All Further Pure Mathematics papers

Edexcel · International GCSE · Further Pure Mathematics

May/June 2024 — Paper 1 · Replacement.

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

  • Arithmetic and geometric series
  • The use of the basic addition formulae of trigonometry
  • Use of vectors to establish simple properties of geometrical figures
  • The straight line and its equation
  • The point dividing a line in a given ratio
  • Applications to simple linear kinematics and to determination of areas and volumes
  • The condition for two lines to be parallel or to be perpendicular
  • The distance between two points
  • Simple inequalities, linear and quadratic
  • Simple examples involving functions of the roots of a quadratic equation
  • Radian measure, including use for arc length and area of sector
  • The functions $a^x$ and $\log_b x$ (where $b$ is a natural number greater than one)
  • Use and properties of indices and logarithms, including change of base
  • Use of the sine and cosine formulae
  • The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar
  • Use of the binomial series $(1 + x)^n$
  • Solution of simple trigonometric equations for a given interval
  • Rationalising the denominator

Questions in this paper

  • Q1Rationalising the denominator4 marks
  • Q2bUse of the binomial series $(1 + x)^n$2 marks
  • Q2aUse of the binomial series $(1 + x)^n$6 marks
  • Q3aUse of the sine and cosine formulae3 marksincludes a figure
  • Q3cUse of the sine and cosine formulae3 marksincludes a figure
  • Q3bUse of the sine and cosine formulae2 marksincludes a figure
  • Q4bSimple inequalities, linear and quadratic4 marksincludes a figure
  • Q4aRadian measure, including use for arc length and area of sector3 marksincludes a figure
  • Q4cRadian measure, including use for arc length and area of sector2 marksincludes a figure
  • Q5a(i)Arithmetic and geometric series3 marks
  • Q5a(ii)Arithmetic and geometric series2 marks
  • Q5bArithmetic and geometric series2 marks
  • Q5cArithmetic and geometric series4 marks
  • Q6aApplications to simple linear kinematics and to determination of areas and volumes2 marks
  • Q6bApplications to simple linear kinematics and to determination of areas and volumes4 marks
  • Q7aThe functions $a^x$ and $\log_b x$ (where $b$ is a natural number greater than one)4 marks
  • Q7bUse and properties of indices and logarithms, including change of base5 marks
  • Q8cUse of vectors to establish simple properties of geometrical figures4 marksincludes a figure
  • Q8bUse of vectors to establish simple properties of geometrical figures5 marksincludes a figure
  • Q8aThe addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar1 marksincludes a figure
  • Q9aThe straight line and its equation2 marks
  • Q9bThe point dividing a line in a given ratio2 marks
  • Q9cThe condition for two lines to be parallel or to be perpendicular6 marks
  • Q9dThe distance between two points2 marks
  • Q10aSimple examples involving functions of the roots of a quadratic equation8 marks
  • Q10bSimple examples involving functions of the roots of a quadratic equation4 marks
  • Q11aThe use of the basic addition formulae of trigonometry3 marks
  • Q11cApplications to simple linear kinematics and to determination of areas and volumes3 marksincludes a figure
  • Q11bSolution of simple trigonometric equations for a given interval5 marksincludes a figure

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