Hello and welcome to the Maths Department at Reigate College.
My name is Simon King and I’m Head of the Maths Department. Along with our excellent team of Maths teachers, I’m very much looking forward to welcoming you in person at the start of the academic year and getting going on our interesting and challenging A Level programme.
To help introduce you to the course, we’re setting some activities for you to complete over the coming months. These tasks will develop some of the ideas you’re familiar with from GCSE and give you an insight into the approach required at advanced level. They have been designed for you to complete independently from home and there’ll be the chance to review them when you start the course in September.
The tasks are organised in three distinct steps and should all be completed by Choices Day on 27 August 2025. This is to give you the best insight into what the courses will be like and/or help prepare you for them.
Please note, some Course Leaders (for example for Music) may release their tasks earlier, as they may form part of the College’s audition process. If this applies to you, you’ll be notified separately.
New Starters Course Tasks and Activities
| Release date | Suggested Completion Dates | |
| Explore your Subject | 1 June | 1 July |
| Get Going | 1 June | 1 August |
| Aim High | 1 June | 1 September |
At A Level, Mathematics and Further Mathematics become more interesting and more complex; you’ll find you have to problem-solve more than at GCSE and that there are often many different ways of solving questions.
During this series of tasks and activities we’ll be looking at both Pure and Applied Mathematics.
For a short taste of Pure Maths, have a look at this video with Matt Parker and James Grime. They’re exploring The Difference of Two Squares using different methods. Don’t worry if the algebra becomes a little more complex towards the end, just do your best to follow and enjoy it!
Exploring statistics
As part of the Applied Maths content of the A Level course, we will be looking at Statistics. But what is Statistics? What perceptions do people have of the word? Can Statistics be misleading? For example, if we consider the following question:
Find the mean, median and mode of: 1, 1, 2, 1000, 9 000 000
The mode is 1, the median is 2, the mean is 18 000 200.8
So which is most representative? What would you think if these figures were:
- time taken to complete a question on a website?
- monthly pocket money for students?
Question: Click on the link below to watch a TED talk with Alan Smith as he explores some of these issues:
Practicing your essential skills
We’d now like you to return to some of the Pure topics you met in the ‘Explore your Subject’ section.
COMPULSORY TASK 1: Please use the below worksheet to improve and revise the number skills you need to succeed in the first term. This work is a compulsory submission for your first week of A Level Maths.
You can either print out and write on the worksheet, or show your workings on lined paper.
Taking it Further
If you enjoy a challenge or are thinking of taking Further Maths, try the following extension activity. It uses Maths that you will have encountered at GCSE.
EXTENSION TASK: Two-way algebra
Copy out the below table.
Each column and row has a property which an equation or inequality may or may not have. If an example has the properties of the corresponding row and column, then it can appear in that cell.
We have omitted some row and column headings, and some entries in cells. Can you complete the table? The missing headings are:
- Simultaneous Equations in x and y
- No real solutions
- Negative solutions only
- Equations in x
Here are some questions to think about (either once you have a solution or as you are working on it):
- Did you have any choice about where to put the missing row and column headings?
- Can you simplify any of your examples?
- Do all your examples require some ‘solving’ to check they fit the attributes of the cell? If not, can you make it so that they all do?
- If we required all the cells to contain quadratics, would it still be possible to fill all the cells?
Solution
A possible solution is given here:
https://undergroundmathematics.org/thinking-about-algebra/two-way-algebra/a-possible-solution
How similar is this to your own solution?
Introducing Mechanics
As part of the Mechanics section of the Applied Maths content, we will look at Newton’s Second Law of Motion:
Force = Mass x Acceleration (F = ma)
Question: Watch the following video to see why it is almost impossible to run the 100m in 9 seconds as a result of F = ma.
Practising your essential skills
COMPULSORY TASK 2: Please complete the following worksheets in preparation for the A Level course, making sure you set out your working clearly, and then bring them with you to your first lesson, alongside the worksheets from the Get Going section above. Your teachers are looking forward meeting you and seeing your work:
You may use desmos.com graphing software to help you. Please attempt all the questions on your own first, before marking them with the answer sheet. Knowledge of algebra and graphs is vital to your success in the first year of the course.
You can either print out and write on the worksheet, or show your workings on lined paper.
Taking it Further
If you enjoy a challenge, try the following extension activity. If you’re thinking of taking Further Maths, you should bring your answers to your first Further Maths lesson.
Extension Task: Mega Quadratic Equations
1. There are six possible solutions to each of the following equations. Can you find them all?
2. Can you find some more Mega Quadratic Equations like these?
If you need a hint to get started, consider what numbers p and q work for this equation: pq = 1
What value of q will work for any value of p?
What value of p will work for any value of q? What other value of p will work for certain values of q?
Solution
- Have you checked that any solutions you’ve found do definitely work by substituting into the original equation?
- Can you write out clear working for your solution to one of the problems showing what you did and why?
- Were you able to find more Mega Quadratic Equations?
Take a look at some of the solutions submitted by students here:
Head of Mathematics
