IGCSE math video link

Number

Percentages

• What is a percentage?
• Finding a percentage of a quantity
• more to follow shortly ....

Indices

• Introduction
• Multiplication rule 1
• Multiplication rule 2
• Division
• Negative indices
• Fractions raised to a negative index
• Rational (fractional) indices
• Simplifying (negative powers)
• Expressing terms in the form axⁿ
• Equations in which the power has to be found

Standard Form (Scientific notation)

• Expressing a number in standard form or scientific form

Surds

• Simplifying
• Addition and subtraction
• Multiplication
• Division
• Rationalising

Algebra

Expanding brackets

• Expanding a single bracket
• A quick way to square a bracket

Solving Equations (Linear type)

• Before you start - What is a term?
• Linear equations with a positive x-term
• Linear equations with a negative x-term
• Equations with two x terms and 2 constants
• Equations with brackets
• Fractional equations (1)
• Fractional equations (2)
• Fractional equations (3)
• Fractional equations (4)
• Fractional equations (5)

Functions

• Functions - notation

Factorising

• Introduction
• HCF types
• Grouping types
  • Quadratic expressions
    • Introduction
    • HCF (Highest Common Factor) types
    • Difference of two squares type
    • Trinomials : (grouping method)
    • Trinomials : (inspection method) 1 | 2 | 3 | 4 | 5 | 6 | 7
• Miscellaneous Exercise
  • Exercise

Completing the Square

• How to do it
• Applications
  • Sketching graphs

Quadratic Equations

• Equations
  • Solve by factorising
  • Solve by completing the square
  • Solve by the quadratic formula

Quadratic Graphs

• Sketching quadratic graphs

Graph Transformations

• Basic graphs used in transformations
  • Translations y = f(x ± a ) and y= f(x) ± a
  • Reflections y = - f(x) and y = f(-x)
  • Stretches y = a f(x) and y = f(ax)

Simultaneous Equations

• Elimination method for linear types
  • Elimination method for linear equations
• Substitution Method for linear and non linear types
  • Substitution method

Inequalities

• Linear inequalities
  • introduction
  • rules for reversing the inequality sign
  • solving a linear type
  • solving a double inequality

Rational expressions

• Simplifying
• Addition and subtraction
• Multiplication
• Division

The straight line

• Gradient
  • Line segment
  • Parallel lines
  • Perpendicular lines
• Lines
  • Equation of a line
  • Distance between two points
  • Mid-point of a line segment
  • Equation of a parallel line

Intersection of graphs

• Two straight lines
• Curve and line / two curves

Geometry

Pythagoras' Theorem

• The theorem

Trigonometry

• Right-Angled Triangles
  • Naming the sides
  • Trig ratios sinθ, cosθ and tanθ
  • Finding a length (1)
  • Finding a length (2)
  • Finding an angle
• Non Right-Angled Triangles
  • Area of a triangle given two sides and an included angle
  • Sine rule
  • Cosine rule
• Graphs
  • Trigonometric graphs
  • Transformations of trig graphs
  • Translations
  • Reflections

Sectors: area and arc length

• area and arc length

Vectors

• What is a vector and a scalar quantity?
• Notation
• Position vectors
• Equal and negative vectors
• Addition and subtraction of vectors
  • example 1
  • example 2
• Magnitude of a 2 dimensional vector

Statistics

Mean

• Mean for discrete data
• Calculating the mean from a frequency table

Median and Quartiles

• Median, lower, upper quartiles and interquartile range for discrete data
• Cumulative frequency curves
• Estimating the median from a grouped frequency table

Statistical diagrams

• Stem and leaf diagrams
• Box and whisker plots
• Histograms

Probability

Possibility Space (sample space)

• Possibility space diagrams

Tree diagrams

• Probability tree diagrams
  • Combining probabilities
    • Examples

Differentiation (IGCSE) only

• terms of the form axⁿ