Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 746 · 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 distance between the points (6, 8) and (15, 20)? (a) 225 (b) 21 (c) 16 (d) 15
2. 2.What is the distance between the points (9, 5) and (21, 14)? (a) 225 (b) 21 (c) 15 (d) 16
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
4. 4.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 60° (d) 30°
5. 5.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 160° (d) 155°
6. 6.A bag has 11 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 2 (c) 21 (d) 13
7. 7.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 132 (c) 144 (d) 78
8. 8.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) 28 (b) 21 (c) 29 (d) 22
9. 9.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 170° (d) 95°
10. 10.Two angles of a triangle are 50° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 105° (d) 75°
11. 11.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/8 (c) 1/4 (d) 3/4
12. 12.What is the mean of 15, 9, 8, 20 and 18? (a) 16 (b) 14 (c) 15 (d) 13
13. 13.A drawer has lots of red, yellow and white 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) 6 (d) 3
14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 470 (c) 588 (d) 597
15. 15.In a class of 34 children, 10 like cricket, 22 like football and 7 like both. How many like only cricket? (a) 10 (b) 3 (c) 15 (d) 12
16. 16.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) 12 (b) 16 (c) 6 (d) 2
17. 17.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
18. 18.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 529 (c) 193 (d) 277
19. 19.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 136 (c) 118 (d) 127
20. 20.A bag has 2 green, 5 red and 9 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/7 (b) 1/8 (c) 1/3 (d) 7/8
21. 21.In a class of 30 children, 12 like cricket, 18 like football and 3 like both. How many like at least one of the two? (a) 27 (b) 28 (c) 24 (d) 30
22. 22.How many factors does 74 have? (a) 5 (b) 2 (c) 3 (d) 4
23. 23.In a class of 35 children, 9 like maths, 22 like science and 4 like both. How many like only maths? (a) 9 (b) 13 (c) 18 (d) 5
24. 24.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 66 (c) 121 (d) 55
25. 25.What is the 25th term of the AP 12, 21, 30, 39, …? (a) 216 (b) 225 (c) 228 (d) 237
26. 26.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
27. 27.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 5 (d) 6
28. 28.What is the 34th term of the AP 5, 11, 17, 23, …? (a) 203 (b) 198 (c) 209 (d) 204
29. 29.What is the midpoint of the line joining (9, 10) and (13, 20)? (a) (2, 5) (b) (22, 30) (c) (15, 11) (d) (11, 15)
30. 30.How many factors does 118 have? (a) 5 (b) 2 (c) 4 (d) 3
31. 31.Which term of the AP 3, 8, 13, 18, … is 63? (a) 13th (b) 15th (c) 12th (d) 14th
32. 32.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
33. 33.A drawer has lots of white, yellow, blue, green 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) 10 (b) 2 (c) 5 (d) 6
34. 34.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x + 6)(x + 9) (c) (x + 1)(x + 54) (d) (x − 6)(x − 9)
35. 35.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 12 (c) 35 (d) 70
36. 36.What is the midpoint of the line joining (1, 0) and (9, 8)? (a) (4, 5) (b) (4, 4) (c) (5, 4) (d) (10, 8)
37. 37.A drawer has lots of yellow, green and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3
38. 38.What is the missing term in the AP 1, 3, ?, 7, 9? (a) 7 (b) 5 (c) 4 (d) 6
39. 39.How many prime numbers are there between 80 and 100? (a) 2 (b) 3 (c) 4 (d) 5
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12

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