Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 983 · 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.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 11) (b) (x + 1)(x + 27) (c) (x − 3)(x − 9) (d) (x + 3)(x + 9)
2. 2.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
3. 3.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) 27 (c) 9 (d) 30
4. 4.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 7744 (b) 8474 (c) 8464 (d) 8104
5. 5.What is the mode of 13, 18, 13, 14, 14, 14 and 2? (a) 13 (b) 2 (c) 18 (d) 14
6. 6.In a class of 24 children, 11 like cricket, 10 like football and 2 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 3
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
8. 8.A bag has 3 black balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 4 (c) 15 (d) 5
9. 9.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) 15 (c) 45 (d) 5
10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
12. 12.A bag has 7 white balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 13 (c) 8 (d) 2
13. 13.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
14. 14.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
15. 15.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 45 (d) 90
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
17. 17.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 21 (b) 14 (c) 15 (d) 13
18. 18.If a + b = 6 and ab = 5, what is (a − b)²? (a) 16 (b) 4 (c) 26 (d) 36
19. 19.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 11 (d) 1
20. 20.4 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) 9 (c) 20 (d) 24
21. 21.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 2 (d) 23
22. 22.What is the midpoint of the line joining (10, 11) and (12, 9)? (a) (11, 10) (b) (10, 11) (c) (1, 1) (d) (22, 20)
23. 23.What is the sum of all the whole numbers from 1 to 39? (a) 780 (b) 741 (c) 781 (d) 1560
24. 24.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 42 (c) 36 (d) 12
25. 25.The mean of 3 numbers is 20. When the number 16 is added to them, what is the new mean? (a) 20 (b) 19 (c) 18 (d) 21
26. 26.What is the distance between the points (7, 18) and (19, 9)? (a) 225 (b) 15 (c) 16 (d) 21
27. 27.A drawer has lots of yellow, blue, 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) 2 (b) 8 (c) 5 (d) 4
28. 28.Which term of the AP 17, 25, 33, 41, … is 113? (a) 15th (b) 14th (c) 13th (d) 12th
29. 29.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
30. 30.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1774 (b) 1764 (c) 1604 (d) 1444
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
32. 32.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
33. 33.A bag has 8 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 9 (c) 13 (d) 2
34. 34.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
35. 35.A bag has 3 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 14 (c) 4 (d) 2
36. 36.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
37. 37.How many factors does 81 have? (a) 3 (b) 6 (c) 5 (d) 4
38. 38.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2² × 3 × 5
39. 39.The mean of 4 numbers is 25. When the number 15 is added to them, what is the new mean? (a) 25 (b) 20 (c) 23 (d) 24
40. 40.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 140° (d) 280°

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