Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 27 · 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 42? (a) 15 (b) 14 (c) 4 (d) 16
2. 2.A bag has 3 black balls and 9 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) 12 (c) 10 (d) 4
3. 3.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 2 and 36 (c) 1 and 72 (d) 1 and 16
4. 4.What is the median of 33, 38, 4, 19, 24, 8 and 34? (a) 24 (b) 25 (c) 19 (d) 33
5. 5.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 702 (d) 676
6. 6.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 27 (b) 102 (c) 87 (d) 174
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 4/11 (d) 5/36
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 176 sq cm
9. 9.In a class of 30 children, 22 like mangoes, 18 like bananas and 11 like both. How many like only mangoes? (a) 22 (b) 12 (c) 7 (d) 11
10. 10.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 15° (c) 75° (d) 105°
11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
12. 12.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
13. 13.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 125° (b) 120° (c) 65° (d) 115°
14. 14.What is the midpoint of the line joining (1, 0) and (13, 6)? (a) (14, 6) (b) (3, 7) (c) (6, 3) (d) (7, 3)
15. 15.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 3 (d) 10
16. 16.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 6416 (b) 7056 (c) 5776 (d) 7066
17. 17.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°
18. 18.A bag has 4 yellow balls and 3 white 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) 5 (c) 4 (d) 7
19. 19.A bag has 5 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 10 (c) 6 (d) 7
20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
22. 22.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 50 (c) 25 (d) 30
23. 23.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
24. 24.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x + 4)(x + 8) (c) (x − 4)(x − 8) (d) (x + 1)(x + 32)
25. 25.In a class of 40 children, 24 like dance, 10 like music and 4 like both. How many like only dance? (a) 24 (b) 20 (c) 30 (d) 6
26. 26.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 105°
27. 27.In a class of 26 children, 10 like tea, 20 like coffee and 2 like neither. How many like both? (a) 4 (b) 24 (c) 2 (d) 6
28. 28.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 308 sq cm (d) 616 sq cm
31. 31.What is the smallest prime factor of 247? (a) 19 (b) 2 (c) 13 (d) 1
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
33. 33.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x + 1)(x + 6) (c) (x − 2)(x − 5) (d) (x + 2)(x + 5)
34. 34.What is the distance between the points (5, 14) and (29, 7)? (a) 26 (b) 31 (c) 625 (d) 25
35. 35.In a class of 30 children, 15 like maths, 20 like science and 1 like neither. How many like both? (a) 29 (b) 6 (c) 1 (d) 5
36. 36.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
37. 37.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 32 (c) 28 (d) 56
38. 38.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 24 (d) 48
39. 39.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 24 (c) 63 (d) 7

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