Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 882 · 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.A drawer has lots of blue, red, yellow 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) 8 (c) 5 (d) 2
2. 2.What is the mean of 5, 11, 12, 5 and 7? (a) 9 (b) 8 (c) 10 (d) 7
3. 3.What is the mean of 11, 7, 17 and 17? (a) 13 (b) 12 (c) 15 (d) 14
4. 4.In a class of 22 children, 9 like dance, 14 like music and 2 like neither. How many like both? (a) 1 (b) 20 (c) 2 (d) 3
5. 5.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) 18 (b) 54 (c) 6 (d) 21
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 14 (b) 3 (c) 13 (d) 15
7. 7.How many factors does 82 have? (a) 2 (b) 3 (c) 4 (d) 5
8. 8.What is the midpoint of the line joining (0, 2) and (6, 4)? (a) (6, 6) (b) (3, 3) (c) (3, 1) (d) (4, 3)
9. 9.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
10. 10.What is the sum of all the whole numbers from 1 to 61? (a) 1891 (b) 3782 (c) 1892 (d) 1830
11. 11.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 21 (d) 25
12. 12.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x + 2)(x + 8) (c) (x − 2)(x − 8) (d) (x + 1)(x + 16)
13. 13.What is the mode of 11, 6, 10, 14, 6, 11 and 11? (a) 10 (b) 11 (c) 6 (d) 14
14. 14.What is the median of 24, 36, 31, 2 and 3? (a) 31 (b) 24 (c) 25 (d) 3
15. 15.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
16. 16.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
17. 17.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 155° (b) 70° (c) 135° (d) 45°
18. 18.How many factors does 111 have? (a) 2 (b) 3 (c) 4 (d) 5
19. 19.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
20. 20.In a class of 32 children, 24 like mangoes, 12 like bananas and 3 like neither. How many like both? (a) 7 (b) 29 (c) 4 (d) 3
21. 21.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 11 (d) 1
22. 22.A bag has 9 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 2 (c) 21 (d) 11
23. 23.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 42 (c) 10 (d) 24
24. 24.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 35 (b) 171 (c) 342 (d) 189
25. 25.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 80° (b) 55° (c) 125° (d) 155°
26. 26.In a class of 27 children, 17 like maths, 19 like science and 1 like neither. How many like both? (a) 9 (b) 26 (c) 10 (d) 1
27. 27.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
28. 28.A drawer has lots of yellow, red, 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) 4 (b) 2 (c) 8 (d) 5
29. 29.In a class of 30 children, 24 like mangoes, 15 like bananas and 12 like both. How many like neither? (a) 3 (b) 12 (c) 4 (d) 15
30. 30.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 6) (b) (x + 1)(x + 4) (c) (x − 2)(x − 3) (d) (x + 2)(x + 3)
31. 31.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 308 sq cm
32. 32.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6399 (b) 6561 (c) 6251 (d) 6241
33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 21 (d) 30
34. 34.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) 21 (b) 14 (c) 15 (d) 22
35. 35.A drawer has lots of 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) 3 (b) 2 (c) 6 (d) 4
36. 36.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
37. 37.A drawer has lots of yellow, green, blue, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 5 (d) 2
38. 38.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
39. 39.In a class of 26 children, 18 like cricket, 15 like football and 4 like neither. How many like both? (a) 7 (b) 11 (c) 4 (d) 22
40. 40.If a + b = 12 and ab = 11, what is a² + b²? (a) 166 (b) 133 (c) 144 (d) 122

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