Algebra and Functions

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)

Algebraic Long Division

• Algebraic long division
  • missing terms
  • finding the remainder

Factor Theorem

• The factor theorem
  • showing that x-1 is a factor of a cubic polynomial
  • factorising a cubic polynomial
  • solving a cubic equation
  • finding constants in a polynomial given the factors

Remainder Theorem

• The remainder theorem
  • finding the remainder when a cubic polynomial is divided by x+1
  • finding the remainder when a quartic polynomial is divided by 2x-1
  • finding constants in a polynomial given the remainders

• Exam questions on the Factor and Remainder theorems

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

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

• Exam questions

Circles

• Equation
• Finding the centre and radius
• Equation of a tangent
• Equation of a circle through 3 points
• Circle properties
• Exam Questions on Circles

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

• Definite integration
• Infinite integrals
• Area under a curve