Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 204 · 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.What is the smallest prime factor of 247? (a) 2 (b) 1 (c) 13 (d) 19
2. 2.What is the midpoint of the line joining (3, 13) and (11, 7)? (a) (7, 10) (b) (4, 3) (c) (14, 20) (d) (10, 7)
3. 3.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
4. 4.5 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) 20 (b) 7 (c) 10 (d) 15
5. 5.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
7. 7.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 78 (d) 91
8. 8.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 295° (c) 25° (d) 115°
9. 9.A bag has 4 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 12 (c) 6 (d) 2
10. 10.What is the median of 38, 4, 20, 7, 24, 15 and 31? (a) 7 (b) 15 (c) 20 (d) 24
11. 11.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 22 (c) 69 (d) 198
12. 12.A bag has 4 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 9 (c) 6 (d) 2
13. 13.How many factors does 102 have? (a) 6 (b) 7 (c) 9 (d) 8
14. 14.What is the mean of 17, 14, 8, 5, 5 and 17? (a) 10 (b) 11 (c) 13 (d) 12
15. 15.In a class of 49 children, 25 like cricket, 28 like football and 10 like both. How many like only cricket? (a) 15 (b) 25 (c) 21 (d) 18
16. 16.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
17. 17.4 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) 8 (b) 20 (c) 32 (d) 16
18. 18.A drawer has lots of blue 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) 3 (b) 2 (c) 4 (d) 5
19. 19.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 18 (c) 8 (d) 15
20. 20.A bag has 12 red balls and 7 white 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) 19 (c) 8 (d) 13
21. 21.In a class of 24 children, 17 like maths, 6 like science and 2 like both. How many like at least one of the two? (a) 21 (b) 23 (c) 24 (d) 19
22. 22.What is the mode of 8, 10, 18, 10, 8, 8 and 6? (a) 18 (b) 10 (c) 6 (d) 8
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 21 (c) 22 (d) 28
24. 24.The mean of 9 numbers is 23. When the number 33 is added to them, what is the new mean? (a) 23 (b) 28 (c) 25 (d) 24
25. 25.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6399 (b) 6251 (c) 6241 (d) 6561
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
27. 27.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 40 (b) 11 (c) 35 (d) 70
28. 28.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
29. 29.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 144 (d) 24
30. 30.A bag has 10 green balls and 5 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) 11 (c) 6 (d) 15
31. 31.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
32. 32.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) 36 (d) 49
33. 33.A bag has 4 green, 3 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 8/15 (b) 1/3 (c) 7/15 (d) 7/8
34. 34.How many factors does 103 have? (a) 4 (b) 3 (c) 1 (d) 2
35. 35.What is the mode of 13, 11, 8, 8, 13, 8 and 4? (a) 13 (b) 11 (c) 8 (d) 4
36. 36.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
37. 37.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 35° (c) 130° (d) 25°
38. 38.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 135° (c) 136° (d) 315°
39. 39.If a + b = 19 and ab = 84, what is (a − b)²? (a) 361 (b) 193 (c) 5 (d) 25
40. 40.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120

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