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

Review and some pending material from Pure Math 1

(One week or 5 classes)

  • Functions review, dealing with translations, $f(|x|)$ vs $|f(x)|$
  • Co-ordinate geometry

Algebra

(Chapter 1, Chapter 7 one week.)
We have seen most of this in Additional Mathematics. The main things we will focus on are:

  • More on the modulus function
  • Dealing with up to 4th degree polynomials (factorisation with remainder)
  • Partial fractions

Logarithmic and exponential functions

(Chapter 2, 2 classes)

  • Some review
  • What is $e$?

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

Differentiation

(Chapter 4, 3 weeks)

  • Review
  • Formal introduction to the idea of limits
  • Differentiation of parametric and implicit functions
  • Differentiation of trigonometric functions (including compound angle and inverse functions)

Numerical solutions of equations

(Chapter 6, one week)

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

August

Integration

(Chapter 5, three weeks)

  • Volume of revolution
  • Integration of trigonometric functions (including compound angle)
  • Integration by substitution
  • Integration by parts
  • Integration using partial fractions

Differential equations

(Chapter 10, 8 classes)

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

(First term exam portion ends here)

October

Vectors

(Chapter 9, 8 classes; ideally find time in September for this)

  • Review and problems
  • Scalar product of two vectors

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

From October 18th will use all 8 class periods for stat 2

December

Solve old papers

January

Revision and some timed tests

Mock exam

February

Final Exams

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