Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 289 · 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 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) 22 (b) 198 (c) 66 (d) 69
2. 2.What is the sum of the first 5 terms of the AP 4, 8, 12, …? (a) 20 (b) 120 (c) 60 (d) 70
3. 3.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 7 (d) 24
4. 4.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 60° (d) 30°
5. 5.What is the midpoint of the line joining (6, 10) and (18, 6)? (a) (12, 8) (b) (24, 16) (c) (8, 12) (d) (6, 2)
6. 6.A bag has 12 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 18 (c) 14 (d) 13
7. 7.In a class of 32 children, 20 like tea, 23 like coffee and 12 like both. How many like at least one of the two? (a) 19 (b) 43 (c) 31 (d) 32
8. 8.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 25 (c) 24 (d) 13
9. 9.What is the midpoint of the line joining (3, 14) and (13, 8)? (a) (16, 22) (b) (8, 11) (c) (5, 3) (d) (11, 8)
10. 10.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81
11. 11.A bag has 7 red balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 18 (b) 8 (c) 2 (d) 9
12. 12.A bag has 11 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 12 (c) 2 (d) 13
13. 13.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
14. 14.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 105 (d) 91
15. 15.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 333 (c) 343 (d) 300
16. 16.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 9025 (b) 11035 (c) 11025 (d) 10025
17. 17.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
18. 18.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 306 (b) 279 (c) 55 (d) 558
19. 19.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 140° (d) 145°
20. 20.What is the mean of 19, 13, 5, 20 and 13? (a) 16 (b) 13 (c) 14 (d) 15
21. 21.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x − 6)(x − 8) (c) (x + 6)(x + 8) (d) (x + 1)(x + 48)
22. 22.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
23. 23.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 24 (d) 48
24. 24.If a + b = 13 and ab = 30, what is (a − b)²? (a) 49 (b) 7 (c) 169 (d) 109
25. 25.In a class of 28 children, 15 like cricket, 15 like football and 11 like both. How many like only cricket? (a) 13 (b) 11 (c) 15 (d) 4
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
27. 27.What is the mean of 8, 13, 3 and 16? (a) 9 (b) 11 (c) 8 (d) 10
28. 28.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 5 (c) 6 (d) 12
29. 29.What is the mode of 19, 18, 12, 18, 19, 11 and 19? (a) 19 (b) 12 (c) 18 (d) 11
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
31. 31.In which quadrant does the point (−7, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
32. 32.A drawer has lots of red 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) 3 (c) 2 (d) 4
33. 33.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
34. 34.What is the 11th term of the AP 18, 25, 32, 39, …? (a) 95 (b) 77 (c) 70 (d) 88
35. 35.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 361 (b) 451 (c) 401 (d) 441
36. 36.A bag has 9 black balls and 7 red 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) 16 (c) 8 (d) 10
37. 37.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
38. 38.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
39. 39.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
40. 40.What is the midpoint of the line joining (6, 3) and (18, 5)? (a) (24, 8) (b) (4, 12) (c) (6, 1) (d) (12, 4)

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