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

# 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,÷, conjugation) and their geometric interpretation
• Square roots of a complex number

Final Exams