All Further Pure Mathematics papers

Edexcel · International GCSE · Further Pure Mathematics

October/November 2024 — Paper 2.

29 structured questions · 100 marks

Download question paper (PDF)Mark scheme — for enrolled students

The mark scheme comes with the Further Pure Mathematics course.

Topics covered

  • Radian measure, including use for arc length and area of sector
  • Graphs of polynomials and rational functions with linear denominators
  • The factor and remainder theorems
  • The solution of equations and transcendental functions by graphical methods
  • Arithmetic and geometric series
  • Use of vectors to establish simple properties of geometrical figures
  • Use and properties of indices and logarithms, including change of base
  • Applications to simple linear kinematics and to determination of areas and volumes
  • Simple inequalities, linear and quadratic
  • The use of the basic addition formulae of trigonometry
  • The equations of tangents and normals to the curve $y = f(x)$
  • Differentiation of a product, quotient and simple cases of a function of a function
  • Application of calculus to rates of change and connected rates of change
  • Differentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$

Questions in this paper

  • Q1aRadian measure, including use for arc length and area of sector2 marksincludes a figure
  • Q1bRadian measure, including use for arc length and area of sector3 marksincludes a figure
  • Q2Simple inequalities, linear and quadratic6 marks
  • Q3Differentiation of a product, quotient and simple cases of a function of a function5 marks
  • Q4aThe solution of equations and transcendental functions by graphical methods2 marks
  • Q4cThe solution of equations and transcendental functions by graphical methods4 marks
  • Q4bThe solution of equations and transcendental functions by graphical methods2 marks
  • Q5Application of calculus to rates of change and connected rates of change5 marks
  • Q6iUse and properties of indices and logarithms, including change of base4 marks
  • Q6iiUse and properties of indices and logarithms, including change of base7 marks
  • Q7bThe factor and remainder theorems4 marks
  • Q7cArithmetic and geometric series3 marks
  • Q7eArithmetic and geometric series2 marks
  • Q7dArithmetic and geometric series1 marks
  • Q7fArithmetic and geometric series4 marks
  • Q7aThe factor and remainder theorems2 marks
  • Q8a(ii)Use of vectors to establish simple properties of geometrical figures2 marksincludes a figure
  • Q8bUse of vectors to establish simple properties of geometrical figures4 marksincludes a figure
  • Q8cUse of vectors to establish simple properties of geometrical figures5 marksincludes a figure
  • Q8a(i)Use of vectors to establish simple properties of geometrical figures1 marksincludes a figure
  • Q9cApplications to simple linear kinematics and to determination of areas and volumes8 marksincludes a figure
  • Q9aThe use of the basic addition formulae of trigonometry2 marks
  • Q9bDifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$4 marks
  • Q10b(i)Graphs of polynomials and rational functions with linear denominators1 marks
  • Q10cGraphs of polynomials and rational functions with linear denominators3 marks
  • Q10b(ii)Graphs of polynomials and rational functions with linear denominators1 marks
  • Q10a(i)Graphs of polynomials and rational functions with linear denominators1 marks
  • Q10a(ii)Graphs of polynomials and rational functions with linear denominators1 marks
  • Q10dThe equations of tangents and normals to the curve $y = f(x)$11 marks

Enrolled students get the full paper bank for Further Pure Mathematics. See the course