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FAST FORWARD REVISION CLASSES
COMPLETE GCSE MATHS REVISION IN 5 DAYS
MODULE 1; NUMERACY - FOUNDATION
Integers, Negative Numbers, Decimals, Fractions, Operations, Household Finance, Decimal Places, Significant Figures, Upper/Lower Bounds (Error Intervals), Standard Index Form, Prime Numbers, Perfect Squares & Cubes, Decimals, Fractions, Percentages, Ratios, Factor Trees, Surds, Sequences, Proportion, Estimates, Trial & Improvement
order positive and negative integers, decimals and fractions use the symbols =, ≠, , ≤, ≥ , understand and use proportion as equality of ratios, solve problems involving direct and inverse proportion, including graphical and algebraic representations, express one quantity as a fraction of another, solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics, apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative, place value, significant figures, prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem, apply systematic listing strategies,use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 & fractional powers, standard form, use ratio notation, including reduction to simplest form, use standard units of mass, length, time, money and other measures, estimation, use compound units such as speed, rates of pay, unit pricing, density and pressure
MODULE 2a; ALGEBRA - FOUNDATION
Solving Equations & Inequalities, Expanding, Factorising, Difference Of Two Squares, Index Rules, Vectors, Linear Graphs, Transformations, Iteration
use and interpret algebraic notation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a2 in place of a × a, a3 in place of a × a × a, a2 b in place of a × a × b • a b in place of a ÷ b • coefficients written as fractions rather than as decimals • brackets, substitute numerical values into formulae and expressions, including scientific formulae, understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors, identities, simplify and manipulate algebraic expressions by: simplify and manipulate algebraic expressions (including those involving surds) by: simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: • collecting like terms • multiplying a single term over a bracket • taking out common factors • simplifying expressions involving sums, products and powers, including the laws of indices, understand and use standard mathematical formulae rearrange formulae to change the subject, interpret simple expressions as functions with inputs and outputs, work with coordinates, plot graphs of equations that correspond to straight-line graphs, identify and interpret gradients as rates of change and intercepts of linear functions graphically and algebraically, recognise, sketch and interpret graphs of linear, quadratic, cubic amd reciprocal functions, direct and inverse proportion, find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration, solve linear equations in one unknown algebraically find approximate solutions using a graph, solve quadratic equations algebraically by factorising, solve two simultaneous equations in two variables (linear/linear) algebraically find approximate solutions using a graph, translate simple situations or procedures into algebraic expressions or formulae derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution, solve linear inequalities in one variable solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable represent the solution set on a number line, generate terms of a sequence from either a term-to-term or a position-to-term rule, recognise and use sequences of triangular, square and cube numbers and simple arithmetic progressions including Fibonacci-type sequences, quadratic sequences, and simple geometric progressions r n where n is an integer and r is a rational number > 0), deduce expressions to calculate the nth term of linear sequences, change freely between related standard units (eg time, length, area, volume/capacity, mass) and compound units (eg speed, rates of pay, prices) in numerical contexts compound units (eg density, pressure) in numerical and algebraic contexts, use scale factors, scale diagrams and maps
MODULE 2a; ALGEBRA - HIGHER
Solving Quadratics (Graphically, Factorising, Quadratic Formula & Completing the Square), Simultaneous Equations (Linear And Quadratic), Equations of Circles,
simplify surd expressions involving squares (eg 12 = 4×3= 4 × 3=2 3 ) and rationalise denominators
MODULE 3a; GEOMETRY - FOUNDATION
Areas, Surface Areas, Volumes, Linear/Area/Volume Scaling Factors, 3-Figure Bearings, Cosine Rule, Sin Rule, Circle Theorems, Constructing Loci, Scaling Factors, Scale Diagrams,
use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries use the standard conventions for labelling and referring to the sides and angles of triangles draw diagrams from written description, apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles understand and use alternate and corresponding angles on parallel lines derive and use the sum of angles in a triangle, properties of regular polygons (interior and exterior angles), derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus, use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS), isoceles, Pythagoras theorem, rotation, reflection, translation and enlargement, fractional scaling factors, circle definitions and properties, including: centre, radius, chord, diameter, circumference including: tangent, arc, sector and segment, properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres, interpret plans and elevations of 3D shapes, measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings, area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders), know the formulae: circumference of a circle = 2r = d area of a circle = r 2 calculate perimeters of 2D shapes, including circles areas of circles and composite shapes surface area and volume of spheres, pyramids, cones and composite solids, trigonometric ratios (SOHCAHTOA), know the exact values of sin x, tan x and cos for x = 0°, 30°, 45° , 60° and 90°, describe translations as 2D vectors
MODULE 4a; STATISTICS FOUNDATION
Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees,apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments, relate relative expected frequencies to theoretical probability, apply the property that the probabilities of an exhaustive or mutually exclusive set of outcomes sum to 1, enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams, construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities, interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, and know their appropriate use including tables and line graphs for time series data
Mean, Median, Mode, Interquartile Range, Frequency, Tally Charts, Pictograms, Stem and Leaf Diagrams, Pie Charts, Frequency Density Plots, Cumulative Frequency Plots, Probability, Scatter Graphs, 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 • appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers), use and interpret scatter graphs of bivariate data recognise correlation
All Students Receive Our Comprehensive Maths Revision Workbook
Developed to provide students with simple, step-wise methods that can be applied universally to solve every type of maths problem listed on the GCSE Maths exam specification. Every method is illustrated with worked examples of typical exam questions, ranging from easy to challenging. The workbooks also contain simple decision flowcharts, which show students how to store, recall, select and execute the appropriate method for a given maths problem. Students who memorise the methods can enter an exam feeling well-prepared.
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