Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 332 · 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 mean of 3 numbers is 18. When the number 30 is added to them, what is the new mean? (a) 18 (b) 24 (c) 22 (d) 21
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
4. 4.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 130° (c) 50° (d) 230°
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
6. 6.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
7. 7.If a + b = 16 and ab = 60, what is a² + b²? (a) 256 (b) 376 (c) 196 (d) 136
8. 8.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 27 (d) 72
9. 9.What is the 39th term of the AP 9, 14, 19, 24, …? (a) 195 (b) 190 (c) 199 (d) 204
10. 10.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
12. 12.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
13. 13.In a class of 35 children, 13 like dance, 23 like music and 8 like neither. How many like both? (a) 1 (b) 8 (c) 27 (d) 9
14. 14.Which term of the AP 15, 21, 27, 33, … is 195? (a) 30th (b) 33rd (c) 31st (d) 32nd
15. 15.How many factors does 65 have? (a) 3 (b) 5 (c) 4 (d) 2
16. 16.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 24 (c) 11 (d) 32
17. 17.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.What is the smallest prime factor of 55? (a) 1 (b) 5 (c) 2 (d) 11
19. 19.The mean of 5 numbers is 11. When the number 29 is added to them, what is the new mean? (a) 15 (b) 14 (c) 11 (d) 20
20. 20.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 305° (c) 35° (d) 55°
21. 21.A bag has 10 green balls and 4 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) 11 (c) 5 (d) 14
22. 22.How many factors does 78 have? (a) 6 (b) 9 (c) 8 (d) 7
23. 23.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 635 (c) 625 (d) 225
24. 24.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 100 (c) 10 (d) 11
25. 25.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
26. 26.In a class of 33 children, 13 like cricket, 28 like football and 1 like neither. How many like both? (a) 1 (b) 8 (c) 9 (d) 32
27. 27.In a class of 31 children, 14 like tea, 17 like coffee and 10 like both. How many like neither? (a) 0 (b) 20 (c) 11 (d) 10
28. 28.The mean of 7 numbers is 12. When the number 20 is added to them, what is the new mean? (a) 14 (b) 16 (c) 13 (d) 12
29. 29.In a class of 15 children, 6 like maths, 9 like science and 2 like both. How many like only maths? (a) 7 (b) 4 (c) 6 (d) 2
30. 30.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 1/8 (d) 7/8
31. 31.In a class of 11 children, 7 like mangoes, 5 like bananas and 2 like both. How many like only mangoes? (a) 6 (b) 7 (c) 3 (d) 5
32. 32.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 99 (b) 180 (c) 18 (d) 90
33. 33.In a class of 35 children, 13 like maths, 22 like science and 5 like neither. How many like both? (a) 4 (b) 30 (c) 5 (d) 6
34. 34.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
35. 35.What is the midpoint of the line joining (1, 9) and (7, 11)? (a) (4, 10) (b) (10, 4) (c) (3, 1) (d) (8, 20)
36. 36.If a + b = 20 and ab = 99, what is (a − b)²? (a) 2 (b) 202 (c) 400 (d) 4
37. 37.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 115° (c) 65° (d) 50°
38. 38.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
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.A bag has 5 yellow, 3 green and 3 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 5/11 (b) 6/11 (c) 7/11 (d) 1/3

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