Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 565 · 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.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 95° (d) 85°
2. 2.What is the prime factorisation of 24? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3³ (d) 2⁴ × 3
3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 17 (d) 7
4. 4.In a class of 20 children, 7 like dance, 9 like music and 7 like neither. How many like both? (a) 13 (b) 7 (c) 4 (d) 3
5. 5.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 54 (c) 18 (d) 21
6. 6.A drawer has lots of blue, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 6 (d) 4
7. 7.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 1235 (c) 1575 (d) 2025
8. 8.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
9. 9.In a class of 39 children, 17 like dance, 17 like music and 2 like both. How many like at least one of the two? (a) 34 (b) 39 (c) 30 (d) 32
10. 10.In a class of 57 children, 32 like maths, 31 like science and 6 like neither. How many like both? (a) 6 (b) 51 (c) 13 (d) 12
11. 11.What is the distance between the points (9, 18) and (17, 3)? (a) 17 (b) 289 (c) 18 (d) 23
12. 12.What is the mode of 16, 6, 7, 6, 5, 16 and 6? (a) 7 (b) 6 (c) 5 (d) 16
13. 13.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 13 (b) 14 (c) 3 (d) 12
15. 15.Which term of the AP 11, 16, 21, 26, … is 86? (a) 18th (b) 16th (c) 17th (d) 15th
16. 16.A bag has 3 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 2 (c) 10 (d) 4
17. 17.What is the mode of 19, 19, 8, 8, 8, 17 and 2? (a) 17 (b) 2 (c) 19 (d) 8
18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
20. 20.A bag has 7 green balls and 10 red 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) 8 (c) 17 (d) 2
21. 21.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
22. 22.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
23. 23.A cuboid is 10 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 30 cu cm (b) 270 cu cm (c) 22 cu cm (d) 294 cu cm
24. 24.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
25. 25.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁴ × 3² (c) 2⁵ × 3² (d) 2³ × 3²
26. 26.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 81 (d) 36
27. 27.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 12 (d) 24
28. 28.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
29. 29.The mean of 7 numbers is 10. When the number 18 is added to them, what is the new mean? (a) 11 (b) 14 (c) 12 (d) 10
30. 30.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 1 (d) 7
31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 5 (b) 8 (c) 6 (d) 7
32. 32.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 18 (c) 17 (d) 72
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/36 (c) 1/18 (d) 1/12
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 25 times (c) 5 times (d) 10 times
35. 35.What are the roots of x² − 13x + 40 = 0? (a) 1 and 40 (b) 1 and 12 (c) 2 and 20 (d) 5 and 8
36. 36.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/6 (c) 1/3 (d) 1/5
37. 37.A bag has 3 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 4 (c) 8 (d) 2
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
39. 39.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 135° (c) 160° (d) 115°
40. 40.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2² × 5

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