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
• 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,÷, 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

Final Exams