2019 Higher Edexcel GCSE Maths Paper 1

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Description

 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

What You Will Learn!

  • You will develop fluent knowledge, skills and understanding of mathematical methods and concepts.
  • You will acquire and apply mathematical techniques to solve problems.
  • You will be able to reason mathematically, make deductions and draw conclusions.
  • You will be able to present arguments and proofs.

Who Should Attend!

  • Students studying or hoping to study Maths GCSE at a higher level.