202021 As Furthermath Jyothi
This class meets 5 times a week and will cover Pure Math 1 and 3 for the Alevel.
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)
Table of Contents

June
Review and some pending material from Pure Math 1
(One week or 5 classes)
 Functions review, dealing with translations, $f(x)$ vs $f(x)$
 Coordinate 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