1. Welcome to your Year 7 Maths Challenge
Do you want a challenge??

2. Choose one of the following challenges:
Present your work neatly on paper.
With good reasoning.
With full workings.
Justify your answers.

3. Security Cameras A shop owner wants to prevent shoplifting.
He decides to install a security camera on the ceiling of his shop.
He places the camera in the corner of the shop (at point P)
The camera can turn through 360°
The diagram shows a plan view of the shop with ten people standing in it.

4. Security Cameras Which people can the camera NOT see?
The shopkeeper thinks that 15% of the shop is hidden from the camera. Is he right or not? Explain. 
(a) What do you think is the best place for the camera, so that it can see as much of the shop as possible.
(b) How you know that this is the best place for the camera?

5. OR

6. Three of a Kind The picture shows three regular hexagons.
What is the same and what is different about them?
What can you say about the lengths, angles, sizes, areas, symmetry?
Anything else?

7. OR

8. Taxi Cabs
Max and Liz are organising a trip to the airport for a party of 75 people.
They can use two types of taxi.
A small taxi costs £40 for the trip and holds up to 4 people.
A large taxi costs £63 for the trip and holds up to 7 people.
Max says they should order 6 large taxis
1 (a) So how many small taxis would they need?
(b) How much will the total cost be?
Liz thinks that they can organise the journey more cheaply than this!
2. Is Liz right? How many taxis of each type should they order to get the total cost as low as possible?

9. GOOD LUCK AND WE ALL LOOK FORWARD TO WELCOMING YOU INTO THE MATHs DEPARTMENT IN SEPTEMBER!