Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 242 · 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 yellow, red, green 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) 4 (b) 2 (c) 8 (d) 5
2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
3. 3.What is the sum of the first 8 terms of the AP 1, 3, 5, …? (a) 72 (b) 15 (c) 64 (d) 128
4. 4.A bag has 6 white balls and 7 blue 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) 13 (d) 8
5. 5.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
6. 6.What is the missing term in the AP 11, 18, ?, 32, 39? (a) 25 (b) 26 (c) 24 (d) 32
7. 7.What is the median of 5, 29, 4, 3, 36, 10 and 2? (a) 5 (b) 3 (c) 4 (d) 10
8. 8.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) 207 (d) 69
9. 9.What is the mode of 2, 19, 1, 2, 18, 18 and 2? (a) 18 (b) 1 (c) 19 (d) 2
10. 10.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 1)(x + 24) (c) (x − 4)(x − 6) (d) (x + 4)(x + 6)
11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
12. 12.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) 66 (b) 22 (c) 69 (d) 198
13. 13.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 120 (c) 240 (d) 121
14. 14.What is the distance between the points (8, 8) and (20, 13)? (a) 17 (b) 169 (c) 13 (d) 14
15. 15.In a class of 45 children, 24 like cricket, 23 like football and 10 like neither. How many like both? (a) 12 (b) 2 (c) 35 (d) 10
16. 16.Two angles of a triangle are 40° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 105° (c) 75° (d) 140°
17. 17.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 22 (b) 32 (c) 24 (d) 23
18. 18.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 40° (c) 50° (d) 140°
19. 19.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
21. 21.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
23. 23.8 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) 40 (b) 13 (c) 48 (d) 80
24. 24.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
25. 25.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 6 times (d) 2 times
27. 27.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
28. 28.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 55° (c) 46° (d) 90°
29. 29.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
30. 30.In a class of 29 children, 8 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 26 (b) 27 (c) 29 (d) 23
31. 31.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2 × 7³ (c) 2² × 7 (d) 2⁴ × 7
32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 3/8 (d) 1/4
33. 33.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
34. 34.In a class of 33 children, 13 like mangoes, 26 like bananas and 9 like both. How many like at least one of the two? (a) 30 (b) 39 (c) 21 (d) 33
35. 35.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
36. 36.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 270° (c) 90° (d) 125°
37. 37.There are 4 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 28 (c) 32 (d) 11
38. 38.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 10609 (b) 10009 (c) 9409 (d) 10619
39. 39.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 15 (d) 18
40. 40.How many factors does 21 have? (a) 2 (b) 3 (c) 4 (d) 5

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