Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 235 · 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 midpoint of the line joining (0, 1) and (2, 5)? (a) (2, 6) (b) (1, 3) (c) (3, 1) (d) (1, 2)
2. 2.What is the distance between the points (0, 8) and (4, 11)? (a) 6 (b) 7 (c) 5 (d) 25
3. 3.What is the sum of all the whole numbers from 1 to 26? (a) 325 (b) 702 (c) 338 (d) 351
4. 4.The mean of 4 numbers is 19. When the number 14 is added to them, what is the new mean? (a) 19 (b) 20 (c) 17 (d) 18
5. 5.In a class of 33 children, 13 like cricket, 13 like football and 3 like both. How many like at least one of the two? (a) 33 (b) 26 (c) 23 (d) 20
6. 6.What is the 26th term of the AP 4, 7, 10, 13, …? (a) 78 (b) 82 (c) 75 (d) 79
7. 7.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 2 (d) 1
8. 8.A bag has 3 blue balls and 6 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) 4 (c) 9 (d) 7
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 1/6 (d) 7/36
10. 10.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2850 (c) 5852 (d) 2926
11. 11.A bag has 8 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) 13 (c) 9 (d) 6
12. 12.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 15 (d) 22
14. 14.If a + b = 16 and ab = 60, what is a² + b²? (a) 376 (b) 196 (c) 256 (d) 136
15. 15.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 2 (d) 1
16. 16.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) 8 (b) 14 (c) 7 (d) 15
17. 17.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 26° (c) 155° (d) 205°
18. 18.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 160° (d) 260°
19. 19.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
20. 20.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 597 (c) 606 (d) 476
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
22. 22.In a class of 35 children, 20 like maths, 16 like science and 9 like neither. How many like both? (a) 9 (b) 1 (c) 10 (d) 26
23. 23.In a class of 32 children, 12 like cricket, 25 like football and 8 like both. How many like only cricket? (a) 7 (b) 17 (c) 4 (d) 12
24. 24.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 20° (c) 160° (d) 320°
25. 25.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 65° (b) 155° (c) 115° (d) 90°
26. 26.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) 63 (b) 7 (c) 24 (d) 21
27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
28. 28.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
29. 29.The mean of 5 numbers is 16. When the number 10 is added to them, what is the new mean? (a) 16 (b) 13 (c) 14 (d) 15
30. 30.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 10 (c) 48 (d) 24
31. 31.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 264 (b) 37 (c) 150 (d) 132
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 14 (d) 13
33. 33.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 35 (c) 56 (d) 11
34. 34.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
35. 35.How many factors does 29 have? (a) 2 (b) 4 (c) 1 (d) 3
36. 36.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 207 (c) 72 (d) 23
37. 37.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 770 (b) 385 (c) 65 (d) 418
38. 38.A bag has 7 green, 9 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 7/23 (c) 16/23 (d) 17/23
39. 39.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 6 (d) 5
40. 40.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 270° (c) 125° (d) 90°

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