Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 335 · 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.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
2. 2.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
3. 3.A bag has 7 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 8 (c) 10 (d) 9
4. 4.What is the mean of 18, 4, 17, 12 and 14? (a) 15 (b) 13 (c) 12 (d) 14
5. 5.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/8 (d) 3/4
6. 6.What is the 14th term of the AP 2, 6, 10, 14, …? (a) 54 (b) 56 (c) 58 (d) 52
7. 7.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
8. 8.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
9. 9.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 72 (d) 24
10. 10.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 55° (b) 30° (c) 150° (d) 155°
11. 11.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
12. 12.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 310° (c) 40° (d) 130°
13. 13.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 115° (b) 100° (c) 145° (d) 80°
14. 14.In a class of 39 children, 15 like dance, 30 like music and 5 like neither. How many like both? (a) 34 (b) 6 (c) 11 (d) 5
15. 15.A bag has 11 black balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 12 (c) 2 (d) 15
16. 16.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 2 (d) 11
17. 17.What is the missing term in the AP 13, 15, ?, 19, 21? (a) 16 (b) 18 (c) 17 (d) 19
18. 18.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
19. 19.A bag has 4 white balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 5 (c) 6 (d) 10
20. 20.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
21. 21.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
23. 23.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 25 (c) 10 (d) 20
24. 24.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 5776 (b) 6416 (c) 7056 (d) 7066
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
26. 26.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 400 sq cm (d) 100 sq cm
27. 27.A bag has 12 green balls and 13 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 13 (c) 2 (d) 25
28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
29. 29.A bag has 9 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 20 (c) 10 (d) 2
30. 30.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
31. 31.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 86° (d) 85°
32. 32.What is the missing term in the AP 4, 9, ?, 19, 24? (a) 19 (b) 15 (c) 14 (d) 13
33. 33.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) 21 (b) 28 (c) 22 (d) 29
34. 34.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
35. 35.What is the smallest prime factor of 93? (a) 2 (b) 31 (c) 3 (d) 1
36. 36.What is the smallest prime factor of 155? (a) 5 (b) 1 (c) 2 (d) 31
37. 37.A bag has 10 yellow balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 5 (c) 14 (d) 2
38. 38.A bag has 11 green balls and 12 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) 2 (c) 12 (d) 23
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
40. 40.A bag has 11 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) 12 (b) 9 (c) 19 (d) 2

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