Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 355 · 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.In a class of 16 children, 9 like tea, 7 like coffee and 2 like neither. How many like both? (a) 1 (b) 3 (c) 14 (d) 2
2. 2.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 49 (b) 28 (c) 13 (d) 56
3. 3.If a + b = 21 and ab = 108, what is (a − b)²? (a) 441 (b) 9 (c) 225 (d) 3
4. 4.What is the median of 29, 40, 38, 30 and 1? (a) 31 (b) 29 (c) 38 (d) 30
5. 5.What is the mean of 19, 5, 4, 12, 15 and 23? (a) 14 (b) 15 (c) 12 (d) 13
6. 6.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 8 (b) 6 (c) 5 (d) 9
8. 8.A drawer has lots of yellow and blue 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) 5 (c) 3 (d) 4
9. 9.What is the distance between the points (7, 10) and (22, 2)? (a) 18 (b) 17 (c) 23 (d) 289
10. 10.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 45° (c) 115° (d) 110°
11. 11.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
12. 12.The mean of 8 numbers is 26. When the number 62 is added to them, what is the new mean? (a) 26 (b) 30 (c) 31 (d) 44
13. 13.A drawer has lots of green and black 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) 4 (c) 3 (d) 5
14. 14.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
15. 15.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
16. 16.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 155° (d) 125°
17. 17.Using (a − b)² = a² − 2ab + b², what is 25²? (a) 635 (b) 875 (c) 625 (d) 1225
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 8 (b) 5 (c) 7 (d) 6
19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
20. 20.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 28 (d) 49
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
22. 22.A drawer has lots of black and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 3
23. 23.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 39 (d) 108
24. 24.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 5635 (b) 4225 (c) 5625 (d) 4925
25. 25.In a class of 39 children, 15 like mangoes, 22 like bananas and 6 like both. How many like only mangoes? (a) 9 (b) 17 (c) 16 (d) 15
26. 26.In a class of 34 children, 21 like maths, 13 like science and 10 like both. How many like neither? (a) 10 (b) 20 (c) 0 (d) 11
27. 27.In a class of 36 children, 13 like dance, 19 like music and 4 like both. How many like only dance? (a) 9 (b) 13 (c) 15 (d) 17
28. 28.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 7/8 (d) 1/8
29. 29.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/8 (d) 1/4
30. 30.In a class of 35 children, 19 like dance, 19 like music and 5 like both. How many like only dance? (a) 14 (b) 16 (c) 5 (d) 19
31. 31.If a + b = 13 and ab = 30, what is (a − b)²? (a) 49 (b) 169 (c) 109 (d) 7
32. 32.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
33. 33.A bag has 12 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 14 (c) 15 (d) 13
34. 34.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 86 (c) 96 (d) 104
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
36. 36.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
37. 37.A bag has 8 blue balls and 12 red 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) 20 (c) 13 (d) 9
38. 38.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 27 cu cm (c) 324 cu cm (d) 486 cu cm
40. 40.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)

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