← Further Maths syllabus

EnglandFurther Maths

Core Pure: further calculus

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve first and second order differential equations, and how do they model simple harmonic motion and damping?

First order linear differential equations by the integrating factor, second order linear constant-coefficient equations via the auxiliary equation and particular integral, and applications to simple harmonic motion and damped systems.
A focused answer to the OCR A-Level Further Mathematics A content on differential equations, covering first order linear equations by the integrating factor, second order constant-coefficient equations via the auxiliary equation and a particular integral, and applications to simple harmonic motion and damped systems.
12 min answer →

How do you evaluate an integral with an infinite limit or an unbounded integrand, and how do you decide whether it converges?

Improper integrals with an infinite limit of integration or an integrand that is unbounded at an endpoint, evaluated as a limit, and deciding whether such an integral converges or diverges.
A focused answer to the OCR A-Level Further Mathematics A content on improper integrals, covering integrals with an infinite limit of integration and integrals whose integrand is unbounded at an endpoint, evaluating each as a limit of a proper integral, and deciding whether the integral converges to a finite value or diverges.
11 min answer →

How do you build the Maclaurin series of a function, and how is it used to approximate functions?

The Maclaurin series of a function, the standard series for e^x, ln(1+x), sin x and cos x, finding a series by repeated differentiation or by combining known series, and using a truncated series to approximate values.
A focused answer to the OCR A-Level Further Mathematics A content on the Maclaurin series, covering the general formula, the standard series for e^x, ln(1+x), sin x and cos x, finding a series by repeated differentiation or by substituting into and combining known series, and using a truncated series to approximate function values.
11 min answer →

How do you find the volume generated when a region is rotated about an axis?

Volumes of revolution about the x-axis and y-axis, volumes generated by the region between two curves, and parametric and improper cases, using integration of pi y squared or pi x squared.
A focused answer to the OCR A-Level Further Mathematics A content on volumes of revolution, covering the formulae for rotation about the x-axis and the y-axis, the volume of the solid between two curves, and parametric and improper variants, all using integration of pi y squared or pi x squared.
11 min answer →