These are the Paper 1 Topics that are coved in this course:

•Multiples, factors, LCM and HCF and prime factor decomposition

•Fractions and ratio problems

•Standard constructions using a compass (including triangles)

•Bearings with geometrical problem

•Averages and range, problems and comparing distributions

•Simplify algebraic indices

•Expand single and double brackets

•Use a cumulative frequency graph to compare distributions (median and IQR)

•Probability tree for independent events

•Simplify algebraic indices

•Algebraic fractions

•Factorising quadratic expressions, including difficult where a > 1

•Perimeter and area of triangles and quadrilaterals, including trapezium

•Recurring decimal to fraction (prove)

•Simplify and manipulate surds

•Surface area and volume of cylinders

•Completing the Square and turning points

•Composite and inverse functions

•Draw transformations and combination of transformations

•Graphical solution to equations, including quadratic roots

•Geometrical problems, alternate /corresponding angles and angles in a segment

•Graphs of trigonometric functions Translations and reflections of a function

•These are the complete list of topics that will be covered in the higher GCSE course:

Number

••BIDMAS (brackets)

•Interpret calculator displays

•Rounding and estimation, error intervals

•Compare fractions, decimals and percentages

•Fractions and ratio problems

•Recurring decimal to fraction (prove)

•Index Laws (division, negative and fractional)

•Multiples, factors, LCM and HCF and prime factor decompositionFractions and ratio problems

•Adding, subtracting, multipling and dividing fractions (problem)

•Changing from standard form into an ordinary number

•Calculating with standard form (calculator)

•Upper and lower bounds (including calculations)

•Simplify and manipulate surds

Algebra

•Forming expression, formulae and equations (then solving)

•Substitution

•Mid-point and distance between two coordinates

•Simplify algebraic indices

•Expand single and double brackets

•nth term of a linear sequence

•Linear equations (including variable on both sides)

•Drawing graphs of linear functions

•Finding the equation of a line, and parallel and perpendicular lines

•Simultaneous equations (linear) problem

•Factorise single bracket

•Factorising quadratic expressions, including where a > 1

•Quadratic equations (including when needs re-arrangement)

•Recognise Fibonacci and quadratic sequences

•nth term of a quadratic sequence

•Drawing quadratic graphs

•Rearranging Formulae (including when subject appears twice / factorising)

•Represent linear inequalities on number line and graphically

•Solving linear inequalities and represent on number line and graphically

•Represent quadratic inequalities graphically

•Solving quadratic inequalities

•The Quadratic Formula

•Completing the Square and turning points

•Simultaneous equations (linear/quadratic)

•Draw and recognise reciprocal and cubic graphs

•Graphs of exponential functions and growth and decay

•Graphical solution to equations, including quadratic roots

•Composite and inverse functions

•General iterative processes

•Algebraic fractions

•Algebra proof

•Graphs of trigonometric functions Translations and reflections of a function

Ratio, Proportion and Rates of Change

•Ratio and proportion problems

•Comparing quantities as a ratio and division of a quantity as a ratio

•Division of a quantity as a ratio

•Problems involving ratio

•Converting metric units

•Scale drawings

•Express one quantity as the percentage of another

•Compound interest and financial maths

•Reverse percentages and reverse percentage change

•Compare lengths, area, volume

•Problems involving compound units (including pressure)

•Direct and inverse proportion

•Non-standard real life graphs

•Reciprocal real-life graphs

•Gradient of graphs

•Distance-time graphs

•Area under a graph (compare estimate with actual)

Geometry and Measures

•Properties of 2D Shapes

•Geometrical problems, alternate /corresponding angles and angles in polygons

•Perimeter and area of triangles and quadrilaterals, including trapezium

•Area of a triangle using Area = ½absin C

•Perimeter and area of composite shapes

•Circumference of a circle, arc length and perimeter and area of a sector

•Properties of 3D Shapes and plans and elevations

•Surface area and volume of prisms, pyramids, cones and spheres

•Draw transformations and combination of transformations

•Pythagoras’ Theorem, including in 3D

•Trigonometry (SOH CAH TOA), including in 3D

•Standard constructions using a compass (including triangles)

•Loci

•Bearings (possibly with trigonometry or a geometrical problem)

•Scale factors and similarity

•Circle theorems

•Sine Rule

•Cosine Rule

•Vectors

Probability

•Relative frequency

•Sampling and unbiased samples

•Venn diagrams

•Probability trees for both independent events and conditional probability Frequency trees

Statistics

•Averages and range, problems and comparing distributions

•Comparing data on statistical diagrams, including time series graphs

•Mean from a discrete frequency table

•Scatter graphs and correlation

•Constructing and interpreting a boxplot

•Use a cumulative frequency graph to compare distributions (median and IQR)

•Histograms