All Further Pure Mathematics papers

Edexcel · International GCSE · Further Pure Mathematics

May/June 2019 — Paper 1 · Replacement.

32 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
  • Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables
  • The solution of equations and transcendental functions by graphical methods
  • Maxima and minima
  • The manipulation of quadratic expressions
  • The straight line and its equation
  • Radian measure, including use for arc length and area of sector
  • The distance between two points
  • Use of the sine and cosine formulae
  • Use of vectors to establish simple properties of geometrical figures
  • The condition for two lines to be parallel or to be perpendicular
  • Application of calculus to rates of change and connected rates of change
  • The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar
  • The equations of tangents and normals to the curve $y = f(x)$
  • Use and properties of indices and logarithms, including change of base
  • Differentiation of a product, quotient and simple cases of a function of a function
  • The point dividing a line in a given ratio
  • Unit vector
  • Applications to simple linear kinematics and to determination of areas and volumes
  • Use of the $\sum$ notation

Questions in this paper

  • Q1aRadian measure, including use for arc length and area of sector1 marksincludes a figure
  • Q1bRadian measure, including use for arc length and area of sector2 marksincludes a figure
  • Q2aUse of the sine and cosine formulae4 marksincludes a figure
  • Q2bUse of the sine and cosine formulae2 marksincludes a figure
  • Q3bUse and properties of indices and logarithms, including change of base6 marks
  • Q3aUse and properties of indices and logarithms, including change of base1 marks
  • Q4bThe equations of tangents and normals to the curve $y = f(x)$6 marks
  • Q4aDifferentiation of a product, quotient and simple cases of a function of a function4 marks
  • Q5Application of calculus to rates of change and connected rates of change5 marks
  • Q6bArithmetic and geometric series3 marks
  • Q6cArithmetic and geometric series4 marks
  • Q6aUse of the $\sum$ notation3 marks
  • Q7cUse of vectors to establish simple properties of geometrical figures4 marks
  • Q7aThe addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar2 marks
  • Q7bUnit vector2 marks
  • Q8cThe solution of equations and transcendental functions by graphical methods3 marks
  • Q8dThe solution of equations and transcendental functions by graphical methods4 marks
  • Q8aThe solution of equations and transcendental functions by graphical methods2 marks
  • Q8bThe solution of equations and transcendental functions by graphical methods2 marks
  • Q9bMaxima and minima5 marksincludes a figure
  • Q9cMaxima and minima1 marksincludes a figure
  • Q9aMaxima and minima4 marksincludes a figure
  • Q10cSolutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables4 marks
  • Q10b(ii)The manipulation of quadratic expressions1 marks
  • Q10aThe manipulation of quadratic expressions3 marks
  • Q10b(i)The manipulation of quadratic expressions1 marks
  • Q10dApplications to simple linear kinematics and to determination of areas and volumes4 marks
  • Q11aThe straight line and its equation2 marks
  • Q11eThe distance between two points4 marks
  • Q11dThe condition for two lines to be parallel or to be perpendicular3 marks
  • Q11cThe condition for two lines to be parallel or to be perpendicular6 marks
  • Q11bThe point dividing a line in a given ratio2 marks

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