Parallelogram 30 Year 10 4 Jun 2020Slinky Physics

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Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

  1. a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.
  • Tackle each Parallelogram in one go. Don’t get distracted.
  • When you finish, remember to hit the SUBMIT button.
  • Finish by Sunday night if your whole class is doing parallelograms.

IMPORTANT – it does not really matter what score you get, because the main thing is that you think hard about the problems... and then examine the solution sheet to learn from your mistakes.

1. Professor Wiseman’s puzzles

Another puzzle from Professor Wiseman, whose website is really worth a visit when you’ve completed this Parallelogram.

2 marks

1.1 Which NUMBER comes next in this sequence?

77, 49, 36, …

Correct Solution: 18

Show Hint (–1 mark)
–1 mark

Instead of 77, think of it as 7 and 7... and then think of the 4 basic operations in maths

Think of 77 as 7 × 7 = 49, then think of 49 as 4 × 9 = 36, and so on.

2. Intermediate Maths Challenge Problem (UKMT)

4 marks

2.1 What fraction of a 24-hour day does school take up, if school starts at 8:30am and finishes at 3:15pm?

  • 932
  • 2596
  • 1348
  • 3196
  • 1832

The required fraction =63424=2796=932.

3. Intermediate Maths Challenge Problem (UKMT)

4 marks

3.1 Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces (head, body and tail) in order to weigh it.

The tail weighed 9kg and the head weighed the same as the tail plus one third of the body. The body weighed as much as the head and tail together.

How much did the whole fish weigh?

  • 18 kg
  • 27 kg
  • 54 kg
  • 77 kg
  • 84 kg
Show Hint (–1 mark)
–1 mark

Let the weights in kg of the head and body of the fish be h and b respectively.

Then and h=9+13b and b=h+9.

Let the weights in kg of the head and body of the fish be h and b respectively.

Then and h=9+13b and b=h+9.

So b=9+13b+9, that is 23b=18, which gives b=27.

Hence h=18, so the whole fish weighed 54kg.

4. Celebrating teachers

You have probably realised this already, but it is always worth reminding ourselves that teachers can play a really important role in our lives.

In the clip below, former England footballer Ian Wright pays tribute to a childhood teacher that changed the course of his life.

The teacher in question, the great Mr Pigden, passed away in 2017.

(If you have problems watching the video, right click to open it in a new window)

5. Intermediate Maths Challenge Problem (UKMT)

4 marks

5.1 A 1 × 2 × 3 block is placed on an 8 × 8 board as shown, with the 1 × 2 face ‘X’ at the bottom.

It is rolled over an edge, without slipping, onto the 1 × 3 face Y, then onto the 2 × 3 face Z, then onto X, then Y, then Z again in that order.

How many different squares on the board has the block occupied altogether, including the starting and ending positions?

  • 18
  • 19
  • 20
  • 21
  • 22

The two dark squares are those on which the block stands originally.

After the first move, it occupies the squares labelled ‘1’ or ‘1/5’. After the second move it occupies the squares labelled ‘2’ and so on.

After the fifth and final move, it occupies the squares labelled ‘5’ or ‘1/5’.

As can be seen, 19 squares are occupied altogether.

6. Slinky physics

3 marks

6.1 Take a look at this video and decide what will happen.

(If you have problems watching the video, right click to open it in a new window)

  • The bottom end falls first
  • The top end falls first
  • The top and bottom fall together (so the slinky maintains its length for a while)
  • The top falls down and the bottoms moves up at the same time

(If you have problems watching the video, right click to open it in a new window)

There will be more next week, so check your email or return to the website on Thursday at 3pm.

In the meantime, you can find out your score, the answers and go through the answer sheet as soon as you hit the SUBMIT button below.

When you see your % score, this will also be your reward score. As you collect more and more points, you will collect more and more badges. Find out more by visiting the Rewards Page after you hit the SUBMIT button.

It is really important that you go through the solution sheet. Seriously important. What you got right is much less important than what you got wrong, because where you went wrong provides you with an opportunity to learn something new.

Cheerio, Simon.