202021 As Furthermath Jyothi

This class meets 5 times a week and will cover Pure Math 1 and 3 for the A-level.

The textbook is Pure Mathematics 2 & 3 by Sue Pemberton and Julianne Hughes published by the Cambridge University Press.

(Reference will also be made to Pure Mathematics 1 by Sue Pemberton)

June

Some pending material from Pure Math 1 Ch. 1-5

  • Functions
  • Quadratics
  • Co-ordinate geometry
  • Circular measure and trigonometry
  • Trigonometry

Trigonometry

(Chapter 3, two weeks)
We have seen most of this in Additional Mathematics. The main things we will focus on are:

  • Inverse functions
  • Trigonometric ratios of sums ('compound angle formulae'): $\sin(a+b)$ etc
  • 'Double angle formulae': $\sin(2a)$ etc

July

Vectors

(Chapter 9, two weeks)

  • Review and problems
  • Scalar product of two vectors

Series

(one week. A quick review from PM1 Chapter 6)

Permutations and Combinations

(one week. Review from Stat 1 Chapter 5)

August

Numerical solutions of equations

(Chapter 6, one week)

  • Using graphs
  • Iterative solutions and ideas of convergence
  • Application and some problems

Complex Numbers

(Chapter 11, two weeks)

  • What is a complex number and why are they useful?Cartesian vs polar form
  • What are the 'real' and 'imaginary' parts? Representation on an 'Argand' diagram
  • Operations on complex numbers in cartesian form (+,-,x,รท, conjugation) and their geometric interpretation
  • Square roots of a complex number

September

Differentiation

(Chapter 4, three weeks)

  • Review from PM1. Chapters 7 & 8
  • Formal introduction to the idea of limits
  • Differentiation of parametric and implicit functions
  • Differentiation of trigonometric functions (including compound angle and inverse functions)

Further Algebra

(Chapter 7, two weeks)

  • Partial fractions
  • Binomial expansions with non-+ve-integer powers

October

Integration

(Chapter 5, three weeks)

  • Volume of revolution
  • Integration of trigonometric functions (including compound angle)

Further Calculus

(Chapter 8, two weeks)

  • Integration by substitution
  • Integration by parts
  • Integration using partial fractions

November

Differential equations

(Chapter 10, two weeks)

  • Repeated integration
  • Basic variable separable equations
  • Using initial conditions

December

Solve old papers

January

Revision and some timed tests

Mock exam

February

Final Exams

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