Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 864 · 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.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 72 (b) 36 (c) 12 (d) 42
2. 2.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) 15 (c) 7 (d) 14
3. 3.What is the midpoint of the line joining (8, 7) and (16, 5)? (a) (24, 12) (b) (12, 6) (c) (6, 12) (d) (4, 1)
4. 4.In which quadrant does the point (−5, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
6. 6.What is the sum of the roots of x² − 16x + 63 = 0? (a) 16 (b) 15 (c) 17 (d) 63
7. 7.If a + b = 15 and ab = 50, what is a² + b²? (a) 125 (b) 175 (c) 225 (d) 325
8. 8.What is the 16th term of the AP 10, 18, 26, 34, …? (a) 130 (b) 138 (c) 120 (d) 128
9. 9.A cuboid is 11 cm long, 4 cm wide and 3 cm high. What is its total surface area? (a) 356 sq cm (b) 132 sq cm (c) 178 sq cm (d) 89 sq cm
10. 10.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 56 (d) 16
11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
12. 12.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 30° (d) 150°
13. 13.A bag has 9 red, 5 blue and 8 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/22 (b) 13/22 (c) 9/13 (d) 1/3
14. 14.A drawer has lots of blue, yellow 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) 3 (b) 6 (c) 4 (d) 2
15. 15.What is the mean of 7, 15, 6, 14 and 18? (a) 15 (b) 10 (c) 12 (d) 13
16. 16.How many factors does 37 have? (a) 1 (b) 4 (c) 2 (d) 3
17. 17.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 30 (c) 33 (d) 10
18. 18.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3599 (b) 3491 (c) 3721 (d) 3481
19. 19.What is the midpoint of the line joining (3, 2) and (11, 10)? (a) (6, 7) (b) (14, 12) (c) (4, 4) (d) (7, 6)
20. 20.In a class of 38 children, 26 like cricket, 10 like football and 7 like both. How many like at least one of the two? (a) 36 (b) 38 (c) 22 (d) 29
21. 21.A drawer has lots of white 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) 4 (b) 5 (c) 2 (d) 3
22. 22.A bag has 6 blue, 4 red and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 11/15 (b) 1/15 (c) 2/3 (d) 1/3
23. 23.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
24. 24.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 100° (c) 160° (d) 81°
25. 25.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 145° (b) 95° (c) 85° (d) 120°
26. 26.What is the median of 11, 31, 39, 37, 13, 26 and 33? (a) 26 (b) 33 (c) 31 (d) 37
27. 27.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 25° (b) 65° (c) 295° (d) 115°
28. 28.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
29. 29.A drawer has lots of 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) 3 (b) 4 (c) 2 (d) 5
30. 30.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 145° (d) 150°
31. 31.What is the midpoint of the line joining (5, 11) and (13, 3)? (a) (4, 4) (b) (7, 9) (c) (9, 7) (d) (18, 14)
32. 32.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 60° (d) 140°
33. 33.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2⁴ × 3
34. 34.In a class of 36 children, 14 like dance, 20 like music and 7 like both. How many like neither? (a) 9 (b) 16 (c) 2 (d) 7
35. 35.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3604 (b) 3364 (c) 3854 (d) 3844
36. 36.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 80° (b) 100° (c) 145° (d) 115°
37. 37.The mean of 7 numbers is 38. When the number 46 is added to them, what is the new mean? (a) 40 (b) 42 (c) 38 (d) 39
38. 38.What is the missing term in the AP 10, 13, 16, ?, 22? (a) 18 (b) 19 (c) 22 (d) 20
39. 39.8 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) 48 (b) 11 (c) 24 (d) 32
40. 40.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 24 (c) 10 (d) 21

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