Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 799 · 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.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 163 (d) 172
2. 2.How many prime numbers are there between 80 and 110? (a) 7 (b) 9 (c) 6 (d) 8
3. 3.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
4. 4.In a class of 24 children, 5 like mangoes, 19 like bananas and 2 like neither. How many like both? (a) 1 (b) 2 (c) 22 (d) 3
5. 5.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
6. 6.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
7. 7.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
8. 8.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
9. 9.In a class of 48 children, 20 like mangoes, 27 like bananas and 10 like neither. How many like both? (a) 8 (b) 10 (c) 9 (d) 38
10. 10.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
11. 11.What is the distance between the points (2, 20) and (7, 8)? (a) 169 (b) 13 (c) 17 (d) 14
12. 12.A cuboid is 7 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 100 cu cm (b) 56 cu cm (c) 14 cu cm (d) 13 cu cm
13. 13.A drawer has lots of black 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) 4 (b) 2 (c) 3 (d) 5
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 1/6 (d) 5/6
15. 15.A drawer has lots of green, red, blue, black 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) 6 (b) 2 (c) 5 (d) 10
16. 16.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
17. 17.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
19. 19.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
20. 20.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 95° (d) 85°
21. 21.The mean of 6 numbers is 31. When the number 10 is added to them, what is the new mean? (a) 29 (b) 27 (c) 31 (d) 28
22. 22.In a class of 28 children, 23 like dance, 12 like music and 8 like both. How many like neither? (a) 8 (b) 9 (c) 1 (d) 2
23. 23.In a class of 35 children, 13 like mangoes, 22 like bananas and 3 like neither. How many like both? (a) 2 (b) 3 (c) 32 (d) 4
24. 24.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 486 (c) 487 (d) 477
25. 25.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 90° (d) 46°
26. 26.The mean of 9 numbers is 27. When the number 37 is added to them, what is the new mean? (a) 27 (b) 32 (c) 29 (d) 28
27. 27.Which is the correct factorisation of x² + 11x + 24? (a) (x + 3)(x + 8) (b) (x − 3)(x − 8) (c) (x + 1)(x + 10) (d) (x + 1)(x + 24)
28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 25 (c) 240 (d) 20
29. 29.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 180 (d) 20
30. 30.What is the median of 36, 38, 24, 35 and 32? (a) 24 (b) 35 (c) 36 (d) 33
31. 31.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 42 (d) 70
32. 32.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
33. 33.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 170° (d) 85°
34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
36. 36.In a class of 39 children, 12 like tea, 24 like coffee and 10 like neither. How many like both? (a) 10 (b) 7 (c) 29 (d) 8
37. 37.How many factors does 110 have? (a) 7 (b) 9 (c) 6 (d) 8
38. 38.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
39. 39.How many prime numbers are there between 90 and 110? (a) 6 (b) 5 (c) 4 (d) 7
40. 40.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 60 (c) 42 (d) 51

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