← Further Maths syllabus

EnglandFurther Maths

Further Pure options

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

How are the conic sections defined, and how do you work with their tangents, normals and parametric forms?

The parabola, ellipse and hyperbola in Cartesian and parametric form, foci and directrices, tangents and normals, and the rectangular hyperbola.
A focused answer to the Edexcel A-Level Further Mathematics Further Pure coordinate systems content, covering the parabola, ellipse and hyperbola in Cartesian and parametric form, foci and directrices, tangents and normals to conics, and the rectangular hyperbola.
12 min answer →

How do you approximate roots and integrals numerically when no exact method works?

Solving equations numerically by interval bisection, linear interpolation and the Newton-Raphson method, and approximating definite integrals using Simpson's rule and the mid-ordinate rule.
A focused answer to the Edexcel A-Level Further Mathematics Further Pure numerical methods content, covering solving equations by interval bisection, linear interpolation and the Newton-Raphson method, and approximating definite integrals using Simpson's rule and the mid-ordinate rule.
12 min answer →

How do you sum trigonometric series and work with the t-substitution and inverse trig functions?

The t-substitution for trigonometric integrals and equations, summing series of sines and cosines, the general solution of trigonometric equations, and inverse trigonometric functions.
A focused answer to the Edexcel A-Level Further Mathematics Further Pure further trigonometry content, covering the t-substitution for trigonometric integrals and equations, summing finite series of sines and cosines, finding general solutions of trigonometric equations, and working with the inverse trigonometric functions.
12 min answer →

How do you build power series approximations of functions and use them to solve differential equations?

Maclaurin and Taylor series of standard functions, finding series solutions of differential equations, and using series to approximate functions and limits.
A focused answer to the Edexcel A-Level Further Mathematics Further Pure series content, covering Maclaurin and Taylor series of standard functions, finding series solutions of differential equations, and using power series to approximate functions and evaluate limits.
12 min answer →