KIS Senior Maths Challenge
“Problems worthy of attack …
… prove their worth by fighting back!”
The above quotation, widely attributed to the Danish mathematician (and inventor, designer, scientist, poet, author) Piet Hein, nicely sums up the notion that there is great satisfaction to be had in tackling and solving problems that don’t easily surrender. It feels very rewarding to get to the end of a mathematical problem, knowing that you used a variety of skills and knowledge in order to make it yield.
Our weekly Maths Challenge allows all students to experience this sense of satisfaction. That said, our Year 12 and Year 13 Maths A-level students were recently given the opportunity to have a much more intense experience, by taking on a 90-minute Olympiad-style examination – the KIS Senior Maths Challenge. The underlying philosophy of this type of examination is not necessarily to urge students to build more mathematical knowledge; rather such tests encourage students to do more with the knowledge they have. The exam consisted of 25 multiple-choice questions, drawn from recent UKMT tests. No calculators were allowed, and no manipulatives (not even squared paper!) were allowed. And, just to spice things up a little, wrong answers received negative marks.
Here are a three of the more straightforward questions on the paper that should give you a flavour of the challenge:
Question 1: The teenagers Sam and Jo notice the following facts about their ages:
- the difference between the squares of their ages is four times the sum of their ages
- the sum of their ages is eight times the difference between their ages.
What is the age of the older of the two?
Question 2: Isbobel – ” Josh is innocent” Genotan – “Tegan is guilty” Josh – ” Genotan is guilty” Tegal – “Isobel is innocent”. Only the guilty person is lying, all the others are telling the truth. Who is guilty?
a) Isobel b) Josh c) Genotan d) Tegan e) More information is required.
Question 3: How many pairs (x,y) of positive integers satisfy the equation 4x = y2 + 15?
Our students coped very well indeed with the challenge and we will award participation and achievement certificates to them at the upcoming end of term assembly.
Head of Secondary Maths