Algebra and Functions

Indices

• Introduction
• Multiplication rule 1
• Multiplication rule 2
• Division
• Negative indices
• Fractions to negative indices
• Fractional type
• Simplifying (negative powers)
• Expressing terms in the form axⁿ
• Exam questions

Surds

• multiplication rule
• combining and simplifying
• division rule
• rationalising
• surds on a calculator
• Exam questions

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
• Exam questions

Completing the Square

• How to do it
  • Various other types : 1 | 2 | 3
  • Applications
    • Sketching graphs
• Exam questions

Quadratic Equations

• Equations
  • Solve by factorising
  • Solve by completing the square
  • Solve by formula
  • Proof of quadratic formula
  • Extension - Solving in some function of x

Quadratic Graphs

• Sketching quadratic graphs

Polynomials

• Polynomials

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)
  • Stretches y = f (ax)
  • Exam questions

Simultaneous Equations

• Elimination method for linear types
  • Examples :
    • 1 | 2 | 3 | 4 | 5 (method 1) | 5 (method 2)
• Substitution Method for linear and quadratic types
  • Examples :
    • 1 | 2
• Exam Questions

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 and Division (still to do)

Fractional Equations

• Solving fractional equations (still to do)

Coordinate geometry

Gradient

• Line segment
• Parallel lines
• Perpendicular lines

Lines

• Equation of a line
• Equation of a parallel line

Intersection of graphs

• Two straight lines
• Curve and line / two curves

Trigonometry

Right-Angled Triangles

• Naming the sides
• Trig ratios sinθ, cosθ and tanθ
• Finding a length (1)
• Finding a length (2)
• Finding an angle

Graphs

• Trigonometric graphs
• Transformations of trig graphs
  • Translations
  • Reflections

Non Right-Angled Triangles

• Area of a triangle given two sides and an included angle
• Sine rule
• Cosine rule

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