Maths Club B

                                           Challenge 4

There’s a zombie outbreak in a city of 15 million people and the army has been ordered to deal with it, and as the general that means you have to decide what to do. You could send in all your troops, but then you would have none spare if there’s another outbreak somewhere else. Instead, you decide to send in a skeleton force of just 1,600 soldiers with orders to recruit members of the public to help them fight the zombies. It’s a novel solution, and leaves you with plenty of men in case there are any other outbreaks, but no one else thinks it’ll work. To prove them wrong, you set out to do the maths. You know that each soldier can hunt down and kill twenty zombies a day. In the evening, each soldier can also recruit one new soldier from the people in the city who will join the fight the following day. However, each night the zombies will fight back and infect five normal people who then become zombies. You know there’s currently 50,000 zombies in the city. Have you made the right decision?

A: Yes, the maths shows this is the right decision. It might take a while, but the strategy will work and the soldiers will regain control of the city.

B: The maths shows that while the strategy is sound, you’d need to send in more troops at the start for it to be successfully implemented.

c: No. The maths shows that this is the wrong decision. No matter how many soldiers you sent in, the strategy will never work. This is because the number of zombies keeps increasing at a rate faster than the soldiers can kill them. The only thing which can stop the outbreak spreading is to nuke the entire city before the situation gets any worse.

Challenge 3

The apocalypse has come and, with the exception of a few small, scattered groups of survivors, the entire population of the world has been turned into zombies. That means there’s 7 billion undead walking around, looking for human flesh to feast on. You’re lucky enough to be holed up in an old military bunker you stumbled upon while escaping from the city. You know that zombies, being re-animated dead bodies, will eventually rot away, making it safe for you to go outside again. You work out that zombies have a half-life of 28 days. This means that every 28 days the number of zombies will decrease by 50%. How long will be before all the zombies are gone and it’s safe for you to go outside again?

Task

1)Work out the answer to the question, clearly showing all workings.

Justify your reasons using clear statements and mathematical language

2)State any assumptions you have made, or any limitations to your answer

3)Draw a graph showing the zombie numbers over time. What type of graph do you have? Can you see any problems with modelling the situation like this?

Challenge 2

There’s 20 walking dead coming up the street towards your house. You know you need to shoot the zombies in the head to kill them but you’re scared so your aim is off. This means there’s only a 60% chance of you killing a zombie with each shot. What’s the fewest number of shots you will to fire before you are certain to have killed them all?

A: 32.

B: 34.

C: 33.

D: 35.

Task

1)Work out the answer to the question, clearly showing all workings.

Justify your reasons using clear statements and mathematical language

2)State any assumptions you have made, or any limitations to your answer

3)What would the probability be of killing any given zombie if it took you only 27 shots to kill all of the zombies?

Challenge 1

You hear the first reports on the news that the dead have started to rise and attack the living. You knew this was going to happen and you’re ready. You grab your ‘bug out bag’ and a baseball bat before leaping into your car. The safe house you’ve been carefully preparing and provisioning for the last year is 74 miles away and if you drive fast enough you’ll be there in an hour at the most; then you’ll be safe. As you start your engine you glance at the fuel gauge and realise your room mate’s not only borrowed your car yet again without asking, but he’s also not topped up the tank so it’s only a quarter full. You know your tank holds 11 gallons when it’s full and your car does 27 miles to the gallon. What do you do?

A: I’ve got enough fuel to get there, so I’m leaving the city while I still can.

B: There’s not enough fuel left in the tank. I’ll need to get some more before I head off. It’ll be risky but at least I won’t end up stranded in the middle of nowhere when I run out.

Task

1) Work out the answer to the question, clearly showing all workings.

Justify your reasons using clear statements and mathematical language

2)State any assumptions you have made, or any limitations to your answer

3)Draw a linear graph for miles against gallons

1)Make a table of values  

2)Draw and label axis

3)Plot the and join together the points