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

Surds

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

Functions

• Functions - notation

Factorising (1)

• Introduction
• HCF types
• Grouping types

Quadratics

• Factorising
• Completing the square
  • Sketching graphs
  • Solving 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
• Roots and Discriminant
  • Exam questions
• Quadratic graphs (still to be completed)

Polynomials

• Polynomials (still to be completed)

Graphs

• More graphs
• Transformations of graphs
  • 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

• Simultaneous equations
  • linear type
  • linear - quadratic type
  • Exam Questions

Inequalities

• Linear inequalities
  • introduction
  • rules for reversing sign
  • solving
  • Exam Questions
• Quadratic inequalities

Exam Questions

Sequences and series

• Recurrence relationships
• Sigma notation
• Arithmetic sequences and series
  • Exam Questions

Coordinate geometry

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
• Equation of a perpendicular bisector

Intersection of graphs

• Two straight lines
• Curve and line / two curves

Exam questions

Differentiation

• The gradient function dy/dx
  • Differentiation from 1st principles
• axⁿ type
• Tangents and normals

Exam Questions

• The second derivative
• Stationary points, Maximum and Minimum
• Applications
• Increasing and decreasing functions

Integration

• axⁿ type
• Finding the constant of integration

Exam Questions