During key stage 4 (foundation) pupils consolidate their understanding of basic mathematics, which will help them to tackle unfamiliar problems in the workplace and everyday life and develop the knowledge and skills they need in the future.   They become increasingly proficient in calculating fractions, percentages and decimals. Building on their understanding of numbers, they make generalisations using letters, manipulate simple algebraic expressions and apply basic algebraic techniques to solve problems.   They extend their use of mathematical vocabulary to talk about numbers and geometrical objects.   They begin to understand and follow a short proof and use geometrical properties to find missing angles and lengths.   They collect data, learn simple statistical techniques to analyse data and use ICT to present and interpret the results. During key stage 4 (higher) pupils refine their calculating skills to include powers, roots and numbers expressed in standard form.  T hey learn the importance of precision and rigour in mathematics.   They use proportional reasoning and develop skills of algebraic manipulation and simplification.  They extend their knowledge of functions and related graphs and solve a range of equations, including those with non-integer coefficients. They use short chains of deductive reasoning, develop their own proofs, and begin to understand the importance of proof in mathematics.   Pupils use definitions and formal reasoning to describe and understand geometrical figures and the logical relationships between them.   They learn to handle data through practical activities including sampling.  Pupils develop the flexibility to solve unfamiliar problems and to use ICT appropriately.

Click on to down load examples and questions.

Click on to down load results

Applies only to signed up members and students.

	Types of number		Primes, squares, cubes and relating numbers to their higher powers.
	Prime numbers		Extended understanding of prime numbers, list primes and find primes. Find all factors of non primes.
	Sequences		Give the nth. term for a given series. Deduces which numbers foe a given set are members of the same sequences
	Ratios		Use ratio notation, including reduction to its simplest form and its various links to fraction notation
	Indices		Use the terms square, positive square root, cube, express standard index form both in conventional notation and with a calculator.
	Factors		Add, subtract, multiply and divide any number use brackets and the hierarchy of operations
	Fractions		Multiplication and division and determination of fractions.
	Percentages		Determine percentages, percentages changes
	Irrational numbers		Logic of rational and irrational numbers.
	Decimals and surds		Simplification of expressions and calculations
	Conversion		Converting between metric and Imperial units
	Estimating		Accuracy of result, rounding of given numbers and estimating calculations.
	Regular polygons		Four and five sided polygons calculate angles and deduce polygon from known internal angle
	Perimeters and areas		Determine perimeters and areas from a verity of shapes
	Symmetry		Identify, and use pattern and symmetry in algebraic contexts and make constructions
	Volumes		Calculate volumes from cones and bodies made of part known shapes.
	Geometry		Calculate angles on interesting lines, triangles, trapeziums. and other irregular shapes.
	Circle geometry		Angles and tangents.
	Loci and constructions		Construct maps from given part diagrams and other information.
	Loci and coordinates in 3D		Construct solids from given data
	Congruence and similarity		Decide which triangles are congruence and other properties
	Transformations		Use two dimensional grids to expand and rotate shapes
	3D shapes		Calculate volumes, perimeters cross-section areas
	Scatter diagrams		Draw scatter plot and determine what type of correlation exists
	Velocity vs time graphs		Use graphs to determine speeds, distances and other deductions
	Standard index form		Use of index form to express numbers and manipulate them
	Powers and roots		Negative and fraction powers simplification and solving simple algebraic equations
	Pythagoras' theorem		Pythagoras et el
	Trigonometry		Angles, distances and sides
	The sine rule		Angles, distances and sides using sins
	The cosine rule		Angles, distances and sides using cosines
	Sin, cos and tan graphs		Plot curves of sins, cosines determine positive and negative values.
	Vectors		Evaluate vectors and write in vector notation.
	Mean, median and range		Calculate them form a data sets.
	Probability		Dice and spinners and their probabilities
	Frequency tables		Complete tables and deduce facts from them
	Grouped frequency tables		Calculation of means, medians and modal class.
	Cumulative frequency		Draw an cumulative frequency curve from a data set. Calculate quartiles.
	Histograms		Stem and leaf diagrams and draw histograms from given data
	Correlation		Draw straight line curve from data set. Estimate possibility of correlation various pairs. Comment on distributions of given graphs.
	Sampling methods		Explain how to take a random sample, moving averages.
	Straight line graphs		From various equations show which can be represented as straight lines. Draw lines from a data set in one and two variables.
	Collecting data		Data sampling methods
	Linear programming		From given information deduce inequalities and draw graphs.
	Coordinates		Simple coordinates geometry, distance between two coordinates points and information triangles from its coordinates
	Solving equations		Graphical methods of solving in higher powers of a single variable and deductions from a given non linear curve
	Simultaneous equations		Graphical methods of solving simultaneous equations and quadratics in a single variable.
	Simultaneous equations		Solving quadratic equations by completing the square
	Tangents and gradients		Solving pair of simultaneous equations, substituting to form a quadratic in one variable
	Finding equations		Graph interpretation on cubics and irregular curves
	Basic algebra		Adding, subtraction, factorising and simplifying algebraic expressions
	Solving equations		Single variable equations containing roots and powers
	Rearranging formulas		Collecting terms and expressing the equation in a different term
	Inequalities		Solve single and double inequalities
	Proportion		Relating an expression to solvable equations by direct and inverse methods
	Factorising quadratics.		Solving and rearranging quadratics
	The quadratic formula		Understanding the coefficients of a quadratic, solving and determining whether possible solutions exist
	Completing the square		Solving quadratic equations by completing the square
	Trial and improvement		Using a calculator to find an approximate solution to cubic equations
	Growth and decay		Interest rates and changes using percentages
	Variation		Rearrangement of equations and the relationship of the variables in the equation