Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 570 · 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.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
3. 3.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
4. 4.Which term of the AP 4, 13, 22, 31, … is 346? (a) 39th (b) 40th (c) 38th (d) 41st
5. 5.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 40° (c) 100° (d) 140°
6. 6.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
7. 7.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 24 (d) 48
8. 8.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
9. 9.How many factors does 24 have? (a) 9 (b) 8 (c) 7 (d) 6
10. 10.What is the mean of 11, 13, 19, 6 and 6? (a) 13 (b) 11 (c) 10 (d) 12
11. 11.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 25 (d) 240
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
13. 13.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
14. 14.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 125° (b) 85° (c) 95° (d) 140°
15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
16. 16.In a class of 47 children, 30 like tea, 25 like coffee and 11 like both. How many like at least one of the two? (a) 47 (b) 33 (c) 44 (d) 55
17. 17.A bag has 12 green balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 20 (d) 13
18. 18.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
21. 21.Using (a + b)² = a² + 2ab + b², what is 44²? (a) 1296 (b) 1946 (c) 1616 (d) 1936
22. 22.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 42 (c) 10 (d) 21
23. 23.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
24. 24.What is the distance between the points (7, 4) and (19, 9)? (a) 169 (b) 17 (c) 14 (d) 13
25. 25.In a class of 41 children, 30 like cricket, 19 like football and 10 like both. How many like neither? (a) 10 (b) 12 (c) 3 (d) 2
26. 26.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
27. 27.In a class of 36 children, 21 like tea, 24 like coffee and 10 like both. How many like at least one of the two? (a) 25 (b) 45 (c) 36 (d) 35
28. 28.What is the midpoint of the line joining (0, 9) and (6, 5)? (a) (6, 14) (b) (7, 3) (c) (3, 7) (d) (3, 2)
29. 29.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
30. 30.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
32. 32.In a class of 12 children, 6 like cricket, 5 like football and 2 like both. How many like only cricket? (a) 3 (b) 6 (c) 7 (d) 4
33. 33.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 90 (d) 45
34. 34.The mean of 5 numbers is 21. When the number 45 is added to them, what is the new mean? (a) 25 (b) 21 (c) 26 (d) 33
35. 35.The mean of 6 numbers is 19. When the number 12 is added to them, what is the new mean? (a) 19 (b) 17 (c) 20 (d) 18
36. 36.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 25 (b) 20 (c) 40 (d) 9
37. 37.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 28 (c) 21 (d) 42
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/9 (c) 4/11 (d) 1/11
39. 39.Which term of the AP 16, 21, 26, 31, … is 76? (a) 14th (b) 12th (c) 13th (d) 15th
40. 40.What is the mean of 3, 6, 16, 7, 18 and 22? (a) 14 (b) 13 (c) 11 (d) 12

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