Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 671 · 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.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 150° (d) 125°
2. 2.The mean of 6 numbers is 34. When the number 13 is added to them, what is the new mean? (a) 30 (b) 32 (c) 34 (d) 31
3. 3.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x − 8)(x − 9)
4. 4.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2415 (c) 4970 (d) 2450
5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
6. 6.A drawer has lots of green, white, blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 8 (c) 5 (d) 2
7. 7.In a class of 27 children, 9 like maths, 18 like science and 3 like both. How many like only maths? (a) 3 (b) 9 (c) 15 (d) 6
8. 8.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
10. 10.In a class of 36 children, 14 like cricket, 21 like football and 5 like neither. How many like both? (a) 3 (b) 31 (c) 5 (d) 4
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
12. 12.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 9 (d) 5
13. 13.In which quadrant does the point (5, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.A drawer has lots of yellow, blue, black, red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 10 (d) 6
15. 15.What is the sum of the first 11 terms of the AP 2, 8, 14, …? (a) 385 (b) 704 (c) 62 (d) 352
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/36 (d) 1/12
17. 17.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
18. 18.A bag has 7 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 16 (c) 8 (d) 2
19. 19.What is the median of 27, 11, 18, 7 and 40? (a) 19 (b) 27 (c) 18 (d) 11
20. 20.How many factors does 115 have? (a) 4 (b) 5 (c) 3 (d) 2
21. 21.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
22. 22.If a + b = 9 and ab = 20, what is (a − b)²? (a) 81 (b) 1 (c) 41 (d) 61
23. 23.A bag has 2 red, 2 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 2/3 (b) 1/6 (c) 1/3 (d) 5/6
24. 24.A bag has 3 green balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 4 (d) 7
25. 25.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 160° (c) 120° (d) 140°
26. 26.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
27. 27.A bag has 12 black balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 2 (c) 23 (d) 14
28. 28.In a class of 25 children, 13 like maths, 13 like science and 8 like both. How many like only maths? (a) 8 (b) 12 (c) 13 (d) 5
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/11 (d) 1/6
30. 30.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 160° (c) 155° (d) 45°
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
32. 32.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 625 (b) 925 (c) 1235 (d) 1225
33. 33.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 5 (d) 1
34. 34.What is the median of 36, 5, 20, 11, 9, 28 and 6? (a) 11 (b) 20 (c) 12 (d) 9
35. 35.What is the median of 33, 21, 25, 4 and 36? (a) 33 (b) 25 (c) 26 (d) 21
36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 64? (a) 17 (b) 15 (c) 16 (d) 6
37. 37.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
38. 38.What is the distance between the points (7, 9) and (31, 2)? (a) 25 (b) 625 (c) 26 (d) 31
39. 39.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
40. 40.In a class of 25 children, 12 like dance, 13 like music and 8 like both. How many like neither? (a) 9 (b) 16 (c) 0 (d) 8

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