Parallelogram 31 Year 10 10 Jun 2021Pi

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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. Dihydrogen Monoxide

Here is an important video about the chemical dihydrogen monoxide.

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

2 marks

1.1 Should you sign a petition to ban dihydrogen monoxide?

  • Yes, ban it.
  • No, don’t ban it.
  • Not sure – I need more information.

You might need more information, but you really should know that dihydrogen monoxide is simply water, H20. If you’re confused, then just rewatch the video above (everything is true) or this other video.

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

2. Intermediate Maths Challenge Problem (UKMT)

3 marks

2.1. Which of these numbers is biggest?

  • 19×99
  • 199×99
  • 1999
  • 19×99
  • 1999

19×99 and 199×99 are both less than 1992 and hence less than 1999; 99<1999; 1999=19=1.

3. Intermediate Maths Challenge Problem (UKMT)

4 marks

11.1 "20% off everything", screamed the sale poster. I paid £60. What would I have paid before the sale?

  • £60
  • £66
  • £72
  • £75
  • £80

Let the original price be £x. Then 0.8x = 60, therefore x = 60 ÷ 0.8 = 75.

4. Staggering Pi Phenomenon

This is one of the most shocking videos I have ever seen. Watch in awe.

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

4 marks

4.1 If the small block is 1 Kg, and you want to calculate 3 digits of π, then what mass would the large block have to be?

  • 1 Kg
  • 10 Kg
  • 100 Kg
  • 1 tonne
  • 10 tonnes
4 marks

4.2 If the small block is 1 Kg, and you want to calculate 20 digits of π, then what mass would the large block have to be?

  • Same as the Moon
  • Same as the Earth
  • Five times the mass of the Sun
  • Ten times the mass of a supermassive black hole
  • Twice the mass of the universe

All the answers are in the video, but if you want to know more, if you want to know why, then watch this follow-up video... it is hard, but worth a look if you are curious.

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

5. Intermediate Maths Challenge Problem (UKMT)

5 marks

5.1 When exactly is the value of the product 1+121+131+14 ... 1+1n equal to an integer?

  • when n is odd
  • when n is even
  • when n is a multiple of 3
  • always
  • never
Show Hint (–1 mark)
–1 mark

The product = 32×43×54×65× ... ×n+1n.

The product = 32×43×54×65× ... ×n+1n. The numerator of each fraction except the last cancels with the denominator of the next fraction, leaving n+12. This is equal to an integer only when n is odd.

6. Riddle

3 marks

6.1 Two mothers and two daughters go out for lunch. They order 6 slices of pizza and can share the slices equally between them. How?

  • There is only one mother.
  • There is only one daughter.
  • There is a grandmother in the group
  • There are six people altogether
  • They are one person

If we have a grandmother and a daughter and a grand-daughter, then we have two mothers and two daughters, but only three people.

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.