Edexcel · International GCSE · Further Pure Mathematics

October/November 2023 — Paper 1.

26 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
Use of the binomial series $(1 + x)^n$
The manipulation of quadratic expressions
Applications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)
Differentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$
The factor and remainder theorems
Arithmetic and geometric series
Use of the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$
The condition for two lines to be parallel or to be perpendicular
Solution of simple trigonometric equations for a given interval
Use and properties of indices and logarithms, including change of base
Applications to simple linear kinematics and to determination of areas and volumes
The straight line and its equation
The use of the basic addition formulae of trigonometry
Simple manipulation of surds
Application of calculus to rates of change and connected rates of change

Questions in this paper

Q1Simple manipulation of surds4 marksincludes a figure
Q2bThe manipulation of quadratic expressions2 marks
Q2cThe manipulation of quadratic expressions2 marks
Q2aThe manipulation of quadratic expressions3 marks
Q3aDifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$5 marks
Q3bThe factor and remainder theorems3 marks
Q4bThe condition for two lines to be parallel or to be perpendicular6 marks
Q4aThe straight line and its equation3 marks
Q5Applications to simple linear kinematics and to determination of areas and volumes8 marksincludes a figure
Q6dApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q6cApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q6aApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)3 marksincludes a figure
Q6bApplications to simple problems in two or three dimensions (including angles between a line and a plane and between two planes)2 marksincludes a figure
Q7aArithmetic and geometric series2 marks
Q7bArithmetic and geometric series2 marks
Q7cArithmetic and geometric series5 marks
Q8aDifferentiation of a product, quotient and simple cases of a function of a function5 marks
Q8bApplication of calculus to rates of change and connected rates of change3 marks
Q9aUse of the binomial series $(1 + x)^n$3 marks
Q9bUse of the binomial series $(1 + x)^n$4 marks
Q9cDifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$4 marks
Q10bUse of the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$4 marks
Q10cSolution of simple trigonometric equations for a given interval6 marks
Q10dDifferentiation and integration of sums of multiples of powers of $x$ (excluding integration of $\frac{1}{x}$), $\sin ax$, $\cos ax$, $e^{ax}$4 marks
Q10aThe use of the basic addition formulae of trigonometry3 marks
Q11Use and properties of indices and logarithms, including change of base8 marks

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