All Further Pure Mathematics papers

Edexcel · International GCSE · Further Pure Mathematics

October/November 2020 — Paper 1.

31 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

  • Differentiation of a product, quotient and simple cases of a function of a function
  • The distance between two points
  • The equations of tangents and normals to the curve $y = f(x)$
  • Arithmetic and geometric series
  • Use of the sine and cosine formulae
  • The manipulation of quadratic expressions
  • The use of the basic addition formulae of trigonometry
  • Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)
  • The solution of equations and transcendental functions by graphical methods
  • Application of calculus to rates of change and connected rates of change
  • Rectangular Cartesian coordinates
  • Radian measure, including use for arc length and area of sector
  • Trigonometry
  • The condition for two lines to be parallel or to be perpendicular
  • The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar
  • The graphical representation of linear inequalities in two variables
  • Use of vectors to establish simple properties of geometrical figures
  • Applications to simple linear kinematics and to determination of areas and volumes
  • Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables

Questions in this paper

  • Q1Differentiation of a product, quotient and simple cases of a function of a function3 marks
  • Q2aThe graphical representation of linear inequalities in two variables3 marksincludes a figure
  • Q2bThe graphical representation of linear inequalities in two variables1 marksincludes a figure
  • Q3cApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
  • Q3bApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
  • Q3aApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
  • Q4aThe solution of equations and transcendental functions by graphical methods3 marksincludes a figure
  • Q4bThe solution of equations and transcendental functions by graphical methods4 marksincludes a figure
  • Q5bThe distance between two points2 marks
  • Q5cRectangular Cartesian coordinates2 marks
  • Q5aThe condition for two lines to be parallel or to be perpendicular3 marks
  • Q6bArithmetic and geometric series2 marks
  • Q6cArithmetic and geometric series4 marks
  • Q6aArithmetic and geometric series4 marks
  • Q7aThe manipulation of quadratic expressions2 marks
  • Q7bThe manipulation of quadratic expressions2 marks
  • Q7dApplications to simple linear kinematics and to determination of areas and volumes5 marks
  • Q7cSolutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables4 marks
  • Q8aDifferentiation of a product, quotient and simple cases of a function of a function5 marks
  • Q8bDifferentiation of a product, quotient and simple cases of a function of a function2 marks
  • Q8cThe equations of tangents and normals to the curve $y = f(x)$3 marks
  • Q9aUse of the sine and cosine formulae2 marksincludes a figure
  • Q9cThe use of the basic addition formulae of trigonometry4 marksincludes a figure
  • Q9bUse of the sine and cosine formulae4 marksincludes a figure
  • Q9dTrigonometry2 marksincludes a figure
  • Q10bApplication of calculus to rates of change and connected rates of change3 marks
  • Q10aRadian measure, including use for arc length and area of sector4 marksincludes a figure
  • Q10cApplication of calculus to rates of change and connected rates of change5 marks
  • Q11aThe addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar5 marksincludes a figure
  • Q11cUse of vectors to establish simple properties of geometrical figures4 marksincludes a figure
  • Q11bUse of vectors to establish simple properties of geometrical figures4 marksincludes a figure

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