Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 62 · 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.The mean of 3 numbers is 22. When the number 38 is added to them, what is the new mean? (a) 22 (b) 26 (c) 30 (d) 27
2. 2.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 59° (c) 60° (d) 61°
3. 3.In a class of 22 children, 10 like dance, 15 like music and 4 like both. How many like only dance? (a) 7 (b) 10 (c) 6 (d) 11
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
5. 5.How many factors does 41 have? (a) 4 (b) 2 (c) 1 (d) 3
6. 6.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 95° (b) 150° (c) 115° (d) 85°
7. 7.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.What is the sum of the roots of x² − 14x + 45 = 0? (a) 13 (b) 15 (c) 14 (d) 45
9. 9.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
10. 10.5 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) 35 (b) 30 (c) 11 (d) 60
11. 11.In which quadrant does the point (3, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
12. 12.What is the sum of the first 9 terms of the AP 9, 12, 15, …? (a) 189 (b) 192 (c) 378 (d) 33
13. 13.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 45 (d) 90
14. 14.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 49 (d) 37
15. 15.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 33 cu cm (d) 1331 cu cm
16. 16.A bag has 7 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 16 (c) 9 (d) 2
17. 17.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
18. 18.What is the missing term in the AP 14, 19, ?, 29, 34? (a) 25 (b) 23 (c) 29 (d) 24
19. 19.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 8 (c) 32 (d) 20
20. 20.What is the mode of 10, 9, 10, 4, 4, 10 and 3? (a) 4 (b) 3 (c) 10 (d) 9
21. 21.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
22. 22.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 42 (d) 13
23. 23.A bag has 11 blue 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) 23 (b) 2 (c) 13 (d) 12
24. 24.What is the mode of 19, 18, 18, 5, 13, 18 and 19? (a) 5 (b) 13 (c) 19 (d) 18
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 14 (b) 15 (c) 13 (d) 4
26. 26.What is the distance between the points (3, 20) and (8, 8)? (a) 169 (b) 13 (c) 17 (d) 14
27. 27.A bag has 7 black balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 8 (c) 12 (d) 18
28. 28.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x + 1)(x + 11) (c) (x + 3)(x + 9) (d) (x − 3)(x − 9)
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
30. 30.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
31. 31.Which term of the AP 11, 18, 25, 32, … is 221? (a) 32nd (b) 30th (c) 31st (d) 33rd
32. 32.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 95° (b) 145° (c) 85° (d) 120°
33. 33.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 115° (d) 145°
34. 34.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 7 (d) 8
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/11 (c) 1/6 (d) 6/11
37. 37.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1764 (b) 1444 (c) 1604 (d) 1774
38. 38.What is the mean of 7, 12, 3 and 14? (a) 9 (b) 8 (c) 12 (d) 10
39. 39.What is the prime factorisation of 24? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3³ (d) 2⁴ × 3
40. 40.A bag has 4 green, 2 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 2/5 (b) 7/10 (c) 1/3 (d) 3/5

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