Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 415 · 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 are the roots of x² − 8x + 15 = 0? (a) 3 and 5 (b) 1 and 15 (c) 2 and 6 (d) 1 and 7
2. 2.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 153 (b) 25 (c) 162 (d) 306
3. 3.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 54 cu cm (c) 27 cu cm (d) 9 cu cm
4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
6. 6.What is the sum of the first 7 terms of the AP 8, 9, 10, …? (a) 14 (b) 77 (c) 78 (d) 154
7. 7.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
8. 8.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
9. 9.A bag has 5 yellow, 9 blue and 9 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 14/23 (b) 1/3 (c) 9/23 (d) 15/23
10. 10.A bag has 6 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 17 (c) 8 (d) 7
11. 11.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 12 (d) 48
12. 12.What is the mode of 18, 13, 18, 13, 11, 3 and 18? (a) 13 (b) 3 (c) 18 (d) 11
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 24 (d) 25
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
15. 15.What is the sum of the first 9 terms of the AP 10, 12, 14, …? (a) 171 (b) 26 (c) 162 (d) 324
16. 16.What is the mode of 19, 13, 12, 12, 13, 4 and 12? (a) 4 (b) 13 (c) 12 (d) 19
17. 17.In a class of 26 children, 13 like maths, 6 like science and 2 like both. How many like only maths? (a) 13 (b) 4 (c) 11 (d) 20
18. 18.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
19. 19.A drawer has lots of white, yellow, green, black 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) 5 (b) 6 (c) 10 (d) 2
20. 20.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
21. 21.If a + b = 20 and ab = 99, what is (a − b)²? (a) 4 (b) 400 (c) 2 (d) 202
22. 22.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 12 (d) 36
23. 23.A bag has 3 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 10 (c) 8 (d) 2
24. 24.A cube has edges of 6 cm. What is its volume? (a) 144 cu cm (b) 18 cu cm (c) 216 cu cm (d) 217 cu cm
25. 25.What is the distance between the points (9, 11) and (21, 2)? (a) 21 (b) 16 (c) 15 (d) 225
26. 26.What is the product of the roots of x² − 10x + 16 = 0? (a) 16 (b) 10 (c) 15 (d) 17
27. 27.In a class of 52 children, 27 like mangoes, 31 like bananas and 6 like neither. How many like both? (a) 6 (b) 12 (c) 46 (d) 13
28. 28.Which term of the AP 9, 17, 25, 33, … is 97? (a) 11th (b) 14th (c) 13th (d) 12th
29. 29.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) 22 (b) 15 (c) 14 (d) 21
30. 30.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 18 (c) 54 (d) 6
31. 31.In a class of 29 children, 16 like dance, 14 like music and 7 like both. How many like neither? (a) 6 (b) 13 (c) 5 (d) 7
32. 32.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 60 (c) 30 (d) 11
33. 33.In a class of 29 children, 12 like cricket, 17 like football and 6 like both. How many like at least one of the two? (a) 24 (b) 17 (c) 29 (d) 23
34. 34.Two angles of a triangle are 20° and 150°. What is the third angle? (a) 30° (b) 160° (c) 170° (d) 10°
35. 35.What is the sum of all the whole numbers from 1 to 78? (a) 3003 (b) 3042 (c) 3081 (d) 6162
36. 36.If a + b = 12 and ab = 20, what is (a − b)²? (a) 144 (b) 8 (c) 104 (d) 64
37. 37.What is the sum of the first 7 terms of the AP 2, 6, 10, …? (a) 98 (b) 26 (c) 112 (d) 196
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
39. 39.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
40. 40.There are 6 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 30 (c) 48 (d) 24

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