Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 388 · 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.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 49 (d) 21
2. 2.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9
3. 3.There are 6 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) 30 (b) 48 (c) 24 (d) 10
4. 4.A bag has 12 blue balls and 8 yellow 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) 20 (c) 2 (d) 9
5. 5.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 155 (d) 146
6. 6.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
7. 7.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 5° (d) 95°
8. 8.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
9. 9.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 49 (b) 42 (c) 13 (d) 84
10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
12. 12.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) 14 (c) 8 (d) 7
13. 13.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 183 (c) 174 (d) 192
14. 14.The mean of 7 numbers is 25. When the number 9 is added to them, what is the new mean? (a) 24 (b) 23 (c) 25 (d) 17
15. 15.What is the distance between the points (7, 21) and (15, 6)? (a) 18 (b) 23 (c) 17 (d) 289
16. 16.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 33 (d) 289
17. 17.What is the distance between the points (7, 8) and (22, 16)? (a) 23 (b) 18 (c) 289 (d) 17
18. 18.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 45 (c) 90 (d) 20
19. 19.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
20. 20.A bag has 11 green balls and 10 blue 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) 2 (c) 21 (d) 11
21. 21.What is the 13th term of the AP 10, 19, 28, 37, …? (a) 127 (b) 117 (c) 118 (d) 108
22. 22.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 36 (d) 72
23. 23.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 88 cm (d) 44 cm
24. 24.In a class of 39 children, 23 like tea, 21 like coffee and 11 like both. How many like only tea? (a) 10 (b) 12 (c) 18 (d) 23
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
26. 26.Which is the correct factorisation of x² + 13x + 36? (a) (x − 4)(x − 9) (b) (x + 1)(x + 12) (c) (x + 4)(x + 9) (d) (x + 1)(x + 36)
27. 27.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 225° (d) 45°
28. 28.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 60° (d) 115°
29. 29.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 64 (d) 28
30. 30.What is the midpoint of the line joining (2, 10) and (12, 18)? (a) (7, 14) (b) (14, 28) (c) (5, 4) (d) (14, 7)
31. 31.A bag has 12 red balls and 13 blue 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) 14 (c) 25 (d) 2
32. 32.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
33. 33.How many factors does 23 have? (a) 1 (b) 3 (c) 2 (d) 4
34. 34.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 343 cu cm (c) 294 cu cm (d) 21 cu cm
35. 35.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 28 (c) 56 (d) 32
36. 36.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 86° (d) 85°
37. 37.What is the product of the roots of x² − 13x + 36 = 0? (a) 35 (b) 37 (c) 13 (d) 36
38. 38.What is the product of the roots of x² − 16x + 63 = 0? (a) 63 (b) 64 (c) 16 (d) 62
39. 39.What is the midpoint of the line joining (0, 5) and (2, 15)? (a) (1, 10) (b) (1, 5) (c) (10, 1) (d) (2, 20)
40. 40.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 586 (b) 416 (c) 576 (d) 256

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