Hello and welcome to the Maths Department at Reigate College.

My name is Mary Pitman and I’m joint Head of the Maths Department, together with my colleague Christine Edwards. We’re 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.

All the tasks should be completed by Choices Day on 25 August.

The activities will be released here in three phases:

### Explore your Subject – 4 May

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!

We’d now like you to try the below **Essential Skills** worksheet, which includes topics that are important for A Level Mathematics. The questions have three levels: Bronze, Silver and Gold. You should be able to complete ALL the Bronze questions, MOST of the Silver questions and SOME of the Gold questions. If you’re planning on studying Further Mathematics, you should be aiming to complete them all.

**You should complete this section of tasks by 1 June.**

### Get Going – 1 June

**You should complete this section of tasks by 1 July.**

#### 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?

**TASK 1: **Click on the link below towatch 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.

**TASK 2: **Please use the below worksheets to improve and revise these skills. You should aim to spend up to 30 minutes on each topic. Start at Q1 if you’re not feeling confident; if you’re already good at the topic, try the second half of the worksheet and the Extension questions:

- Factorising expressions
**1b-1** - Linear inequalities
**1d-1** - Solving linear and quadratic simultaneous equations
**1c-2** - Sketching cubic and reciprocal graphs
**1e**(If you need help, try a table of values on your calculator, type the equation into Google or go to https://www.desmos.com/calculator) - Solving quadratic equations
**1b-3**

**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?

### Aim High – 1 July

**You should complete this section of tasks by Choices
Day on 25 August.**

#### 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)*

**TASK 1: **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

**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. Your teachers are looking forward meeting you and seeing your work:

#### 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:
p ^{q} = 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: