Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 934 · 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 35th term of the AP 6, 8, 10, 12, …? (a) 74 (b) 70 (c) 76 (d) 68
2. 2.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 48 (c) 40 (d) 80
3. 3.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 135° (c) 85° (d) 95°
4. 4.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) 216 (c) 75 (d) 72
5. 5.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x − 8)(x − 9)
6. 6.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 121 (d) 55
7. 7.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 91 (c) 22 (d) 94
8. 8.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
9. 9.What is the mean of 2, 3, 10, 4, 8 and 9? (a) 7 (b) 8 (c) 5 (d) 6
10. 10.What is the 23rd term of the AP 12, 21, 30, 39, …? (a) 210 (b) 207 (c) 219 (d) 198
11. 11.What is the mode of 16, 7, 4, 4, 3, 16 and 16? (a) 7 (b) 4 (c) 16 (d) 3
12. 12.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
13. 13.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 40 (c) 12 (d) 35
14. 14.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 5/8 (d) 3/8
15. 15.In a class of 48 children, 24 like dance, 25 like music and 9 like both. How many like neither? (a) 17 (b) 7 (c) 9 (d) 8
16. 16.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
17. 17.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
19. 19.What is the product of the roots of x² − 11x + 18 = 0? (a) 19 (b) 17 (c) 11 (d) 18
20. 20.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 270° (c) 90° (d) 145°
21. 21.Which term of the AP 3, 7, 11, 15, … is 139? (a) 36th (b) 37th (c) 35th (d) 34th
22. 22.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25
23. 23.A bag has 11 blue balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 9 (d) 19
24. 24.What is the 11th term of the AP 7, 11, 15, 19, …? (a) 47 (b) 40 (c) 51 (d) 44
25. 25.If a + b = 14 and ab = 24, what is (a − b)²? (a) 196 (b) 148 (c) 100 (d) 10
26. 26.A drawer has lots of blue 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) 2 (b) 3 (c) 5 (d) 4
27. 27.What is the missing term in the AP 17, 22, ?, 32, 37? (a) 27 (b) 32 (c) 26 (d) 28
28. 28.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 549 (c) 438 (d) 550
29. 29.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
30. 30.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 32 (d) 50
31. 31.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
32. 32.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 11 (c) 42 (d) 21
33. 33.If a + b = 16 and ab = 63, what is (a − b)²? (a) 4 (b) 256 (c) 130 (d) 2
34. 34.What is the sum of all the whole numbers from 1 to 67? (a) 2279 (b) 2211 (c) 4556 (d) 2278
35. 35.A bag has 4 yellow balls and 6 black 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) 7 (c) 10 (d) 5
36. 36.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 3 (d) 9
37. 37.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 7 (d) 29
38. 38.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 100° (b) 155° (c) 25° (d) 105°
39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
40. 40.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°

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