diagrams

Statistics: cumulative frequency and boxplot

## Year 10

 Fractions Mensuration - Area of Composite shapes, Arc length, Sector Area, Volume and Surface area of prisms. Rational and Irrational Numbers Indices Expressions - Expanding Brackets (linear quadratic and Cubic), Factorising (linear and quadratic including non-monic quadratics) Probability - Tree diagrams (revision),Mutually exclusive events, Independent events, Conditional probability, Venn Diagrams Equations -  Linear equations (revision), Using linear equations to model and solve real life situations Changing the subject - powers, roots and problems involving factorisation Sampling - Random, stratified and systematic Percentages - Percentage change using decimal multiplier, Compound interest, Reverse percentages Averages- Mean mode and median from frequency table, Mean and mode from grouped frequency table, Time series (New GCSE) Pythagoras - 2D Pythagoras,3D Pythagoras, 3D coordinates Sequences - Linear/Arithmetic sequences, Quadratic sequences,  Geometric sequences Straight Line Graphs - y=mx+c , Gradients of perpendicular lines Simultaneous Equations - Both algebraic and graphical method for linear simultaneous equations Similarity - Congruent shapes – four cases for triangles, Similar 2D shapes, emphasis on similar triangles,  Relationship between sides, areas and volumes of similar 3D shapes Quadratic Equations - Solution by factorising, Graphical solution , ax2+bx+c=0 and intersection with straight lines, Model and solve real life problems Proportion - Direct proportion, Inverse proportion Statistical Graphs - Histograms – including finding median Trigonometry - Right angled trig (revision), Angles of depression & elevation (bearing),  Sine and cosine rule,  Area of triangle

## Year 11

 Circle Theorems - Tangent-radius.  Tangents to circle equal length. Perp from centre to  chord bisects, Centre angle double circumference, Angle in semi-circle. Same segment, Cyclic quadrilateral, Alternate segment. Estimation and Accuracy - Estimating results to 1 significant figure, Upper and lower bounds. Vectors - Column vectors, Geometric vectors, Addition and subtraction, Equality of vectors, Proof Inequalities – linear and Quadratic Volume and Surface Area – Pyramids, cones and spheres. Algebraic Fractions - Simplifying – quadratic numerators and denominators.  LCM of quadratic expressions and use in addition and subtraction of fractions. Exponential Functions – growth and decay Iteration Quadratic Equations – Completing the square, Factorising, Formulae Functions – Composite and Inverse Simultaneous Equations – Linear and Quadratic, Graph Equation of Circle Non Right-angled Trigonometry – exact values Graph Transformations 3D shapes – Plans and Elevations Transformations Congruence and Proof Higher Order Graphs - Graphs of reciprocal, cubic, Estimate gradients of graphs, including rates of change. Area under the graph.

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