Goole Academy Mathletes attend the UKMT Intermediate Maths Challenge
Students in Years 9 and 10 at Goole Academy took on the UKMT Intermediate Maths Challenge.
The 60-minute, multiple choice challenge is designed to encourage mathematical reasoning, precision of thought, and fluency in using basic mathematical techniques to solve interesting problems. They are designed to make students think. Most are accessible, yet still challenge those with more experience.
The exasperating 60-minute paper was completed by pupils across the country and the highest scorers are invited to compete in the even more perplexing Kangaroo papers.
Across Goole Academy, pupils earned 2 gold certificates, 14 silver and 20 bronze.
One impressive entrant scored highly enough to automatically qualify for the Pink Kangaroo follow on paper. Some were very close and were invited to participate.
Here is an example question from the challenge.
The five numbers 95, 96, 97, 98, 99 are each paired with one of the five numbers 1, 3, 5, 7, 9 (each number
used once). The larger number of each pair is then divided by the smaller, giving five integer answers.
What is the difference between the smallest and the largest of the five integer answers?
A 96 B 86 C 76 D 66 E 56
And here is a tougher example.
The numbers x and y satisfy the equations x + y = 6 and x3 + y3 =198
What is the value of xy?
A 1 B 2 C 3 D 4 E 5
Solutions
Question 1
97 is prime, so must be paired with
the 1. 97 divided by 1 = 97.
95 is the only multiple of 5, so must
be paired with the 5. 95 divided by
5 = 19.
98 is the only multiple of 7, so must
be paired with the 7. 98 divided by
7 = 14.
99 is the only multiple of 9, so must
be paired with the 9. 99 divided by
9 = 11.
Therefore 96 must be paired with the 3.
96 divided by 3 = 32.
The largest and smallest of the five
integer answers are 97 and 11.
The difference between these is 97 – 11
= 86.
Question 2
The value of xy is 1.