Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 499 · 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 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) 15 (b) 8 (c) 7 (d) 14
2. 2.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 50° (d) 140°
3. 3.In a class of 26 children, 6 like tea, 13 like coffee and 2 like both. How many like only tea? (a) 13 (b) 4 (c) 11 (d) 6
4. 4.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) 72 (b) 69 (c) 207 (d) 23
5. 5.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 72 (c) 216 (d) 24
6. 6.What is the distance between the points (7, 19) and (12, 7)? (a) 169 (b) 17 (c) 13 (d) 14
7. 7.In a class of 36 children, 11 like cricket, 26 like football and 7 like both. How many like neither? (a) 13 (b) 7 (c) 5 (d) 6
8. 8.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) 15 (b) 21 (c) 14 (d) 22
9. 9.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 264 cm (d) 1386 cm
10. 10.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 91 (c) 182 (d) 169
11. 11.What is the sum of all the whole numbers from 1 to 96? (a) 4560 (b) 4608 (c) 9312 (d) 4656
12. 12.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
13. 13.What is the sum of the first 7 terms of the AP 7, 8, 9, …? (a) 13 (b) 70 (c) 71 (d) 140
14. 14.What is the median of 32, 17, 12, 3, 5, 37 and 30? (a) 3 (b) 12 (c) 17 (d) 30
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/11 (c) 1/36 (d) 1/18
16. 16.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 280° (c) 140° (d) 80°
17. 17.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 70° (c) 30° (d) 60°
18. 18.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
19. 19.A drawer has lots of green, yellow, blue, red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 10 (d) 2
20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
21. 21.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
22. 22.What is the distance between the points (7, 24) and (14, 0)? (a) 26 (b) 25 (c) 31 (d) 625
23. 23.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
24. 24.A drawer has lots of 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) 3 (d) 4
25. 25.What is the median of 13, 22, 23, 5 and 20? (a) 22 (b) 20 (c) 23 (d) 13
26. 26.In a class of 41 children, 27 like mangoes, 21 like bananas and 12 like both. How many like neither? (a) 17 (b) 6 (c) 12 (d) 5
27. 27.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 21 (c) 10 (d) 42
28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 13 (d) 14
29. 29.A bag has 5 yellow, 9 white and 7 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/16 (c) 5/21 (d) 16/21
30. 30.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
31. 31.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
32. 32.If a + b = 19 and ab = 90, what is (a − b)²? (a) 1 (b) 271 (c) 361 (d) 181
33. 33.A drawer has lots of yellow, red, blue 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) 5 (d) 8
34. 34.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
36. 36.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 12 (c) 16 (d) 24
37. 37.A bag has 3 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 6 (c) 4 (d) 2
38. 38.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2 × 3²
39. 39.What is the mean of 2, 8, 12, 11 and 12? (a) 8 (b) 9 (c) 11 (d) 10
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10

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