Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 969 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
3. 3.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 10 (c) 24 (d) 48
4. 4.What is the 30th term of the AP 2, 8, 14, 20, …? (a) 174 (b) 180 (c) 182 (d) 176
5. 5.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 18 (d) 81
7. 7.What is the midpoint of the line joining (3, 3) and (7, 11)? (a) (2, 4) (b) (7, 5) (c) (5, 7) (d) (10, 14)
8. 8.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 99 (d) 11
9. 9.The mean of 3 numbers is 31. When the number 35 is added to them, what is the new mean? (a) 33 (b) 31 (c) 34 (d) 32
10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 21 (c) 49 (d) 42
11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 30 (b) 36 (c) 12 (d) 15
12. 12.Two angles of a triangle are 35° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 45° (c) 80° (d) 135°
13. 13.What is the mean of 5, 10, 13, 14, 18 and 18? (a) 15 (b) 13 (c) 12 (d) 14
14. 14.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
15. 15.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 21 cu cm (c) 294 cu cm (d) 196 cu cm
16. 16.In a class of 23 children, 11 like cricket, 10 like football and 7 like both. How many like only cricket? (a) 11 (b) 4 (c) 13 (d) 3
17. 17.A drawer has lots of red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 5
18. 18.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/3 (d) 1/6
19. 19.Two angles of a triangle are 50° and 45°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 95° (d) 135°
20. 20.What is the sum of all the whole numbers from 1 to 92? (a) 4278 (b) 4186 (c) 8556 (d) 4232
21. 21.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 130 (b) 65 (c) 80 (d) 25
22. 22.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 145° (b) 90° (c) 55° (d) 125°
23. 23.The mean of 3 numbers is 16. When the number 24 is added to them, what is the new mean? (a) 19 (b) 16 (c) 20 (d) 18
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 5 (c) 2 (d) 3
25. 25.In a class of 29 children, 20 like mangoes, 10 like bananas and 2 like both. How many like only mangoes? (a) 20 (b) 18 (c) 8 (d) 19
26. 26.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 14 (d) 15
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
28. 28.In a class of 23 children, 11 like mangoes, 8 like bananas and 4 like both. How many like neither? (a) 8 (b) 9 (c) 12 (d) 4
29. 29.In a class of 40 children, 28 like maths, 22 like science and 11 like both. How many like only maths? (a) 18 (b) 17 (c) 28 (d) 11
30. 30.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.A bag has 3 yellow balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 4 (c) 2 (d) 5
32. 32.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 144 (c) 51 (d) 16
33. 33.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
34. 34.The mean of 7 numbers is 22. When the number 6 is added to them, what is the new mean? (a) 14 (b) 22 (c) 20 (d) 21
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 4 (d) 3
36. 36.What is the mode of 7, 7, 1, 11, 17, 7 and 11? (a) 1 (b) 7 (c) 11 (d) 17
37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
38. 38.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
40. 40.In a class of 44 children, 20 like maths, 19 like science and 10 like neither. How many like both? (a) 10 (b) 5 (c) 6 (d) 34

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