Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 46 · 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.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
2. 2.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3² (d) 2 × 3
3. 3.If a + b = 15 and ab = 36, what is a² + b²? (a) 225 (b) 189 (c) 297 (d) 153
4. 4.In a class of 23 children, 9 like mangoes, 19 like bananas and 6 like both. How many like at least one of the two? (a) 16 (b) 28 (c) 23 (d) 22
5. 5.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 140° (c) 40° (d) 41°
6. 6.What is the prime factorisation of 56? (a) 2² × 7 (b) 2 × 7³ (c) 2³ × 7 (d) 2⁴ × 7
7. 7.What is the mean of 14, 20, 20, 4 and 22? (a) 17 (b) 15 (c) 16 (d) 20
8. 8.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 3/8 (c) 1/4 (d) 7/8
9. 9.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
10. 10.What are the roots of x² − 7x + 10 = 0? (a) 1 and 10 (b) 2 and 5 (c) 1 and 6 (d) 3 and 4
11. 11.If a + b = 19 and ab = 90, what is a² + b²? (a) 541 (b) 181 (c) 271 (d) 361
12. 12.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 1/7 (d) 7/8
13. 13.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 7 (d) 15
14. 14.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 253 (c) 242 (d) 231
15. 15.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
16. 16.A bag has 3 yellow, 2 green and 2 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/5 (b) 5/7 (c) 1/3 (d) 2/7
17. 17.In a class of 23 children, 8 like tea, 13 like coffee and 2 like both. How many like at least one of the two? (a) 17 (b) 23 (c) 19 (d) 21
18. 18.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
19. 19.How many factors does 54 have? (a) 8 (b) 9 (c) 6 (d) 7
20. 20.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
21. 21.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 138 (d) 137
22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 11 (b) 21 (c) 36 (d) 42
23. 23.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
24. 24.In a class of 33 children, 12 like maths, 17 like science and 3 like both. How many like only maths? (a) 14 (b) 12 (c) 16 (d) 9
25. 25.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
26. 26.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) 45 (b) 126 (c) 42 (d) 14
27. 27.What is the distance between the points (7, 0) and (11, 3)? (a) 25 (b) 6 (c) 5 (d) 7
28. 28.What is the sum of the first 7 terms of the AP 4, 8, 12, …? (a) 28 (b) 126 (c) 224 (d) 112
29. 29.3 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 36 (c) 18 (d) 21
30. 30.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 1/4 (d) 5/8
31. 31.What is the distance between the points (6, 18) and (11, 6)? (a) 13 (b) 14 (c) 169 (d) 17
32. 32.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
34. 34.What is the distance between the points (8, 3) and (16, 18)? (a) 23 (b) 289 (c) 18 (d) 17
35. 35.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 3 (d) 11
36. 36.A bag has 4 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) 5 (b) 2 (c) 9 (d) 6
37. 37.In a class of 30 children, 18 like mangoes, 16 like bananas and 1 like neither. How many like both? (a) 5 (b) 4 (c) 29 (d) 1
38. 38.In a class of 32 children, 22 like tea, 13 like coffee and 6 like neither. How many like both? (a) 6 (b) 9 (c) 3 (d) 26
39. 39.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
40. 40.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 5486 (b) 4356 (c) 5476 (d) 4916

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