Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 951 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 16 (b) 17 (c) 6 (d) 18
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
3. 3.What is the 26th term of the AP 17, 23, 29, 35, …? (a) 173 (b) 156 (c) 150 (d) 167
4. 4.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 25° (d) 115°
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 1/18 (d) 2/11
6. 6.What is the mean of 18, 10, 7 and 9? (a) 10 (b) 13 (c) 11 (d) 12
7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 66 (d) 24
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
9. 9.What is the 17th term of the AP 15, 21, 27, 33, …? (a) 117 (b) 111 (c) 102 (d) 96
10. 10.What is the sum of all the whole numbers from 1 to 47? (a) 2256 (b) 1128 (c) 1081 (d) 1129
11. 11.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 8) (c) (x + 2)(x + 4) (d) (x + 1)(x + 5)
12. 12.What is the sum of all the whole numbers from 1 to 94? (a) 8930 (b) 4465 (c) 4371 (d) 4418
13. 13.Which is the correct factorisation of x² + 7x + 10? (a) (x − 2)(x − 5) (b) (x + 2)(x + 5) (c) (x + 1)(x + 6) (d) (x + 1)(x + 10)
14. 14.8 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 64 (b) 40 (c) 12 (d) 32
15. 15.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 35 (c) 11 (d) 28
16. 16.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 486 cu cm (c) 27 cu cm (d) 324 cu cm
17. 17.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
18. 18.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 12 (c) 9 (d) 6
19. 19.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 12 (c) 5 (d) 6
20. 20.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 37 (c) 49 (d) 36
21. 21.A bag has 3 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 4 (b) 5 (c) 2 (d) 9
22. 22.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/4 (c) 1/8 (d) 3/8
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
24. 24.A bag has 10 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 12 (c) 11 (d) 20
25. 25.What is the smallest prime factor of 55? (a) 1 (b) 5 (c) 11 (d) 2
26. 26.How many factors does 49 have? (a) 4 (b) 1 (c) 3 (d) 2
27. 27.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 18 (c) 17 (d) 72
28. 28.A bag has 7 red balls and 12 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) 8 (c) 19 (d) 13
29. 29.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/3 (c) 1/5 (d) 1/6
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
31. 31.What is the midpoint of the line joining (3, 6) and (7, 14)? (a) (10, 20) (b) (5, 10) (c) (2, 4) (d) (10, 5)
32. 32.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7
33. 33.What is the sum of all the whole numbers from 1 to 75? (a) 2850 (b) 2851 (c) 2775 (d) 5700
34. 34.A bag has 12 blue balls and 13 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 25 (b) 2 (c) 14 (d) 13
35. 35.What is the mean of 8, 7, 2, 20, 3 and 2? (a) 8 (b) 7 (c) 9 (d) 6
36. 36.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 40 (c) 12 (d) 32
37. 37.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 20 (d) 8
39. 39.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
40. 40.A bag has 9 blue balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 10 (c) 9 (d) 2

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