Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 944 · 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.The mean of 4 numbers is 33. When the number 23 is added to them, what is the new mean? (a) 32 (b) 33 (c) 28 (d) 31
2. 2.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
3. 3.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 130° (d) 80°
4. 4.What is the prime factorisation of 21? (a) 3 × 7 (b) 3² × 7 (c) 3³ × 7 (d) 3 × 7²
5. 5.What is the 14th term of the AP 6, 8, 10, 12, …? (a) 32 (b) 26 (c) 28 (d) 34
6. 6.In a class of 42 children, 22 like cricket, 18 like football and 2 like both. How many like at least one of the two? (a) 40 (b) 42 (c) 38 (d) 36
7. 7.What is the 36th term of the AP 7, 11, 15, 19, …? (a) 144 (b) 147 (c) 140 (d) 151
8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 20 (d) 25
9. 9.What is the median of 25, 37, 35, 30 and 7? (a) 35 (b) 25 (c) 30 (d) 31
10. 10.What is the mean of 4, 15, 4, 17 and 10? (a) 10 (b) 9 (c) 12 (d) 11
11. 11.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
12. 12.What is the mean of 12, 7, 14, 11 and 6? (a) 11 (b) 9 (c) 12 (d) 10
13. 13.A bag has 6 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 7 (c) 2 (d) 6
14. 14.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
15. 15.What is the mean of 5, 2, 16, 13, 7 and 17? (a) 12 (b) 10 (c) 11 (d) 9
16. 16.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 42 (c) 36 (d) 72
17. 17.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 36 (b) 70 (c) 8 (d) 35
18. 18.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
19. 19.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4851 (c) 9702 (d) 4753
20. 20.A drawer has lots of yellow and red 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) 4 (c) 5 (d) 3
21. 21.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 899 (b) 851 (c) 841 (d) 961
22. 22.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 216 sq cm (d) 144 sq cm
23. 23.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) 15 (b) 14 (c) 22 (d) 21
24. 24.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 4 (d) 5
25. 25.In a class of 37 children, 21 like maths, 12 like science and 5 like both. How many like at least one of the two? (a) 33 (b) 37 (c) 28 (d) 23
26. 26.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/7 (c) 1/8 (d) 7/8
27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
28. 28.In a class of 39 children, 24 like tea, 15 like coffee and 5 like both. How many like at least one of the two? (a) 35 (b) 34 (c) 39 (d) 29
29. 29.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
30. 30.A bag has 4 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 16 (b) 5 (c) 2 (d) 6
31. 31.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 12) (b) (x + 2)(x + 6) (c) (x + 1)(x + 7) (d) (x − 2)(x − 6)
32. 32.What is the sum of the first 9 terms of the AP 2, 3, 4, …? (a) 108 (b) 10 (c) 54 (d) 55
33. 33.In a class of 26 children, 20 like cricket, 13 like football and 9 like both. How many like only cricket? (a) 11 (b) 20 (c) 13 (d) 4
34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 16 (d) 12
35. 35.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
36. 36.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 120 (c) 240 (d) 25
38. 38.A bag has 9 blue, 6 red and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 8/23 (c) 15/23 (d) 16/23
39. 39.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 35° (b) 110° (c) 145° (d) 290°
40. 40.If a + b = 16 and ab = 63, what is (a − b)²? (a) 2 (b) 256 (c) 130 (d) 4

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