# A level Compulsory Further Pure Revision day

Oxford## Overview

**This revision day covers A level Further Compulsory Pure topics which are common to all specifications, and taught in the second year of a two year course.**

## Who will benefit from attending?

Students of A level Further Maths either in year 12 who are taking a one year A level course or in year 13 who want to recap the Common Pure content of the second year of their course.

## Content

**COMPLEX NUMBERS**- De Moivre’s theorem
- = and the form
- Find the n distinct n
^{th}roots of for and know that they form the vertices of a regular n-gon in the Argand diagram - Use complex roots of unity to solve geometric problems
**MATRICES**- Calculate determinants of 3x3 matrices and interpret as scale factors, including the effect on orientation
- Calculate and use the inverse of non-singular 3x3 matrices
- Solve three linear simultaneous equations in three variables by use of the inverse matrix
- Interpret geometrically the solution and failure of solution of three simultaneous linear equations
**FURTHER ALGEBRA AND FUNCTIONS**- formulae for the sums of integers, squares and cubes and use these to sum other series
- The method of differences including partial fractions
- Maclaurin series of a function including the general term
- Maclaurin series for , ln(1+x), sin x, cos x and (1+x)
^{n}and the range of values of x for which they are valid **FURTHER CALCULUS**- Evaluate improper integrals where either the integrand is undefined or the range extends to ∞
- Derive formulae for and calculate volumes of revolution
- Understand and evaluate the mean value of a function
- Integrate using partial fractions
- Differentiate inverse trig functions
- Integrate functions of the form (a
^{2}-x^{2})^{-}^{½}and (a^{2}+x^{2})^{-1}and be able to choose trig substitutions to integrate associated functions **FURTHER VECTORS**- Vector and Cartesian forms of an equation of a straight line in 3D and of a plane
- The dot product and the equation of a plane, and to calculate angles between lines and planes
- Check perpendicular vectors using the dot product
- Find the intersection of a line and a plane and calculate perpendicular distances
**POLAR COORDINATES**- Convert between polar and Cartesian coordinates
- Sketch curves with r as a function of θ, including the use of trig functions
- Find the area enclosed by a polar curve
**HYPERBOLIC FUNCTIONS**- Definitions and graphs of sinh x, cosh x, and tanh x
- Differentiate and integrate hyperbolic functions
- Inverse hyperbolic functions
- Derive and use the logarithmic forms of the hyperbolic functions
- Integrate functions of the form (x
^{2}+a^{2})^{-}^{½}and (x^{2}-a^{2})^{-}^{½}and choose substitutions to integrate associated functions **DIFFERENTIAL FUNCTIONS**- Use an integrating factor
- Find both general and particular solutions to differential equations
- Use differential equations in modelling
- Solve differential equations of the form y
^{’’}+ay^{’}+by=0 or =f(x) - Solve the equation for simple harmonic motion and relate the solution to the motion
- Model damped oscillations using 2
^{nd}order differential equations and interpret their solutions - Analyse and interpret models of situations eg predator-prey models

## Materials and Equipment

You will need to bring pens, paper, and your calculator.

## Other Information

You should bring your own lunch but light refreshments will be available in the morning and afternoon breaks.

**If you want to attend both this revision day and the one on Saturday 4th April than the cost is £40 for both. Please indicate when you apply.**

## Key Facts

##### Event ref:

#7116

##### Audience:

Students

##### Target year:

Year 12 & 13

##### Curriculum focus:

A level Further Mathematics

##### Mathematical focus:

Pure

##### Event format:

Student course

##### Event length:

1 day

##### Region:

South

##### Venue:

The Mathematical Institute, University of Oxford,

Andrew Wiles Building, Radcliffe Observatory Quarter,

Woodstock Road,

Oxford,

Oxfordshire,

OX2 6GG

##### Date:

Sat 18th Apr 2020

##### Course times:

09:00 - 17:00

##### Fee:

£25

### Queries?

If you have any queries about this event, please do not hesitate to contact:

Lesley Swarbrick

[email protected]

07884 183181