GCSE Maths

Number

Standard Form (Scientific Notation)

  1. Expressing a number in standard form or scientific form

Percentages

  1. What is a percentage?
  2. Finding a percentage of a quantity
  3. Converting a fraction to a percentage
  4. Calculating a percentage change
  5. Increasing / decreasing a quantity by a percentage

Surds

  1. Surds - introduction & simplifying
  2. Addition and subtraction of surds
  3. Multiplying surds
  4. Dividing surds
  5. Rationalising surds

Algebra and Functions

Identity or Equation?

  1. Identity or equation - what is the difference?

Expanding Brackets

  1. Expanding a single bracket
  2. Squaring a bracket

Solving Linear Equations

  1. Terms in expressions and equations
  2. Linear equations with a positive x-term
  3. Linear equations with a negative x-term
  4. Linear equations with two x-terms
  5. Linear equations with brackets
  6. Fractional linear equations

Indices

  1. Introduction to indices (exponents)
  2. Multiplication rules for indices
  3. Division rule for indices
  4. Negative indices
  5. Fractions raised to a negative index
  6. Rational (fractional) indices
  7. Simplifying terms with negative powers
  8. Expressing terms in the form axn
  9. Equations in which the power has to be found
  10. Summary of indices

Functions

  1. f(x) notation

Factorising

  1. Introduction to factorising
  2. Highest common factor (HCF)
  3. Factorising by grouping
  4. Factorising quadratic expressions

Completing the Square

  1. Completing the square
  2. Applications of completing the square - sketching graphs

Simultaneous Equations

  1. Elimination method for linear equations
  2. Substitution method for linear and non-linear equations

Quadratics

Quadratic Equations

  1. Solve by factorising
  2. Solve by completing the square
  3. Solve by the quadratic formula

Quadratic Graphs

  1. Sketching quadratic graphs

Inequalities

Inequalities

  1. Linear inequalities
  2. Rules for reversing the inequality sign
  3. Solving a linear type
  4. Solving a double inequality
  5. Shading regions for a linear inequality
  6. Quadratic inequalities

Graph Transformations

Graph Transformations

  1. Basic graphs used in transformations
  2. Translations of graphs
  3. Reflections of graphs

Rational Expressions

Rational Expressions

  1. Simplifying algebraic fractions
  2. Addition and subtraction of algebraic fractions
  3. Multiplication of algebraic fractions
  4. Division of algebraic fractions

Sequences and Series

Working with Sequences and Series

  1. Definition and finding the nth term
  2. Recurrence relationships

Coordinate Geometry 1

Lines

  1. Equation of a straight line: y=mx+c
  2. Equation of a line given the gradient and point
  3. Distance between two points
  4. Mid-point of a line segment
  5. Equation of a parallel line

Intersection of Graphs

  1. Intersection of two straight lines

Trigonometry

Pythagoras’ Theorem

  1. Pythagoras' theorem

Trigonometry: Right-Angled Triangles

  1. Introduction to trigonometry
  2. Finding the length of a side
  3. Finding an angle

Trigonometric Ratios

  1. Trigonometric ratios for 30°, 45° and 60°
  2. Trig ratios for multiples of 30°, 45° and 60°

Trigonometry: Non Right-Angled Triangles

  1. Area of a triangle - Given two sides and an included angle
  2. Sine rule
  3. Cosine rule
  4. Bearings - Applications of the sine and cosine rules

Trigonometry: Graphs

  1. Trigonometric graphs
  2. Translations of trig graphs
  3. Reflections of trig graphs

Shapes

Sectors: area and arc length

  1. Area and arc length

Vectors

Vectors

  1. What is a vector and a scalar quantity?
  2. Vector notation 2d
  3. Position vectors 2d
  4. Equal and negative vectors
  5. Multiplying a vector by a scalar 2d
  6. Addition and subtraction of vectors 2d
  7. Magnitude of a 2 dimensional vector

Probability

Possibility Space (Sample Space)

  1. Possibility space diagrams

Tree Diagrams

  1. Probability tree diagrams
  2. Combining probabilities
  3. Conditional probability in tree diagrams

Statistics

Mean

  1. Mean for discrete data
  2. Calculating the mean from a frequency table

Median and Quartiles

  1. Median, lower, upper quartiles and interquartile range for discrete data
  2. Cumulative frequency curves
  3. Estimating the median, quartiles, percentiles from a grouped frequency table

Statistical diagrams

  1. Stem and leaf diagrams
  2. Box and whisker plots
  3. Histograms

About GCSE Maths

GCSE maths has a grading system that uses numbers 1-9 to identify levels of performance with 9 being the top level. A student will either enter for the Higher tier covering grades 4-9 or for the Foundation tier covering grades 1-5.

There will be three papers at each tier, two papers where candidates can use a calculator and a third paper where calculators are not to be used.

The syllabus is divided into six sections that test

1. Number

2. Algebra

3. Ratio, proportion and rates of change

4. Geometry and measure

5. Probability

6. Statistics

The main examination boards are Edexcel, AQA and OCR.

On this site you will find plenty of video tutorials which hopefully will give you the confidence and support you need to tackle your maths GCSE.