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