Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 424 · 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.If a + b = 6 and ab = 8, what is (a − b)²? (a) 36 (b) 4 (c) 2 (d) 20
2. 2.What is the mean of 13, 13, 11 and 15? (a) 14 (b) 13 (c) 15 (d) 12
3. 3.What is the mean of 10, 15, 9 and 14? (a) 12 (b) 11 (c) 13 (d) 16
4. 4.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 25 (d) 10
5. 5.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 81 (c) 45 (d) 36
6. 6.A drawer has lots of blue, 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) 6 (c) 3 (d) 2
7. 7.What is the midpoint of the line joining (3, 14) and (5, 2)? (a) (4, 8) (b) (8, 4) (c) (8, 16) (d) (1, 6)
8. 8.In a class of 37 children, 26 like cricket, 14 like football and 10 like both. How many like only cricket? (a) 16 (b) 4 (c) 23 (d) 26
9. 9.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 82 cu cm (b) 12 cu cm (c) 6 cu cm (d) 42 cu cm
10. 10.What is the sum of the roots of x² − 13x + 42 = 0? (a) 14 (b) 12 (c) 42 (d) 13
11. 11.What is the distance between the points (8, 8) and (12, 5)? (a) 25 (b) 7 (c) 5 (d) 6
12. 12.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) 24 (b) 75 (c) 216 (d) 72
13. 13.What is the sum of the first 5 terms of the AP 1, 4, 7, …? (a) 70 (b) 38 (c) 13 (d) 35
14. 14.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 382 (c) 465 (d) 456
15. 15.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
16. 16.In a class of 45 children, 19 like mangoes, 24 like bananas and 10 like neither. How many like both? (a) 10 (b) 9 (c) 8 (d) 35
17. 17.What are the roots of x² − 7x + 12 = 0? (a) 1 and 12 (b) 1 and 6 (c) 2 and 6 (d) 3 and 4
18. 18.What is the distance between the points (0, 2) and (3, 6)? (a) 5 (b) 7 (c) 25 (d) 6
19. 19.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 164 (d) 163
20. 20.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 48 (d) 12
21. 21.In a class of 46 children, 26 like dance, 27 like music and 2 like neither. How many like both? (a) 2 (b) 7 (c) 9 (d) 44
22. 22.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 42 (c) 84 (d) 49
23. 23.In a class of 36 children, 20 like mangoes, 8 like bananas and 2 like both. How many like only mangoes? (a) 20 (b) 6 (c) 18 (d) 28
24. 24.What is the 19th term of the AP 6, 10, 14, 18, …? (a) 76 (b) 78 (c) 82 (d) 72
25. 25.In a class of 33 children, 15 like mangoes, 17 like bananas and 8 like both. How many like only mangoes? (a) 16 (b) 9 (c) 15 (d) 7
26. 26.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 7 (d) 5
27. 27.What is the median of 1, 25, 7, 5, 9, 11 and 37? (a) 5 (b) 7 (c) 9 (d) 11
28. 28.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) 21 (c) 15 (d) 14
29. 29.In a class of 26 children, 19 like tea, 15 like coffee and 12 like both. How many like at least one of the two? (a) 22 (b) 10 (c) 34 (d) 26
30. 30.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
31. 31.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5² (c) 2 × 5 (d) 2³ × 5
32. 32.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 7/8 (d) 3/8
33. 33.A bag has 7 red balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 10 (c) 8 (d) 2
34. 34.A drawer has lots of green, red, black, 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) 5 (b) 10 (c) 2 (d) 6
35. 35.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
36. 36.What is the 11th term of the AP 16, 23, 30, 37, …? (a) 86 (b) 70 (c) 93 (d) 77
37. 37.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 56) (c) (x − 7)(x − 8) (d) (x + 1)(x + 14)
38. 38.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 165° (b) 105° (c) 90° (d) 15°
39. 39.What is the midpoint of the line joining (2, 9) and (10, 17)? (a) (4, 4) (b) (6, 13) (c) (12, 26) (d) (13, 6)
40. 40.What is the distance between the points (8, 14) and (13, 2)? (a) 17 (b) 169 (c) 13 (d) 14

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