Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 328 · 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.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 125 cu cm (c) 100 cu cm (d) 15 cu cm
2. 2.What is the sum of the first 8 terms of the AP 4, 5, 6, …? (a) 120 (b) 60 (c) 64 (d) 11
3. 3.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 864 sq cm (d) 576 sq cm
4. 4.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 105° (d) 85°
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
6. 6.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
7. 7.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 155° (b) 140° (c) 115° (d) 65°
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
9. 9.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
10. 10.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 156 (d) 91
11. 11.A bag has 11 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 12 (d) 17
12. 12.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 2 (d) 1
13. 13.What is the midpoint of the line joining (4, 8) and (6, 16)? (a) (5, 12) (b) (12, 5) (c) (10, 24) (d) (1, 4)
14. 14.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 140° (c) 40° (d) 100°
15. 15.Two angles of a triangle are 20° and 80°. What is the exterior angle at the third corner? (a) 260° (b) 80° (c) 100° (d) 160°
16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
17. 17.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 15 (d) 21
18. 18.What is the mode of 10, 18, 10, 12, 12, 7 and 10? (a) 18 (b) 12 (c) 10 (d) 7
19. 19.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
20. 20.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 64 cu cm (d) 12 cu cm
21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 37 (c) 380 (d) 190
22. 22.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 200° (b) 160° (c) 20° (d) 100°
23. 23.A bag has 5 yellow balls and 8 blue 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) 13 (c) 9 (d) 6
24. 24.What is the product of the roots of x² − 10x + 21 = 0? (a) 21 (b) 20 (c) 10 (d) 22
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
26. 26.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
27. 27.In a class of 14 children, 6 like dance, 7 like music and 2 like both. How many like at least one of the two? (a) 11 (b) 14 (c) 13 (d) 9
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 14 (d) 4
29. 29.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 100° (c) 80° (d) 50°
30. 30.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 6 (c) 8 (d) 16
31. 31.A bag has 5 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 2 (c) 6 (d) 14
32. 32.In which quadrant does the point (1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 9 (b) 8 (c) 7 (d) 6
34. 34.In a class of 27 children, 20 like mangoes, 14 like bananas and 8 like both. How many like only mangoes? (a) 20 (b) 6 (c) 13 (d) 12
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
36. 36.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
37. 37.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
38. 38.What is the sum of the roots of x² − 10x + 24 = 0? (a) 9 (b) 11 (c) 24 (d) 10
39. 39.In a class of 44 children, 18 like mangoes, 29 like bananas and 11 like both. How many like neither? (a) 19 (b) 9 (c) 11 (d) 8
40. 40.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7

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