Parallelogram 13 Level 4 30 Nov 2023Prime Time Level 4

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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.
  • 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.

3 marks

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. A riddle

2 marks

2.1. What occurs twice in a week and once in a year, but never in a day? Please express you answer in the shortest form possible.

Correct Solution: E

The answer is the letter 'E'.

3. Sevens

2 marks

3.1. What is 7 + 7 ÷ 7 + 7 × 7 – 7?

Correct Solution: 50

We need to remember the order of operations, so division and multiplication take priority:

7 + 7 ÷ 7 + 7 × 7 – 7 = 7 + (7 ÷ 7) + (7 × 7) – 7 = 7 + 1 + 49 – 7 = 50.

4. Moneyball

Moneyball is a terrific film about baseball and mathematics. It stars Brad Pitt as a struggling coach and Jonah Hill as the mathematician who helps the team achieve the longest winning streak in American League baseball history. I should point out that this is a true story. In fact, some soccer teams are also beginning to use mathematicians to build winning teams.

Read the question below and watch the clip that follows before you answer it.

2 marks

4.1. Which of the following does NOT describe the ways in which a mathematical approach to baseball can help?

  • Mathematicians can better describe the path of the ball and the swing of the bat.
  • Mathematicians can spot good players who are overlooked because of prejudices about age, style and so on.
  • Mathematicians can pinpoint players who are good value for money.
  • Mathematicians use baseball statistics to identify how each player can contribute to the team.
  • (Not answered)

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

5. Intermediate Maths Challenge Problem (UKMT)

3 marks

5.1 What is the sum of the first 2011 digits when 20 ÷ 11 is written as a decimal?

  • 6,013
  • 7,024
  • 8,035
  • 9,046
  • 10,057
  • (Not answered)

We see from the following long division sum

that 20 ÷ 11 has the recurring decimal expansion 1.8181... .

Hence the first 2011 digits consist of 1006 1s and 1005 8s.

So the sum of these digits is 1006 × 1 + 1005 × 8 = 1006 + 8040 = 9046.

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.