Parallelogram 16 Level 5 19 Dec 2024Chrismaths - Part 3

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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.

It’s nearly Christmas, so time for another instalment of your Christmaths challenge paper.

Good luck and happy Chrismaths. Don’t eat too many mince pie charts!

Simon.

PS: I want to say thank you to the UK Mathematics Trust, who own the copyright to these questions.

1.

3 marks

What is the value of a+b+c+d+e+f?

  • 360
  • 540
  • 720
  • 900
  • It depends on the triangle
  • (Not answered)

2.

4 marks

The cuboids below all have the same volume. Which of them has the greatest surface area?

  • A)
  • B)
  • C)
  • D)
  • E)
  • (Not answered)

3.

4 marks

In this addition sum, each letter represents a different non-zero digit.

What is the value of a+w+a+y?

  • 13
  • 15
  • 16
  • 17
  • 18
  • (Not answered)

4.

4 marks

Three rectangular-shaped holes have been drilled passing all the way through a solid 3 x 4 x 5 cuboid. The diagrams show the front, side and top views of the resulting block.

What fraction of the original cuboid remains?

  • 1330
  • 715
  • 12
  • 815
  • 1730
  • (Not answered)

5.

5 marks

If p, q and pq are all positive integers, which of the following is least?

  • q2p2
  • p2q2
  • qp
  • qp
  • pq
  • (Not answered)

Before you hit the SUBMIT button, here are some quick reminders:

  • You will receive your score immediately, and collect your reward points.
  • You might earn a new badge... if not, then maybe next week.
  • Make sure you go through the solution sheet – it is massively important.
  • A score of less than 50% is ok – it means you can learn lots from your mistakes.
  • The next Parallelogram is next week, at 3pm on Thursday.
  • Finally, if you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon.