Intermediate Maths Challenge

Congratulations to the 100 year 9 and 10 students who took part in the UK Intermediate maths challenge last week.  This is a competition that set challenging problems, and is a national competition.  We don't know results yet; they get set off to the UK Maths Trust, but when they do we will let you know who excelled, although all that took part from year 10 maths set 1, and year 9 sets 1 and 2 should be congratulated for their effort in what is a very exacting competition.  Questions are multiple choice, but losing marks for wrongs answers soon discourages you from merely guessing, and don't forget, no calculators!

Example questions from this year are...

9.
Auntie Fi's dog Itchy has a million fleas.  His anti-flea shampoo claims to leave no more than 1% of the original number of fleas after use.  What is the least number of fleas that will be eradicated by the treatment?
A: 900000              B: 990000        C: 999000         D:999990          E: 999999


17.
The first term of a sequence of positive integers is 6.  The other terms in the sequence follow these rules:

• if a term is even then divide it by 2 to get the next term;
• if a term is odd then multiply by 5 and subtract 1 to get the next term.

For which value of n is the nth term equal to n?

A: 10 only               B: 13 only         C: 16 only            D: 10 and 13 only         E: 13 and 16 only

20.
A rectangle with are 125 cm2 has sides in the ratio 4:5. What is the perimeter of the rectangle?
A: 18cm         B: 22.5 cm           C: 36cm            D: 45cm           E: 54 cm

Feel free to offer your answers in a comment below!