Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 710 · 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.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 160° (b) 20° (c) 145° (d) 55°
2. 2.What is the distance between the points (2, 3) and (17, 11)? (a) 17 (b) 289 (c) 23 (d) 18
3. 3.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 56 (d) 28
4. 4.A bag has 5 blue balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 2 (c) 7 (d) 6
5. 5.A bag has 6 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 13 (c) 8 (d) 2
6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 90 (d) 45
7. 7.In a class of 26 children, 10 like tea, 17 like coffee and 5 like both. How many like only tea? (a) 9 (b) 12 (c) 10 (d) 5
8. 8.What is the midpoint of the line joining (2, 3) and (8, 11)? (a) (5, 7) (b) (10, 14) (c) (7, 5) (d) (3, 4)
9. 9.Two angles of a triangle are 45° and 115°. What is the third angle? (a) 135° (b) 160° (c) 65° (d) 20°
10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 120 (c) 25 (d) 240
11. 11.What is the distance between the points (8, 4) and (11, 0)? (a) 5 (b) 25 (c) 7 (d) 6
12. 12.What is the 26th term of the AP 2, 7, 12, 17, …? (a) 132 (b) 130 (c) 125 (d) 127
13. 13.In a class of 42 children, 21 like tea, 23 like coffee and 1 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 41
14. 14.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 150 cu cm (c) 15 cu cm (d) 125 cu cm
15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
16. 16.Which is the correct factorisation of x² + 14x + 45? (a) (x − 5)(x − 9) (b) (x + 1)(x + 45) (c) (x + 1)(x + 13) (d) (x + 5)(x + 9)
17. 17.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 20° (d) 290°
18. 18.What is the midpoint of the line joining (1, 18) and (3, 8)? (a) (1, 5) (b) (4, 26) (c) (13, 2) (d) (2, 13)
19. 19.In a class of 20 children, 6 like cricket, 9 like football and 7 like neither. How many like both? (a) 13 (b) 2 (c) 7 (d) 3
20. 20.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
21. 21.The numbers 1 to 9 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) 5 (c) 15 (d) 45
22. 22.What is the mean of 10, 12, 18 and 12? (a) 12 (b) 15 (c) 14 (d) 13
23. 23.A drawer has lots of yellow, black, white, 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) 10 (b) 2 (c) 5 (d) 6
24. 24.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 135° (c) 65° (d) 115°
25. 25.The mean of 4 numbers is 13. When the number 28 is added to them, what is the new mean? (a) 13 (b) 15 (c) 16 (d) 17
26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
27. 27.If a + b = 21 and ab = 108, what is (a − b)²? (a) 225 (b) 9 (c) 441 (d) 3
28. 28.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
30. 30.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2628 (c) 2592 (d) 5256
31. 31.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 14) (c) (x + 6)(x + 9) (d) (x + 1)(x + 54)
32. 32.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
33. 33.What is the 28th term of the AP 4, 12, 20, 28, …? (a) 216 (b) 224 (c) 220 (d) 228
34. 34.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
35. 35.What is the distance between the points (3, 26) and (10, 2)? (a) 31 (b) 625 (c) 25 (d) 26
36. 36.What is the distance between the points (6, 7) and (18, 2)? (a) 14 (b) 17 (c) 169 (d) 13
37. 37.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 23 (c) 69 (d) 207
38. 38.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
39. 39.What is the sum of the first 8 terms of the AP 8, 10, 12, …? (a) 240 (b) 128 (c) 120 (d) 22
40. 40.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 60°

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