Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 115 · 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 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 45 (d) 14
2. 2.In a class of 30 children, 11 like mangoes, 13 like bananas and 4 like both. How many like neither? (a) 14 (b) 4 (c) 10 (d) 6
3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 28 (b) 13 (c) 56 (d) 49
4. 4.A drawer has lots of black, blue, white and red 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) 4 (c) 8 (d) 5
5. 5.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
7. 7.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
8. 8.What is the product of the roots of x² − 17x + 72 = 0? (a) 73 (b) 72 (c) 17 (d) 71
9. 9.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
11. 11.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
12. 12.A cuboid is 9 cm long, 6 cm wide and 8 cm high. What is its total surface area? (a) 432 sq cm (b) 696 sq cm (c) 348 sq cm (d) 174 sq cm
13. 13.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 1 (d) 2
14. 14.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 132 cu cm (b) 17 cu cm (c) 36 cu cm (d) 72 cu cm
15. 15.If a + b = 18 and ab = 72, what is (a − b)²? (a) 36 (b) 6 (c) 324 (d) 180
16. 16.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
17. 17.What is the distance between the points (6, 7) and (22, 19)? (a) 400 (b) 28 (c) 21 (d) 20
18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
19. 19.What is the mean of 2, 19, 15, 6, 17 and 7? (a) 12 (b) 11 (c) 10 (d) 13
20. 20.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 35°
21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
22. 22.What is the 40th term of the AP 20, 26, 32, 38, …? (a) 240 (b) 234 (c) 260 (d) 254
23. 23.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 51 sq cm (b) 54 sq cm (c) 102 sq cm (d) 204 sq cm
24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 169 (c) 25 (d) 91
25. 25.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 8 (c) 20 (d) 15
26. 26.What is the 15th term of the AP 6, 13, 20, 27, …? (a) 98 (b) 104 (c) 111 (d) 105
27. 27.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
28. 28.What is the smallest prime factor of 39? (a) 3 (b) 1 (c) 13 (d) 2
29. 29.What is the missing term in the AP 6, ?, 18, 24, 30? (a) 18 (b) 13 (c) 12 (d) 11
30. 30.In a class of 46 children, 29 like tea, 20 like coffee and 12 like both. How many like neither? (a) 21 (b) 9 (c) 10 (d) 12
31. 31.What is the median of 21, 13, 26, 8 and 5? (a) 21 (b) 26 (c) 13 (d) 8
32. 32.In a class of 34 children, 9 like cricket, 19 like football and 2 like both. How many like only cricket? (a) 17 (b) 15 (c) 9 (d) 7
33. 33.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 150° (b) 60° (c) 300° (d) 120°
34. 34.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 17 (c) 8 (d) 18
36. 36.What is the sum of the first 8 terms of the AP 2, 4, 6, …? (a) 144 (b) 80 (c) 72 (d) 16
37. 37.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 95° (c) 100° (d) 15°
38. 38.In a class of 28 children, 15 like mangoes, 10 like bananas and 5 like neither. How many like both? (a) 5 (b) 23 (c) 3 (d) 2
39. 39.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 120° (c) 60° (d) 300°
40. 40.What is the 34th term of the AP 5, 8, 11, 14, …? (a) 104 (b) 102 (c) 99 (d) 107

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