Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 529 · 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) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
2. 2.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
3. 3.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 3/4 (d) 1/8
4. 4.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
5. 5.What is the distance between the points (6, 2) and (14, 17)? (a) 23 (b) 17 (c) 18 (d) 289
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 36 (c) 42 (d) 11
7. 7.A bag has 7 blue, 4 red and 3 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 6/7 (c) 3/14 (d) 11/14
8. 8.What is the mode of 8, 10, 2, 2, 2, 14 and 10? (a) 10 (b) 8 (c) 2 (d) 14
9. 9.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 162 (d) 144
10. 10.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 6889 (b) 5929 (c) 5939 (d) 6391
11. 11.In a class of 38 children, 18 like cricket, 26 like football and 12 like both. How many like at least one of the two? (a) 38 (b) 32 (c) 44 (d) 20
12. 12.What are the roots of x² − 15x + 54 = 0? (a) 1 and 54 (b) 2 and 27 (c) 1 and 14 (d) 6 and 9
13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
14. 14.What is the mode of 8, 16, 16, 16, 1, 5 and 8? (a) 5 (b) 1 (c) 16 (d) 8
15. 15.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/6 (c) 1/3 (d) 1/5
16. 16.A bag has 4 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 14 (c) 2 (d) 6
17. 17.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 13 (b) 8 (c) 10 (d) 12
19. 19.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 14 (d) 45
20. 20.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 411 (d) 346
21. 21.What is the smallest prime factor of 49? (a) 3 (b) 7 (c) 2 (d) 1
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/11 (c) 2/11 (d) 1/12
24. 24.In a class of 20 children, 13 like cricket, 8 like football and 3 like both. How many like at least one of the two? (a) 21 (b) 15 (c) 18 (d) 20
25. 25.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x + 2)(x + 8) (c) (x − 2)(x − 8) (d) (x + 1)(x + 16)
26. 26.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
27. 27.A bag has 11 green balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 12 (d) 23
28. 28.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 66° (d) 115°
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
30. 30.In a class of 29 children, 17 like maths, 20 like science and 9 like both. How many like neither? (a) 10 (b) 2 (c) 1 (d) 9
31. 31.A bag has 8 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 2 (c) 9 (d) 10
32. 32.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 11 (b) 8 (c) 10 (d) 9
33. 33.In a class of 36 children, 21 like mangoes, 12 like bananas and 5 like both. How many like neither? (a) 8 (b) 13 (c) 3 (d) 5
34. 34.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 80 sq cm (c) 66 sq cm (d) 132 sq cm
35. 35.What is the sum of the roots of x² − 5x + 6 = 0? (a) 7 (b) 6 (c) 4 (d) 5
36. 36.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 10) (c) (x + 5)(x + 6) (d) (x + 1)(x + 30)
37. 37.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
38. 38.A bag has 3 black balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 13 (d) 15
39. 39.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 264 (c) 254 (d) 274
40. 40.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 105° (d) 115°

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