Parallelogram 13 • Level 2 • 30 Nov 2023Prime Time Level 2
Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/
- 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.
- Finish by midnight on Sunday if your whole class is doing parallelograms.
- Your score & answer sheet will appear immediately after you hit SUBMIT.
- Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.
1. Primes against the clock
Below is a simple website that tests how well you know your prime numbers and how quickly you can apply some prime tests. It will show you a series of numbers and you have to decide whether or not they are prime. If you do not know straight away, then there are some easy checks that you can apply to filter out the non-primes:
- If it is even, then it is divisible by 2.
- If the digits add to 3, 6, or 9, then it is divisible by 3.
- If it ends with a 0 or 5, then it is divisible by 5.
- Remember, 1 is NOT a prime.
Just visit the Is this a prime? website and see how many numbers you can identify as primes or non-primes.
1.1. When you get a score bigger than 15, what does “Game over” page say?
- You correctly sorted x numbers.
- Well done – you correctly sorted x numbers!
- You’re a prime superstar for sorting x numbers!
- Bronze level – you correctly sorted x numbers!
- Sorting x numbers is great, but now aim for 20 numbers.
- (Not answered)
2. Area questions
2.1. Square A has sides 24 cm in length, but Square B has a perimeter of 1 m. Which has a larger area?
- Square A has the larger area
- Square B has the larger area
- (Not answered)
If square B has a perimeter of 1 m, then it has sides of length 25 cm, so it will have a larger area.
2.2. Which triangle has the larger area? Triangle A has sides 5, 5, 6, but Triangle B has sides 5, 5, 8.
Split both triangles into two right-angle triangles and use Pythagoras’ Theorem to work out the height of each right-angle triangle.
If you haven't yet seen this at school, then read about it here then try to answer the question.
- Triangle A has the larger area
- Triangle B has the larger area
- Both triangles have the same area
- (Not answered)
You would need to draw the triangles and see that they can be split into two right-angle triangles. Then use the Pythagorean theorem to work out the height of each right-angle triangle. Then you will see both of the big original triangles is built from two 3-4-5 triangles, but they are arrange differently. So they have the same area.
2.3. What is the area of a triangle with sides 23 cm, 13 cm and 10cm?
Correct Solution: 0 cm2
The quick way to do this is to notice that 23 = 13 + 10, so the two short sides add up to the length of the long side... so we have a flat triangle with no area.
3. Sculpture mystery
3.1 This sculpture of a train coming out of a tunnel is by the artist Cindy Chinn. How long is the steam engine, roughly?
- 1 cm
- 10 cm
- 1 m
- 10 m
- 100 m
- (Not answered)
What is the sculpture made from? Why are the tracks and the train black? Why is everything else made of wood?
It’s carved from a pencil, so the steam engine is about 1 cm long.
4. Junior Maths Challenge Problem (UKMT)
4.1 What is the difference between the smallest 4-digit number and the largest 3-digit number?
- 1
- 10
- 100
- 1,000
- 9899
- (Not answered)
The smallest 4-digit number is 1000. The largest 3-digit number is 999. So their difference is equal to 1000 − 999 = 1.
5. Fractions of
5.1 What is
Correct Solution: 33
5.2 What is
Correct Solution: 38.5
5.3 What is
7 28 18 7 2 7 7 2 - (Not answered)
5.4 What is
Correct Solution: 15.4
5.5 Which is greater?
4 5 6 4 - (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.