Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 824 · 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.If a + b = 13 and ab = 42, what is (a − b)²? (a) 1 (b) 169 (c) 127 (d) 85
2. 2.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 294 cu cm (d) 196 cu cm
3. 3.What is the 16th term of the AP 13, 15, 17, 19, …? (a) 45 (b) 43 (c) 32 (d) 30
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
5. 5.A bag has 12 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 2 (c) 14 (d) 13
6. 6.What is the missing term in the AP 16, ?, 30, 37, 44? (a) 22 (b) 30 (c) 24 (d) 23
7. 7.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 320 (b) 312 (c) 337 (d) 329
8. 8.What is the distance between the points (4, 6) and (16, 22)? (a) 21 (b) 400 (c) 20 (d) 28
9. 9.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
12. 12.What is the mean of 9, 11, 10 and 6? (a) 12 (b) 8 (c) 9 (d) 10
13. 13.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
14. 14.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) 11 (b) 56 (c) 32 (d) 28
15. 15.A bag has 2 blue, 3 red and 3 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/8 (b) 3/4 (c) 1/3 (d) 5/8
16. 16.Which term of the AP 4, 6, 8, 10, … is 32? (a) 14th (b) 15th (c) 16th (d) 17th
17. 17.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
18. 18.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
19. 19.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 15 (c) 10 (d) 20
20. 20.What is the median of 31, 14, 12, 25 and 3? (a) 25 (b) 12 (c) 14 (d) 17
21. 21.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2209 (b) 2809 (c) 2509 (d) 2819
22. 22.In a class of 28 children, 17 like cricket, 11 like football and 3 like both. How many like at least one of the two? (a) 28 (b) 25 (c) 26 (d) 22
23. 23.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 3 (d) 0
24. 24.7 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) 13 (b) 49 (c) 42 (d) 84
25. 25.A bag has 5 yellow, 8 white and 5 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 5/18 (c) 7/9 (d) 13/18
26. 26.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 53 (c) 54 (d) 44
27. 27.What is the 36th term of the AP 19, 26, 33, 40, …? (a) 252 (b) 271 (c) 264 (d) 245
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
29. 29.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
30. 30.How many factors does 106 have? (a) 5 (b) 3 (c) 4 (d) 2
31. 31.What is the midpoint of the line joining (6, 4) and (12, 8)? (a) (9, 6) (b) (3, 2) (c) (18, 12) (d) (6, 9)
32. 32.In a class of 30 children, 11 like mangoes, 17 like bananas and 4 like neither. How many like both? (a) 4 (b) 3 (c) 26 (d) 2
33. 33.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
34. 34.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 2)(x + 4) (c) (x + 1)(x + 8) (d) (x + 1)(x + 5)
35. 35.What is the distance between the points (6, 6) and (9, 10)? (a) 6 (b) 25 (c) 5 (d) 7
36. 36.What is the distance between the points (9, 10) and (12, 6)? (a) 25 (b) 7 (c) 6 (d) 5
37. 37.In a class of 19 children, 12 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 15 (b) 20 (c) 10 (d) 19
38. 38.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 7/8 (d) 3/8
39. 39.A drawer has lots of yellow, blue, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 5 (d) 2
40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 19 (b) 9 (c) 18 (d) 20

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