Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 210 · 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. 1.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
2. 2.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
3. 3.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 2 (d) 1
4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
5. 5.A drawer has lots of red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 2 (d) 3
6. 6.What is the missing term in the AP 4, 6, 8, ?, 12? (a) 9 (b) 10 (c) 11 (d) 12
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
8. 8.What is the smallest prime factor of 187? (a) 2 (b) 17 (c) 1 (d) 11
9. 9.The mean of 3 numbers is 21. When the number 33 is added to them, what is the new mean? (a) 25 (b) 27 (c) 21 (d) 24
10. 10.A bag has 2 yellow, 2 blue and 4 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/8 (b) 1/8 (c) 1/3 (d) 1/2
11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 15 (d) 21
12. 12.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
13. 13.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 45°
14. 14.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
15. 15.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 55 (d) 121
16. 16.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 90° (d) 270°
17. 17.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
18. 18.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 621 (c) 622 (d) 486
19. 19.If a + b = 13 and ab = 22, what is a² + b²? (a) 147 (b) 125 (c) 213 (d) 169
20. 20.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 24 (c) 216 (d) 75
21. 21.In a class of 27 children, 16 like maths, 16 like science and 8 like both. How many like at least one of the two? (a) 32 (b) 24 (c) 27 (d) 16
22. 22.In a class of 35 children, 18 like mangoes, 17 like bananas and 5 like both. How many like only mangoes? (a) 18 (b) 5 (c) 12 (d) 13
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
24. 24.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 80° (b) 100° (c) 140° (d) 120°
25. 25.A bag has 4 black balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 5 (c) 6 (d) 14
26. 26.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 541 (c) 271 (d) 181
27. 27.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 105° (d) 15°
28. 28.In a class of 45 children, 29 like dance, 18 like music and 9 like neither. How many like both? (a) 11 (b) 36 (c) 2 (d) 9
29. 29.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 65 (b) 80 (c) 25 (d) 130
30. 30.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 24 (d) 48
31. 31.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/4 (d) 1/8
32. 32.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
33. 33.In a class of 28 children, 13 like dance, 11 like music and 3 like both. How many like at least one of the two? (a) 21 (b) 28 (c) 24 (d) 18
34. 34.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 308 (b) 19 (c) 154 (d) 155
35. 35.In a class of 39 children, 16 like maths, 26 like science and 10 like both. How many like at least one of the two? (a) 42 (b) 22 (c) 32 (d) 39
36. 36.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 125 cu cm (c) 150 cu cm (d) 100 cu cm
37. 37.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
38. 38.A bag has 11 yellow 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) 5 (b) 12 (c) 15 (d) 2
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
40. 40.A drawer has lots of green and blue 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) 4 (d) 5

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