Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 650 · 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 30. When the number 38 is added to them, what is the new mean? (a) 30 (b) 34 (c) 33 (d) 32
2. 2.The mean of 3 numbers is 10. When the number 14 is added to them, what is the new mean? (a) 10 (b) 12 (c) 11 (d) 13
3. 3.What is the mean of 9, 11, 18 and 14? (a) 12 (b) 13 (c) 14 (d) 15
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
5. 5.The mean of 8 numbers is 29. When the number 56 is added to them, what is the new mean? (a) 31 (b) 32 (c) 33 (d) 29
6. 6.The mean of 7 numbers is 35. When the number 27 is added to them, what is the new mean? (a) 31 (b) 33 (c) 35 (d) 34
7. 7.In a class of 38 children, 15 like maths, 25 like science and 7 like neither. How many like both? (a) 2 (b) 7 (c) 31 (d) 9
8. 8.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 135° (b) 100° (c) 145° (d) 80°
9. 9.What is the mean of 9, 18, 16, 11, 2 and 16? (a) 11 (b) 13 (c) 12 (d) 14
10. 10.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
11. 11.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
12. 12.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
13. 13.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 90 cu cm (b) 54 cu cm (c) 12 cu cm (d) 18 cu cm
14. 14.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
15. 15.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 110° (d) 45°
16. 16.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 3625 (b) 3025 (c) 4235 (d) 4225
17. 17.A bag has 9 blue balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 20 (c) 2 (d) 11
18. 18.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 4 (c) 6 (d) 7
19. 19.A cuboid is 10 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 112 sq cm (d) 60 sq cm
20. 20.What is the sum of the first 12 terms of the AP 6, 7, 8, …? (a) 144 (b) 276 (c) 17 (d) 138
21. 21.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 57 (c) 162 (d) 18
22. 22.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 28 (d) 21
23. 23.What is the midpoint of the line joining (3, 7) and (11, 19)? (a) (14, 26) (b) (4, 6) (c) (7, 13) (d) (13, 7)
24. 24.How many factors does 22 have? (a) 2 (b) 3 (c) 5 (d) 4
25. 25.The mean of 3 numbers is 13. When the number 1 is added to them, what is the new mean? (a) 13 (b) 11 (c) 7 (d) 10
26. 26.What is the mode of 17, 7, 16, 7, 16, 19 and 16? (a) 19 (b) 7 (c) 16 (d) 17
27. 27.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 40° (b) 150° (c) 70° (d) 140°
28. 28.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 24 cu cm (d) 6 cu cm
29. 29.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 80° (d) 40°
30. 30.A bag has 10 green balls and 11 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) 2 (c) 12 (d) 21
31. 31.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 150° (c) 100° (d) 130°
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 7 (d) 19
33. 33.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 45 (c) 20 (d) 90
34. 34.A bag has 12 white balls and 11 black 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) 23 (c) 2 (d) 12
35. 35.How many factors does 60 have? (a) 11 (b) 13 (c) 12 (d) 10
36. 36.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 105° (b) 85° (c) 160° (d) 95°
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
38. 38.What is the median of 16, 22, 5, 34 and 29? (a) 16 (b) 5 (c) 29 (d) 22
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
40. 40.What is the median of 5, 1, 19, 3, 31, 6 and 35? (a) 19 (b) 6 (c) 5 (d) 3

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