Edexcel · International GCSE · Further Pure Mathematics

January 2020 — Paper 2 · Replacement.

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

Simple examples involving functions of the roots of a quadratic equation
Arithmetic and geometric series
Applications to simple linear kinematics and to determination of areas and volumes
Radian measure, including use for arc length and area of sector
Use of the binomial series $(1 + x)^n$
Differentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$
The straight line and its equation
The use of the basic addition formulae of trigonometry
The graphical representation of linear inequalities in two variables
Solution of simple trigonometric equations for a given interval
Graphs of polynomials and rational functions with linear denominators
Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)
Use of the sine and cosine formulae
Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables
Application of calculus to rates of change and connected rates of change

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
Q2aThe straight line and its equation3 marksincludes a figure
Q2bThe graphical representation of linear inequalities in two variables3 marksincludes a figure
Q3Use of the sine and cosine formulae5 marks
Q4bApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q4cApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q4aApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q5cSimple examples involving functions of the roots of a quadratic equation2 marks
Q5aSimple examples involving functions of the roots of a quadratic equation2 marks
Q5bSimple examples involving functions of the roots of a quadratic equation2 marks
Q5dSimple examples involving functions of the roots of a quadratic equation6 marks
Q6aApplication of calculus to rates of change and connected rates of change2 marksincludes a figure
Q6bApplication of calculus to rates of change and connected rates of change4 marksincludes a figure
Q7dArithmetic and geometric series4 marks
Q7aArithmetic and geometric series3 marks
Q7bArithmetic and geometric series3 marks
Q7cArithmetic and geometric series3 marks
Q8aThe use of the basic addition formulae of trigonometry1 marks
Q8bThe use of the basic addition formulae of trigonometry3 marks
Q8cSolution of simple trigonometric equations for a given interval6 marks
Q9dUse of the binomial series $(1 + x)^n$2 marks
Q9aUse of the binomial series $(1 + x)^n$2 marks
Q9cUse of the binomial series $(1 + x)^n$3 marks
Q9bUse of the binomial series $(1 + x)^n$3 marks
Q10bApplications to simple linear kinematics and to determination of areas and volumes6 marks
Q10aDifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$6 marks
Q11cGraphs of polynomials and rational functions with linear denominators3 marks
Q11dSolutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables7 marks
Q11bGraphs of polynomials and rational functions with linear denominators2 marks
Q11aGraphs of polynomials and rational functions with linear denominators2 marks

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