Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 989 · 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.What is the mode of 6, 3, 12, 11, 12, 12 and 11? (a) 6 (b) 12 (c) 11 (d) 3
2. 2.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 135° (c) 80° (d) 100°
3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 16 (b) 15 (c) 4 (d) 14
4. 4.In a class of 35 children, 23 like tea, 18 like coffee and 8 like both. How many like at least one of the two? (a) 25 (b) 41 (c) 35 (d) 33
5. 5.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3³
6. 6.What is the midpoint of the line joining (5, 17) and (17, 7)? (a) (11, 12) (b) (22, 24) (c) (12, 11) (d) (6, 5)
7. 7.What is the mean of 18, 15, 4, 16, 10 and 21? (a) 15 (b) 13 (c) 12 (d) 14
8. 8.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
9. 9.What is the sum of the roots of x² − 8x + 12 = 0? (a) 7 (b) 8 (c) 9 (d) 12
10. 10.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 812 (c) 378 (d) 406
11. 11.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 603 (c) 604 (d) 594
12. 12.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times
13. 13.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 130° (b) 160° (c) 50° (d) 70°
14. 14.If a + b = 13 and ab = 42, what is (a − b)²? (a) 127 (b) 1 (c) 85 (d) 169
15. 15.In a class of 40 children, 15 like maths, 24 like science and 5 like neither. How many like both? (a) 5 (b) 35 (c) 3 (d) 4
16. 16.What is the median of 10, 29, 25, 4 and 12? (a) 16 (b) 12 (c) 25 (d) 10
17. 17.A drawer has lots of green, black 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) 3 (b) 6 (c) 4 (d) 2
18. 18.What is the 29th term of the AP 6, 8, 10, 12, …? (a) 58 (b) 62 (c) 56 (d) 64
19. 19.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 63 (d) 7
20. 20.In a class of 38 children, 23 like mangoes, 19 like bananas and 12 like both. How many like only mangoes? (a) 7 (b) 19 (c) 11 (d) 23
21. 21.A bag has 4 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 6 (c) 11 (d) 2
22. 22.In a class of 36 children, 13 like dance, 22 like music and 2 like both. How many like only dance? (a) 20 (b) 13 (c) 14 (d) 11
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
24. 24.In a class of 38 children, 9 like mangoes, 24 like bananas and 5 like both. How many like only mangoes? (a) 9 (b) 14 (c) 19 (d) 4
25. 25.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 51 (c) 144 (d) 16
26. 26.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 144 cu cm (d) 216 cu cm
27. 27.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°
28. 28.What is the median of 17, 3, 38, 31 and 7? (a) 31 (b) 38 (c) 17 (d) 7
29. 29.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 3 (c) 4 (d) 5
31. 31.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
32. 32.In a class of 28 children, 24 like maths, 7 like science and 1 like neither. How many like both? (a) 27 (b) 1 (c) 4 (d) 3
33. 33.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 110° (d) 35°
34. 34.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 162 (b) 153 (c) 25 (d) 306
35. 35.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 5) (b) (x + 1)(x + 8) (c) (x − 2)(x − 4) (d) (x + 2)(x + 4)
36. 36.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 98 (c) 90 (d) 89
37. 37.A bag has 11 blue balls and 5 white 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) 12 (c) 16 (d) 6
38. 38.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
39. 39.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 140° (b) 65° (c) 105° (d) 115°
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times

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