# Challenging Maths!

Congratulations to three students who have got through the Senior Maths Challenge 2010 to qualify for the next round – the British Maths Olympiad 1 (BMO1). They are: James Whitehead (scoring 109 out of 125), Michael Minshall (100) and Ed Kirkby (who is a year 10 student from Amery Hill) who was achieved 125 – i.e. full marks – and is one of only 14 students nationally to have achieved perfect marks! And he is in year 10! Ed is attending Alton College to study AS Maths to extend his education.

The Senior Maths Challenge consists of 25 challenging(!) non-calculator multiple-choice maths questions in 90 minutes. As in previous years, students start with 25 marks, get 4 marks for each correct answer and lose 1 mark for each incorrect answer, to discourage guessing. Students needed 96 to qualify for this round.

The top 40% of students nationally are awarded a certificate in the ratio of 1:2:3 for Gold, Silver and Bronze.

Based on national average therefore, we *would* have been awarded 6 Gold, 12 Silver and 19 Bronze awards. However, we did significantly better than the national average – once again!

Gold: 11

Silver: 23

Bronze: 23

93 participants.

Three examples of questions (An easy, medium and a hard)

**Q2. What is the smallest possible value of 20p + 10q + r when p, q, and r are different positive integers?**

A: 31 B: 43 C: 53 D: 63 E: 2010

**Q8. Which of the following is equivalent to (x + y + z)(x - y - z) ?**

A: x2 – y2 – z2 B: x2 – y2 + z2 C: x2 – xy – xz – z2

D: x2 – (y + z)2 E: x2 – (y – z)2

**Q25: All the digits of a number are different, the first digit is not zero, and the sum of the digits is 36. There are N x 7! such numbers. What is the value of N?** [Some help: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1]

A: 72 B: 97 C: 104 D: 107 E: 128

**Answers are** Q2. B Q8. D and Q25. D.

90% of the students nationally got Q2 correct, 55% got the Medium question correct and only 3% of students nationally got Q25 correct.