Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 624 · 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.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 27 (c) 8 (d) 72
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
3. 3.The mean of 7 numbers is 10. When the number 26 is added to them, what is the new mean? (a) 12 (b) 13 (c) 10 (d) 18
4. 4.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 20 (b) 220 (c) 120 (d) 110
5. 5.In a class of 13 children, 8 like mangoes, 8 like bananas and 4 like both. How many like at least one of the two? (a) 8 (b) 12 (c) 13 (d) 16
6. 6.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 10 (d) 25
7. 7.What is the midpoint of the line joining (2, 5) and (4, 1)? (a) (1, 2) (b) (6, 6) (c) (4, 3) (d) (3, 3)
8. 8.In a class of 35 children, 10 like dance, 20 like music and 2 like both. How many like neither? (a) 9 (b) 5 (c) 7 (d) 2
9. 9.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 176 (c) 352 (d) 26
10. 10.A bag has 3 green balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 4 (d) 6
11. 11.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 145° (b) 75° (c) 140° (d) 40°
12. 12.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3² (d) 2² × 3
13. 13.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 7 (c) 21 (d) 24
14. 14.The mean of 3 numbers is 26. When the number 34 is added to them, what is the new mean? (a) 30 (b) 29 (c) 26 (d) 28
15. 15.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 21 (d) 36
16. 16.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3³ × 5 × 7
17. 17.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 30° (b) 150° (c) 55° (d) 155°
18. 18.What is the missing term in the AP 18, 20, ?, 24, 26? (a) 22 (b) 24 (c) 23 (d) 21
19. 19.A bag has 8 yellow, 5 green and 5 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 4/9 (c) 11/18 (d) 5/9
20. 20.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 120° (c) 30° (d) 60°
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
22. 22.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
23. 23.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 80° (c) 50° (d) 260°
24. 24.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 45 (d) 18
25. 25.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
26. 26.A cuboid is 10 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 90 cu cm (b) 23 cu cm (c) 332 cu cm (d) 360 cu cm
27. 27.What is the distance between the points (1, 2) and (13, 11)? (a) 16 (b) 15 (c) 21 (d) 225
28. 28.What is the distance between the points (3, 6) and (27, 13)? (a) 25 (b) 31 (c) 625 (d) 26
29. 29.The mean of 3 numbers is 18. When the number 26 is added to them, what is the new mean? (a) 22 (b) 18 (c) 21 (d) 20
30. 30.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 25 (b) 18 (c) 17 (d) 19
31. 31.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 176 (c) 186 (d) 185
32. 32.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 105° (c) 75° (d) 76°
33. 33.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 72 (c) 45 (d) 81
34. 34.In a class of 22 children, 9 like dance, 11 like music and 6 like both. How many like at least one of the two? (a) 20 (b) 8 (c) 14 (d) 22
35. 35.What is the prime factorisation of 63? (a) 3 × 7 (b) 3² × 7 (c) 3 × 7² (d) 3³ × 7
36. 36.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 40° (c) 120° (d) 60°
37. 37.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
38. 38.A bag has 7 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 6 (c) 8 (d) 2
39. 39.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 135° (d) 95°
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 343 sq cm (d) 49 sq cm

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