All Further Pure Mathematics papers

Edexcel · International GCSE · Further Pure Mathematics

May/June 2023 — Paper 2 · Replacement.

30 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

  • Simple inequalities, linear and quadratic
  • Unit vector
  • The roots of a quadratic equation
  • The distance between two points
  • Maxima and minima
  • Graphs of polynomials and rational functions with linear denominators
  • Magnitude of a vector
  • Applications to simple linear kinematics and to determination of areas and volumes
  • The straight line and its equation
  • The equations of tangents and normals to the curve $y = f(x)$
  • Simple examples involving functions of the roots of a quadratic equation
  • Use and properties of indices and logarithms, including change of base
  • The use of the basic addition formulae of trigonometry
  • Solution of simple trigonometric equations for a given interval
  • The condition for two lines to be parallel or to be perpendicular
  • Radian measure, including use for arc length and area of sector

Questions in this paper

  • Q1The roots of a quadratic equation4 marks
  • Q2cSimple inequalities, linear and quadratic1 marks
  • Q2bSimple inequalities, linear and quadratic3 marks
  • Q2aSimple inequalities, linear and quadratic2 marks
  • Q3bMaxima and minima5 marks
  • Q3cMaxima and minima2 marks
  • Q3aRadian measure, including use for arc length and area of sector3 marksincludes a figure
  • Q4bUnit vector2 marks
  • Q4aMagnitude of a vector4 marks
  • Q5bApplications to simple linear kinematics and to determination of areas and volumes2 marks
  • Q5cApplications to simple linear kinematics and to determination of areas and volumes3 marks
  • Q5aApplications to simple linear kinematics and to determination of areas and volumes2 marks
  • Q6aSimple examples involving functions of the roots of a quadratic equation5 marks
  • Q6bSimple examples involving functions of the roots of a quadratic equation5 marks
  • Q7bApplications to simple linear kinematics and to determination of areas and volumes4 marksincludes a figure
  • Q7aSolution of simple trigonometric equations for a given interval3 marksincludes a figure
  • Q8eThe distance between two points4 marks
  • Q8dThe straight line and its equation3 marks
  • Q8cThe straight line and its equation1 marks
  • Q8aThe straight line and its equation3 marks
  • Q8bThe condition for two lines to be parallel or to be perpendicular5 marks
  • Q9aGraphs of polynomials and rational functions with linear denominators2 marks
  • Q9cGraphs of polynomials and rational functions with linear denominators3 marks
  • Q9eThe equations of tangents and normals to the curve $y = f(x)$5 marks
  • Q9bGraphs of polynomials and rational functions with linear denominators2 marks
  • Q9dThe equations of tangents and normals to the curve $y = f(x)$3 marks
  • Q10Use and properties of indices and logarithms, including change of base7 marks
  • Q11bThe use of the basic addition formulae of trigonometry5 marks
  • Q11aThe use of the basic addition formulae of trigonometry3 marks
  • Q11cSolution of simple trigonometric equations for a given interval4 marks

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