Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 331 · 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 two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
3. 3.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8474 (b) 8104 (c) 7744 (d) 8464
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
5. 5.What is the distance between the points (9, 12) and (25, 0)? (a) 28 (b) 21 (c) 400 (d) 20
6. 6.In a class of 26 children, 15 like mangoes, 16 like bananas and 8 like both. How many like at least one of the two? (a) 26 (b) 31 (c) 15 (d) 23
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
8. 8.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
9. 9.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 90° (b) 140° (c) 270° (d) 130°
10. 10.What is the mean of 7, 19, 3 and 15? (a) 13 (b) 11 (c) 10 (d) 12
11. 11.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
13. 13.In a class of 42 children, 28 like dance, 17 like music and 12 like both. How many like only dance? (a) 5 (b) 25 (c) 16 (d) 28
14. 14.In a class of 46 children, 27 like cricket, 24 like football and 7 like both. How many like neither? (a) 9 (b) 7 (c) 2 (d) 3
15. 15.8 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) 16 (b) 24 (c) 32 (d) 10
16. 16.What is the 39th term of the AP 10, 13, 16, 19, …? (a) 124 (b) 127 (c) 117 (d) 114
17. 17.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
18. 18.What is the mode of 15, 10, 19, 6, 19, 6 and 6? (a) 15 (b) 6 (c) 10 (d) 19
19. 19.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 25 (d) 15
20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 16 (d) 17
21. 21.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 55° (c) 125° (d) 105°
22. 22.Two angles of a triangle are 70° and 100°. What is the third angle? (a) 10° (b) 170° (c) 110° (d) 80°
23. 23.What is the mean of 8, 9, 4, 11 and 23? (a) 10 (b) 12 (c) 13 (d) 11
24. 24.A bag has 3 red, 5 blue and 9 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/12 (b) 5/17 (c) 12/17 (d) 1/3
25. 25.A drawer has lots of green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 4 (c) 2 (d) 3
26. 26.What is the 30th term of the AP 19, 21, 23, 25, …? (a) 60 (b) 79 (c) 58 (d) 77
27. 27.In a class of 25 children, 10 like dance, 10 like music and 5 like both. How many like only dance? (a) 6 (b) 5 (c) 10 (d) 15
28. 28.What is the 10th term of the AP 8, 12, 16, 20, …? (a) 36 (b) 44 (c) 48 (d) 40
29. 29.What is the 15th term of the AP 19, 23, 27, 31, …? (a) 75 (b) 56 (c) 60 (d) 79
30. 30.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 48 (d) 15
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
33. 33.A bag has 6 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) 18 (b) 13 (c) 2 (d) 7
34. 34.In a class of 35 children, 15 like dance, 26 like music and 9 like both. How many like neither? (a) 3 (b) 12 (c) 9 (d) 4
35. 35.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 144 (d) 132
36. 36.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 17 (c) 16 (d) 18
37. 37.In a class of 41 children, 22 like dance, 16 like music and 3 like both. How many like only dance? (a) 22 (b) 13 (c) 19 (d) 25
38. 38.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 12 (d) 7
39. 39.How many prime numbers are there between 70 and 90? (a) 6 (b) 4 (c) 5 (d) 7
40. 40.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 21 (d) 42

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