Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 808 · 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 missing term in the AP 20, 23, 26, ?, 32? (a) 28 (b) 30 (c) 29 (d) 32
2. 2.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) 15 (b) 5 (c) 18 (d) 45
3. 3.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
4. 4.What is the mode of 19, 15, 16, 16, 1, 19 and 16? (a) 16 (b) 19 (c) 1 (d) 15
5. 5.What is the distance between the points (4, 7) and (7, 11)? (a) 6 (b) 7 (c) 5 (d) 25
6. 6.What is the smallest prime factor of 217? (a) 1 (b) 31 (c) 7 (d) 2
7. 7.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
8. 8.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 40° (c) 220° (d) 140°
9. 9.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 125° (c) 100° (d) 155°
10. 10.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 140° (b) 100° (c) 120° (d) 80°
11. 11.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
12. 12.A bag has 8 blue balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 9 (c) 6 (d) 2
13. 13.A bag has 9 green balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 11 (d) 10
14. 14.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 475 (c) 474 (d) 465
15. 15.A drawer has lots of green, blue, red and yellow 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) 8 (c) 2 (d) 5
16. 16.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 30° (d) 15°
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
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 day of the week? (a) 14 (b) 21 (c) 15 (d) 22
20. 20.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 80°
21. 21.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
22. 22.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 178 (c) 196 (d) 187
23. 23.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 132 (d) 78
24. 24.What is the mode of 17, 11, 17, 18, 17, 8 and 18? (a) 11 (b) 8 (c) 17 (d) 18
25. 25.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 65° (c) 125° (d) 10°
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
27. 27.If a + b = 11 and ab = 10, what is (a − b)²? (a) 81 (b) 101 (c) 9 (d) 121
28. 28.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 3 (d) 4
29. 29.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
30. 30.In a class of 38 children, 30 like dance, 14 like music and 11 like both. How many like at least one of the two? (a) 22 (b) 33 (c) 44 (d) 38
31. 31.What is the mean of 6, 16, 15 and 19? (a) 15 (b) 13 (c) 14 (d) 16
32. 32.Two angles of a triangle are 35° and 100°. What is the third angle? (a) 135° (b) 80° (c) 145° (d) 45°
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
34. 34.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 28 (c) 21 (d) 9
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
36. 36.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
37. 37.In a class of 48 children, 29 like cricket, 24 like football and 11 like both. How many like neither? (a) 6 (b) 17 (c) 11 (d) 7
38. 38.A bag has 9 red, 2 green and 2 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 9/13 (c) 10/13 (d) 4/13
39. 39.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
40. 40.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 110° (c) 56° (d) 55°

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