Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 672 · 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 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 154 (c) 144 (d) 153
2. 2.What is the smallest prime factor of 51? (a) 17 (b) 1 (c) 2 (d) 3
3. 3.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 3/5 (d) 1/4
4. 4.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 80° (d) 130°
5. 5.What is the midpoint of the line joining (2, 12) and (12, 4)? (a) (14, 16) (b) (5, 4) (c) (7, 8) (d) (8, 7)
6. 6.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
7. 7.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
8. 8.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 155° (d) 130°
9. 9.A bag has 3 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 9 (d) 7
10. 10.A bag has 6 red, 6 white and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 6/17 (c) 12/17 (d) 11/17
11. 11.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 182 (d) 174
12. 12.A drawer has lots of yellow, red, black, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
15. 15.A bag has 4 white, 4 blue and 6 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/7 (b) 1/3 (c) 2/5 (d) 2/7
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
17. 17.In a class of 23 children, 8 like maths, 10 like science and 4 like both. How many like at least one of the two? (a) 18 (b) 23 (c) 10 (d) 14
18. 18.The mean of 8 numbers is 29. When the number 20 is added to them, what is the new mean? (a) 28 (b) 27 (c) 29 (d) 30
19. 19.In a class of 33 children, 14 like dance, 11 like music and 2 like both. How many like at least one of the two? (a) 25 (b) 23 (c) 33 (d) 21
20. 20.In a class of 19 children, 11 like tea, 10 like coffee and 3 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 1
21. 21.What is the sum of all the whole numbers from 1 to 34? (a) 1190 (b) 595 (c) 561 (d) 578
22. 22.In a class of 30 children, 24 like mangoes, 13 like bananas and 10 like both. How many like only mangoes? (a) 24 (b) 17 (c) 3 (d) 14
23. 23.The mean of 4 numbers is 37. When the number 27 is added to them, what is the new mean? (a) 37 (b) 32 (c) 35 (d) 36
24. 24.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 45°
25. 25.In a class of 45 children, 23 like dance, 28 like music and 2 like neither. How many like both? (a) 6 (b) 43 (c) 8 (d) 2
26. 26.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 69 (b) 864 (c) 468 (d) 432
27. 27.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 30 (d) 21
29. 29.Which term of the AP 12, 18, 24, 30, … is 162? (a) 28th (b) 25th (c) 26th (d) 27th
30. 30.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 45 (c) 17 (d) 90
32. 32.In a class of 34 children, 20 like mangoes, 20 like bananas and 6 like neither. How many like both? (a) 13 (b) 6 (c) 28 (d) 12
33. 33.What is the smallest prime factor of 69? (a) 1 (b) 23 (c) 3 (d) 2
34. 34.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 65° (b) 160° (c) 85° (d) 115°
35. 35.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
36. 36.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 14 (d) 49
37. 37.What is the distance between the points (6, 6) and (10, 9)? (a) 6 (b) 5 (c) 7 (d) 25
38. 38.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) 2 (b) 4 (c) 3 (d) 5
39. 39.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
40. 40.What is the sum of all the whole numbers from 1 to 65? (a) 2145 (b) 2146 (c) 4290 (d) 2080

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