Further Pure
Mathematics with
Technology
(FPT)
Tom Button
tom.button@mei.org.uk
Further Pure with Technology (FPT)
FPT is an optional A2 Further Pure unit that can be studied
as one of 12 (or 15) mathematics units.
FPT has been developed with the full support of OCR and
Texas Instruments. MEI is very grateful for this support.
FPT will inform MEI’s approaches to the use of technology in
future developments of A level.
FPT has been approved by Ofqual. The first examination
was on Monday 24th June 2013.
FPT: Use of the technology
Students are expected to have access to
software for the teaching, learning and
assessment that features:
• Graph-plotter
• Spreadsheet
• Computer Algebra System (CAS)
• Programming Language
The expectation has been that students
have used TI-Nspire software and
teaching resources have been created to
support this.
FPT: Technology in Pure Maths
Criteria for inclusion of mathematical topics:
• Technology allows you to access a large
number of results quickly
• Be able to make inferences and
deductions based on these
• Not included elsewhere in A level Maths
or Further Maths
x = t − k sin t, y = 1 − cos t
FPT: Content
• Investigations of
Curves
Investigate the curves for 0 < k < 1.
Describe the common features of these
curves and sketch a typical example.
• Functions of Complex
Variables
• Number Theory
f ( z )  z 3  (3  3i) z 2  6iz  2  i
Solve f(z) = 0.
Show that f’(z) = 0 has a repeated
root.
Create a program to find all the
positive integer solutions to
x² − 3y² = 1 with x<100, y<100.
FPT: Assessment
A timed written paper that
assumes that students have
access to the technology.
For the examination each
student will need access to a
computer with the software
installed and no communication
ability.
FPT: Engagement with schools
We have worked with 10 schools/colleges and expect
around 30-40 students have studied the unit this year.
We have worked with the teachers to support their
development and produce effective teaching and learning
resources.
The resources will be available on Integral from
September.
x = t − k sin t, y = 1 − cos t
Investigate the curves for 0 < k < 1.
Describe the common features of
these curves and sketch a typical
example.
2
f ( z )  z  (3  3i) z  6iz  2  i
Solve f(z) = 0 and plot the roots
on an Argand diagram.
Show that f’(z) = 0 has a
repeated root.
3
Create a program to find all the
positive integer solutions to
x² − 3y² = 1 with x<100, y<100.
Investigate r  a cos  b sin
dr
sin   r cos
dy d

Use
dx dr cos  r sin 
d
to describe the tangent as you move round the
curve.
f ( z) 
1
z
Use a spreadsheet to investigate f(z) as z
moves along the line z  1  ai, a  ¡
Prime pairs are integers n – 1 and n +1
that are prime. Write a program to find all
the prime pairs less than a maximum
integer, m.
List all the prime pairs less than 200.
FPT: Further Information
•
Updates on the MEI website: www.mei.org.uk/fpt
•
Specification and specimen papers on the MEI website:
www.mei.org.uk/fpt
•
Teaching and learning resources: www.integralmaths.org
•
TI-Nspire: www.nspiringlearning.org.uk/
•
Project Euler: projecteuler.net/
tom.button@mei.org.uk