# 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 nth 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 (a2-x2)-½ and (a2+x2)-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 (x2+a2)-½ and (x2-a2)-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 2nd 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

#7116

Students

Year 12 & 13

##### Curriculum focus:

A level Further Mathematics

Pure

Student course

1 day

South

##### Venue:

The Mathematical Institute, University of Oxford,
Andrew Wiles Building, Radcliffe Observatory Quarter,
Oxford,
Oxfordshire,
OX2 6GG

##### Date:

Sat 18th Apr 2020

09:00 - 17:00

##### Fee:

£25

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