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A 60 minute, 25 multiple choice Challenge.
It encourages mathematical reasoning, precision of thought and fluency to make students think.
The problems on the Intermediate Maths Challenge are designed to make students think, most are accessible yet still challenge those with more experience.
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Bronze: ≥47
Silver: ≥61
Gold ≥77
Follow on Olympiads:
Year 9 and Below: Grey Kangaroo ≥72
Year 9 and Below: Cayley Olympiad ≥101
Year 10 and 11: Pink Kangaroo ≥84
Year 10: Hamilton Olympiad ≥106
Year 11: Maclaurin Olympiad ≥110
1. Do not open the paper until the invigilator tells you to do so.
2. Time allowed: 60 minutes. No answers, or personal details, may be entered after the allowed time is over.
3. The use of blank or lined paper for rough working is allowed; squared paper, calculators and measuring instruments are forbidden.
4. Use a B or an HB non-propelling pencil. Mark at most one of the options A, B, C, D, E on the Answer Sheet for each question. Do not mark more than one option.
5. Do not expect to finish the whole paper in the time allowed. The questions in this paper have been arranged in approximate order of difficulty with the harder questions towards the end. You are not expected to complete all the questions during the time. You should bear this in mind when deciding which questions to tackle.
6. Scoring rules:
5 marks are awarded for each correct answer to Questions 1-15;
6 marks are awarded for each correct answer to Questions 16-25;
Each incorrect answer to Questions 16-20 loses 1 mark;
Each incorrect answer to Questions 21-25 loses 2 marks.
7. Your Answer Sheet will be read by a machine. Do not write or doodle on the sheet except to mark your chosen options. The machine will read all black pencil markings even if they are in the wrong places. If you mark the sheet in the wrong place, or leave bits of eraser stuck to the page, the machine will interpret the mark in its own way.
8. The questions on this paper are designed to challenge you to think, not to guess. You will gain more marks, and more satisfaction, by doing one question carefully than by guessing lots of answers. This paper is about solving interesting problems, not about lucky guessing.
The mean of p and q is 13; the mean of q and r is 16; the mean of r and p is 7.
What is the mean of p, q and r?
In the diagram, PQRS is a square, PST is an equilateral triangle and SRUVW is a regular pentagon.
What is the size of angle WTS?
A picture, together with its frame, makes a square of side length 80 cm. The frame is 4 cm wide.
What percentage of the area of the square is covered by the frame?
Jill was given a large jar of jam. She gave one sixth of the jam to Jan. Jill then gave one thirteenth of the remaining jam to Jas. Jill was left with 1 kg of jam.
What was the weight, in kg, of the jam in Jill’s jar at the start?
Eight of the digits from 0 to 9 inclusive are used to fill the cells of the crossnumber. What is the sum of the two digits which are not used?
Three sectors of a circle are removed from a regular hexagon to form the shaded shape shown.
Each sector has perimeter 18 mm. What is the perimeter, in mm, of the shaded shape formed?
Merryn wrote down the numbers 2, 0, 2, 3 and one further number.
What was the median of her five numbers?
The ‘Penny’s Puddings’ company uses one tonne of rice to make twenty-five thousand cans of rice pudding. Each tonne of rice contains approximately fifty million grains ofrice. Approximately how many grains of rice are there in a can of Penny’s rice pudding?
Four of these points lie on a circle.
Which of the points does not lie on that circle?
To draw a 3 by 3 square grid you need 8 straight lines, as shown.
How many straight lines do you need to draw a n by n square grid?
The ages of Grannie’s seven grandchildren are consecutive positive integers.
The youngest three grandchildren have a mean age of 6.
What is the mean age of the oldest three grandchildren?
We know that 1 + 2 + 3 + 4 = 10.
It is also true that 13 + 23 + 33 + 43 = 10n for some integer n.
What is this integer?
The shorter sides of a right-angled triangle have lengths √5 and √12.
What is the length of the hypotenuse?
The diagram shows a square, its two diagonals and two line segments, each of which connects two midpoints of sides of the square.
What fraction of the area of the square is shaded?
The diagram shows the square PQRS and T, the midpoint of the side PQ.
What fraction of the area of the square PQRS is shaded?
What is the difference between the smallest two-digit prime and the largest two-digit prime?
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