Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 700 · 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.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 85° (b) 120° (c) 25° (d) 155°
2. 2.The mean of 3 numbers is 31. When the number 35 is added to them, what is the new mean? (a) 32 (b) 33 (c) 31 (d) 34
3. 3.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
4. 4.Which term of the AP 11, 17, 23, 29, … is 95? (a) 16th (b) 15th (c) 17th (d) 14th
5. 5.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/4 (c) 3/8 (d) 1/8
6. 6.In a class of 41 children, 22 like mangoes, 23 like bananas and 12 like both. How many like neither? (a) 20 (b) 9 (c) 12 (d) 8
7. 7.A bag has 5 green, 8 white and 6 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 14/19 (b) 15/19 (c) 5/19 (d) 1/3
8. 8.What is the mode of 13, 10, 5, 10, 5, 16 and 10? (a) 5 (b) 13 (c) 16 (d) 10
9. 9.The mean of 5 numbers is 29. When the number 23 is added to them, what is the new mean? (a) 27 (b) 29 (c) 28 (d) 26
10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
11. 11.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 187 (c) 196 (d) 178
12. 12.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 1235 (b) 925 (c) 1225 (d) 625
13. 13.What is the mode of 2, 15, 2, 15, 13, 2 and 3? (a) 15 (b) 3 (c) 13 (d) 2
14. 14.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x − 6)(x − 8) (c) (x + 6)(x + 8) (d) (x + 1)(x + 48)
15. 15.The mean of 5 numbers is 24. When the number 30 is added to them, what is the new mean? (a) 26 (b) 24 (c) 25 (d) 27
16. 16.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 24 (c) 72 (d) 216
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
18. 18.What is the median of 5, 38, 9, 31 and 35? (a) 9 (b) 32 (c) 31 (d) 35
19. 19.In a class of 37 children, 21 like mangoes, 17 like bananas and 11 like both. How many like neither? (a) 10 (b) 21 (c) 11 (d) 9
20. 20.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 115°
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 4 (c) 15 (d) 16
22. 22.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 33 cu cm (c) 1331 cu cm (d) 726 cu cm
23. 23.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
24. 24.What are the roots of x² − 11x + 30 = 0? (a) 1 and 10 (b) 2 and 15 (c) 5 and 6 (d) 1 and 30
25. 25.What is the distance between the points (6, 22) and (14, 7)? (a) 18 (b) 289 (c) 17 (d) 23
26. 26.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
27. 27.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
28. 28.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 110° (b) 115° (c) 45° (d) 135°
29. 29.If a + b = 17 and ab = 72, what is a² + b²? (a) 145 (b) 289 (c) 217 (d) 433
30. 30.In a class of 22 children, 14 like mangoes, 8 like bananas and 5 like both. How many like at least one of the two? (a) 12 (b) 22 (c) 17 (d) 18
31. 31.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 144 (c) 78 (d) 156
32. 32.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
33. 33.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
34. 34.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
35. 35.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 140° (d) 100°
36. 36.If a + b = 19 and ab = 88, what is (a − b)²? (a) 9 (b) 3 (c) 185 (d) 361
37. 37.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3844 (b) 3604 (c) 3364 (d) 3854
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 56 (d) 64
40. 40.A drawer has lots of yellow and red 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) 3 (c) 4 (d) 5

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