Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 617 · 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 book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 126 (c) 144 (d) 136
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
3. 3.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
4. 4.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 42 (c) 21 (d) 49
5. 5.What is the sum of the first 12 terms of the AP 10, 13, 16, …? (a) 318 (b) 336 (c) 636 (d) 43
6. 6.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 270° (b) 140° (c) 130° (d) 90°
7. 7.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 110° (b) 70° (c) 90° (d) 160°
8. 8.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
10. 10.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 40 (c) 25 (d) 9
11. 11.A bag has 10 green balls and 4 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) 5 (c) 14 (d) 11
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
13. 13.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
14. 14.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
15. 15.What is the median of 18, 6, 1, 36 and 25? (a) 18 (b) 25 (c) 1 (d) 6
16. 16.What is the 17th term of the AP 6, 15, 24, 33, …? (a) 159 (b) 153 (c) 150 (d) 144
17. 17.In a class of 28 children, 16 like tea, 16 like coffee and 5 like both. How many like only tea? (a) 5 (b) 11 (c) 16 (d) 12
18. 18.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 9 (b) 11 (c) 13 (d) 10
19. 19.A drawer has lots of green, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 6 (d) 4
20. 20.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 110 (d) 66
21. 21.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7066 (b) 7056 (c) 6416 (d) 5776
22. 22.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 170° (c) 10° (d) 190°
23. 23.A bag has 8 green balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 2 (c) 12 (d) 10
24. 24.A bag has 9 white balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 19 (d) 11
25. 25.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 39 (d) 36
26. 26.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 105 (c) 196 (d) 91
27. 27.What is the prime factorisation of 40? (a) 2² × 5 (b) 2 × 5³ (c) 2³ × 5 (d) 2⁴ × 5
28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
29. 29.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
30. 30.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/8 (d) 3/4
31. 31.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
32. 32.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
33. 33.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
34. 34.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
35. 35.What is the distance between the points (0, 13) and (5, 1)? (a) 14 (b) 17 (c) 13 (d) 169
36. 36.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 115° (c) 85° (d) 160°
37. 37.In a class of 32 children, 12 like mangoes, 17 like bananas and 5 like neither. How many like both? (a) 5 (b) 2 (c) 3 (d) 27
38. 38.How many factors does 30 have? (a) 7 (b) 6 (c) 9 (d) 8
39. 39.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 60 (c) 30 (d) 36
40. 40.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3

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