2. Further Pure Mathematics with Technology
(FPT)
Tom Button

3. 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 will be in June 2013.

4. 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 is that students will be using TI-Nspire software and teaching resources will be created to support this.

5. 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

6. FPT: Content Investigations of Curves Functions of Complex Variables
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.
FPT: Content
Investigations of Curves
Functions of Complex Variables
Number Theory
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.

7. 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.

8. FPT: Engagement with schools
We are working with 10 schools/colleges and expect around 50 students to take the unit in the first year.
We are working with the teachers to support their development and produce effective teaching and learning resources.
We are also interested in whether engagement with this unit will have a positive impact on teachers’ use of technology in other areas of mathematics.

9. 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.
Investigate the curve for a<b and a>b.
Show the curve has a minimum at x=0.
Use a spreadsheet to generate the first 10 terms in the sequence: zn+1 = zn²+c, z0 = 0 for
c = 1, c = i, c = – i, c = 0.5–0.5i
Solve f(z) = 0 and plot the roots on an Argand diagram. Show that f’(z) = 0 has a repeated root.
Euler’s totient function, φ(n), counts the number of positive integers less than n that are co-prime with n.
Create a program to find φ(n). Use the program to find φ(11), φ(27), φ(72) and φ(1024).
Create a program to find all the positive integer solutions to x² − 3y² = 1 with x<100, y<100.

10. FPT: Further Information
Updates on the MEI website:
TI-Nspire:
Project Euler: projecteuler.net/