Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 525 · 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 fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
2. 2.In a class of 17 children, 12 like maths, 11 like science and 1 like neither. How many like both? (a) 16 (b) 1 (c) 7 (d) 6
3. 3.What is the missing term in the AP 16, 23, ?, 37, 44? (a) 30 (b) 37 (c) 31 (d) 29
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 9 (b) 6 (c) 8 (d) 7
5. 5.A drawer has lots of green 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) 3 (c) 2 (d) 5
6. 6.What is the median of 9, 38, 19, 20 and 2? (a) 9 (b) 20 (c) 19 (d) 18
7. 7.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 144 (d) 24
8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 14 (d) 21
9. 9.In a class of 40 children, 22 like cricket, 23 like football and 8 like both. How many like only cricket? (a) 17 (b) 14 (c) 15 (d) 22
10. 10.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
11. 11.A bag has 8 yellow, 9 white and 2 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 10/19 (b) 1/3 (c) 9/19 (d) 9/10
12. 12.What is the 20th term of the AP 8, 17, 26, 35, …? (a) 179 (b) 188 (c) 171 (d) 180
13. 13.What is the mean of 14, 4, 11, 2 and 4? (a) 7 (b) 8 (c) 9 (d) 6
14. 14.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1326 (c) 1352 (d) 1378
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
16. 16.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 96 (b) 20 (c) 90 (d) 180
17. 17.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 270° (c) 90° (d) 125°
18. 18.The numbers 2 to 10 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) 54 (c) 6 (d) 18
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 36 (d) 24
20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
21. 21.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 90 (c) 19 (d) 84
22. 22.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 14 (d) 8
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 28 (d) 29
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
25. 25.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 105° (b) 115° (c) 40° (d) 140°
26. 26.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 16 (d) 12
27. 27.If a + b = 19 and ab = 84, what is (a − b)²? (a) 193 (b) 361 (c) 25 (d) 5
28. 28.A drawer has lots of yellow, red, black, blue 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) 2 (b) 5 (c) 6 (d) 10
29. 29.What is the mean of 3, 13, 7 and 21? (a) 10 (b) 13 (c) 12 (d) 11
30. 30.Which term of the AP 15, 17, 19, 21, … is 49? (a) 18th (b) 20th (c) 17th (d) 19th
31. 31.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2² × 5 × 7
32. 32.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 110° (b) 125° (c) 55° (d) 235°
33. 33.The mean of 8 numbers is 27. When the number 18 is added to them, what is the new mean? (a) 27 (b) 25 (c) 28 (d) 26
34. 34.What is the midpoint of the line joining (3, 3) and (9, 13)? (a) (8, 6) (b) (6, 8) (c) (12, 16) (d) (3, 5)
35. 35.In a class of 32 children, 14 like mangoes, 15 like bananas and 6 like both. How many like only mangoes? (a) 14 (b) 9 (c) 17 (d) 8
36. 36.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 27 (c) 81 (d) 9
37. 37.What are the roots of x² − 15x + 56 = 0? (a) 7 and 8 (b) 1 and 14 (c) 1 and 56 (d) 2 and 28
38. 38.What is the sum of the roots of x² − 9x + 20 = 0? (a) 20 (b) 8 (c) 10 (d) 9
39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 65° (c) 155° (d) 130°
40. 40.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 18 (c) 5 (d) 15

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