Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 953 · 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 coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
2. 2.What is the midpoint of the line joining (6, 5) and (8, 11)? (a) (8, 7) (b) (1, 3) (c) (7, 8) (d) (14, 16)
3. 3.A cuboid is 10 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 180 sq cm (b) 432 sq cm (c) 216 sq cm (d) 108 sq cm
4. 4.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 28 (c) 56 (d) 11
5. 5.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 30° (d) 150°
6. 6.In a class of 49 children, 26 like maths, 22 like science and 8 like both. How many like neither? (a) 1 (b) 9 (c) 8 (d) 17
7. 7.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
8. 8.Which term of the AP 5, 13, 21, 29, … is 101? (a) 15th (b) 13th (c) 12th (d) 14th
9. 9.A bag has 4 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 6 (d) 5
10. 10.In a class of 19 children, 9 like mangoes, 10 like bananas and 3 like both. How many like only mangoes? (a) 9 (b) 3 (c) 6 (d) 7
11. 11.In a class of 40 children, 27 like cricket, 17 like football and 6 like neither. How many like both? (a) 34 (b) 4 (c) 10 (d) 6
12. 12.In which quadrant does the point (1, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 63) (c) (x + 7)(x + 9) (d) (x + 1)(x + 15)
14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
15. 15.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 120° (d) 125°
16. 16.What is the median of 2, 31, 9, 32 and 18? (a) 19 (b) 9 (c) 18 (d) 31
17. 17.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 348 (c) 415 (d) 414
18. 18.What is the median of 17, 15, 1, 27, 19, 6 and 35? (a) 17 (b) 27 (c) 19 (d) 15
19. 19.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
20. 20.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 135° (b) 85° (c) 95° (d) 130°
21. 21.A bag has 11 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 21 (b) 13 (c) 12 (d) 2
22. 22.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 84 (c) 13 (d) 48
23. 23.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 120° (b) 130° (c) 110° (d) 70°
24. 24.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 1 (d) 4
25. 25.What are the roots of x² − 11x + 30 = 0? (a) 2 and 15 (b) 5 and 6 (c) 1 and 30 (d) 1 and 10
26. 26.In a class of 28 children, 16 like maths, 12 like science and 9 like both. How many like at least one of the two? (a) 20 (b) 10 (c) 19 (d) 28
27. 27.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 80°
28. 28.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
30. 30.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 1 (d) 2
31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
32. 32.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 1 (d) 2
33. 33.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 1 (d) 7
34. 34.What is the distance between the points (5, 7) and (14, 19)? (a) 225 (b) 21 (c) 15 (d) 16
35. 35.What is the mode of 2, 7, 7, 5, 5, 6 and 7? (a) 2 (b) 6 (c) 7 (d) 5
36. 36.If a + b = 13 and ab = 40, what is (a − b)²? (a) 9 (b) 169 (c) 3 (d) 89
37. 37.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 272 (d) 136
38. 38.What is the sum of the first 8 terms of the AP 7, 11, 15, …? (a) 336 (b) 35 (c) 168 (d) 184
39. 39.The mean of 9 numbers is 24. When the number 14 is added to them, what is the new mean? (a) 19 (b) 23 (c) 24 (d) 22
40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13

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