Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 758 · 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.A bag has 4 green balls and 7 yellow 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) 11 (c) 5 (d) 2
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/8 (c) 1/4 (d) 3/8
3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
4. 4.In a class of 48 children, 23 like cricket, 19 like football and 10 like neither. How many like both? (a) 10 (b) 5 (c) 4 (d) 38
5. 5.In which quadrant does the point (−8, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 15 (b) 16 (c) 14 (d) 4
7. 7.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 4 (d) 6
8. 8.The mean of 4 numbers is 30. When the number 20 is added to them, what is the new mean? (a) 25 (b) 30 (c) 29 (d) 28
9. 9.How many factors does 68 have? (a) 4 (b) 7 (c) 5 (d) 6
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 18
11. 11.A bag has 9 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 13 (d) 10
12. 12.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 40 (c) 13 (d) 80
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
14. 14.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 66 (d) 132
15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
16. 16.What is the mean of 12, 20, 11 and 13? (a) 16 (b) 13 (c) 15 (d) 14
17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
18. 18.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
19. 19.In which quadrant does the point (−8, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
20. 20.In a class of 41 children, 25 like dance, 25 like music and 10 like both. How many like at least one of the two? (a) 41 (b) 40 (c) 30 (d) 50
21. 21.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
22. 22.A bag has 6 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 18 (c) 2 (d) 8
23. 23.If a + b = 14 and ab = 33, what is (a − b)²? (a) 64 (b) 196 (c) 130 (d) 8
24. 24.In a class of 40 children, 24 like tea, 19 like coffee and 7 like both. How many like only tea? (a) 12 (b) 21 (c) 24 (d) 17
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
26. 26.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
27. 27.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
29. 29.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 1)(x + 8) (c) (x + 4)(x + 5) (d) (x − 4)(x − 5)
30. 30.A drawer has lots of yellow, 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) 6 (c) 4 (d) 2
31. 31.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 9025 (b) 8125 (c) 9035 (d) 7225
32. 32.What is the midpoint of the line joining (6, 10) and (12, 2)? (a) (18, 12) (b) (6, 9) (c) (9, 6) (d) (3, 4)
33. 33.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 7 cu cm (b) 32 cu cm (c) 12 cu cm (d) 6 cu cm
34. 34.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
35. 35.A bag has 8 blue balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 9 (c) 10 (d) 2
36. 36.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 24 (d) 36
37. 37.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 40° (c) 50° (d) 70°
38. 38.What is the sum of the roots of x² − 5x + 6 = 0? (a) 6 (b) 4 (c) 5 (d) 7
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
40. 40.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) 14 (b) 21 (c) 15 (d) 22

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