Before you start the IVMO challenge, please read the following:
 There are 40 multiple choice questions in the challenge, each with 5 possible answers.
 Questions 1 – 25 each carry 2 marks, Questions 26 – 35 each carry 3 marks, and Questions 36 – 40 each carry 4 marks.
 The challenge is one hour long.
 Once you click on “Start” a clock will countdown and at the end of one hour your answers will be automatically saved and submitted.
 You can end the test before that by clicking on “Submit Test” on the final question.
 The grid of squares at the top will show you which questions you have answered.
 You can skip a question and come back to it later or revisit any question you have already answered by clicking on any question number in the grid.
 You will need paper for rough workings.
 You must not use a calculator or any other electronic device.
All the Best!!!
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Question 1 of 40
1. Question
2 point(s)Questions 1 – 25: Score 2 marks for each correct answer and 0 marks for each incorrect answer
2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2))))))

Question 2 of 40
2. Question
2 point(s)0.0000426×0.005

Question 3 of 40
3. Question
2 point(s)From the prime numbers less than 20, what is the difference between the squares of the highest and lowest?

Question 4 of 40
4. Question
2 point(s)7946 × 9992

Question 5 of 40
5. Question
2 point(s)Which of the following is not a multiple of 9?

Question 6 of 40
6. Question
2 point(s)What is 36.4% of $25

Question 7 of 40
7. Question
2 point(s)What is the whole number remainder when 242871 is divided by 897?

Question 8 of 40
8. Question
2 point(s)2023 has a square factor whose square root ends in 7. What is that square root?

Question 9 of 40
9. Question
2 point(s)The One Day International World Cup Final took place at Narendra Modi Stadium in Ahmedabad on 19th November 2023. It was a sellout event. The stadium is the largest in the world and can seat 132000 people. The total takings from sale of tickets was $46 596 000. What was the mean price of each ticket?

Question 10 of 40
10. Question
2 point(s)79³

Question 11 of 40
11. Question
2 point(s)992²

Question 12 of 40
12. Question
2 point(s)When placed in order of size, which fraction is in the middle?

Question 13 of 40
13. Question
2 point(s)A, B and C are three digits. B and C add up to 10.
A B x A C 4216 What is the value of A?

Question 14 of 40
14. Question
2 point(s)Callisto and Europa are two moons of Jupiter with orbital periods of 408 hours and 84 hours. If they start in line, after how many hours will they be in the same position again?

Question 15 of 40
15. Question
2 point(s)What are the vinculum digits in the Nikhilam multiplication of 524 X 492 when using a working base of 500 and a real base of 1000?

Question 16 of 40
16. Question
2 point(s)Triangle ABC is equilateral and D is the midpoint of BC. Triangle AEF is rightangled and isosceles. What is the size of angle x?

Question 17 of 40
17. Question
2 point(s)Three spheres, A, B and C, are such that the volume of B is 50% more than A and the volume of C is 60% more than B. What fraction is the volume of A of the volume of C?

Question 18 of 40
18. Question
2 point(s)Three identical rightangled triangles and a square are placed together with measurements as shown. What is the outside perimeter of the whole shape?

Question 19 of 40
19. Question
2 point(s)A sequence starts, 4, 5, 8, 13, 20,…What is the 98th term in this sequence?

Question 20 of 40
20. Question
2 point(s)When converted into a decimal, the fraction, 10 ,has 44 digits in its recurring pattern. What are the first seven decimal digits? 89 
Question 21 of 40
21. Question
2 point(s)Which of the following is the correct fraction equivalent to the partly recurring decimal, 0.327 (= 0.3272727…) ?

Question 22 of 40
22. Question
2 point(s)A regular octagon (8 sides) and a regular dodecagon (12 sides) share a comon edge, AB. Vertices D and C are joined with a line. What is the size of angle DCB?

Question 23 of 40
23. Question
2 point(s)At the Rio Cafe in Alexandria, Anthony buys three cups of coffee and four cups of mint tea for a total of $15.70. Meanwhile, Cleopatra buys two cups of coffee and five cups of mint tea for $14.90.
What is the cost of a cup of coffee at the cafe?

Question 24 of 40
24. Question
2 point(s)Which of the following is an equation of the straight line which passes through the point (3, 2) and that is perpendicular to the line with equation, 5x −3y =19 ?

Question 25 of 40
25. Question
2 point(s)Four of the following points are vertices of the same kite. Which point is not a vertex of this kite?

Question 26 of 40
26. Question
3 point(s)Questions 26 – 35: Score 3 marks for each correct answer and 1 mark for each incorrect answer.
When the denominator of 3√3 is rationalised, the anwer is, 3− √3 
Question 27 of 40
27. Question
3 point(s)Which of the following is a factor of 3x³ +11x² +30x +72 ?

Question 28 of 40
28. Question
3 point(s)After the decimal point, how many nonrecurring digits are there in the decimal equivalent for 17 ? 384 
Question 29 of 40
29. Question
3 point(s)SPT is tangent to the circle with centre O. Points Q and R lie on the circumference. Angle TPQ = 64˚ and angle RQO = 28˚ What is the size of angle RPO?

Question 30 of 40
30. Question
3 point(s)The men’s world record for a 100 metre sprint is 9.58 seconds, set by Usain Bolt in 2009. How fast is this in kilometres per hour? (Answer to the nearest whole number)

Question 31 of 40
31. Question
3 point(s)What is the value of x for which, 2^{2x }×8^{x1} =16^{x+3} ?

Question 32 of 40
32. Question
3 point(s)A, B, C and D are points on a straight line.
The ratio AB : BD = 2 : 5.
The ratio AC : CD = 7 : 3.
What is the ratio, AB : BC : CD? 
Question 33 of 40
33. Question
3 point(s)Each square in this grid has side length one unit. Two circles, each with diameter one unit are placed in two opposite squares. What is the shortest distance between the two circles?

Question 34 of 40
34. Question
3 point(s)What is the simplified form of, (2x^{2 }+3x +1)² −(x^{2 }−3x −1)² ?

Question 35 of 40
35. Question
3 point(s)The graph of a parabola has yintercept at (0, 13) and turning point at (4, 3). Which of the following is the equation for the parabola?

Question 36 of 40
36. Question
4 point(s)Questions 36 – 40: Score 4 marks for each correct answer and 2 marks for each incorrect answer.
What is the value of p, given that,(4x^{2 } −3px +2)(x^{2 } + px +1) = 4x^{4 } + px^{3 } −7px^{2 } − px +2

Question 37 of 40
37. Question
4 point(s)How many threedigit numbers can be written as the sum of five different powers of 3, including 3˚?

Question 38 of 40
38. Question
4 point(s)In this magic square, the products of numbers in each row, each column and each diagonal are all the same. The missing numbers are 2, 4, 5, 10, 25, 50 and 100. Which number must be placed in the square labelled M?

Question 39 of 40
39. Question
4 point(s)A rectangular piece of card is 3 cm longer than its width. It has 3 cm by 3 cm squares cut away from each corner. The area of the resulting shape is numerically the same as the perimeter. What is the area?

Question 40 of 40
40. Question
4 point(s)Three circles, each with a radius of one unit, are set out as shown with the circumference of the middle circle passing through the centres of the outer two circles. What is the area of the shaded region in terms of π?