Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 939 · 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 cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 216 cu cm (c) 18 cu cm (d) 144 cu cm
2. 2.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
3. 3.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 115° (c) 145° (d) 65°
4. 4.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 28) (b) (x − 4)(x − 7) (c) (x + 4)(x + 7) (d) (x + 1)(x + 10)
5. 5.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 140° (b) 40° (c) 80° (d) 220°
6. 6.What is the mode of 4, 4, 15, 15, 5, 16 and 4? (a) 4 (b) 15 (c) 5 (d) 16
7. 7.Which term of the AP 2, 4, 6, 8, … is 16? (a) 7th (b) 10th (c) 8th (d) 9th
8. 8.In which quadrant does the point (8, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
9. 9.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
10. 10.A bag has 9 blue, 8 red and 8 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/17 (b) 8/25 (c) 17/25 (d) 1/3
11. 11.A bag has 2 white, 2 yellow and 8 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/5 (b) 5/6 (c) 1/3 (d) 1/6
12. 12.In a class of 19 children, 14 like maths, 11 like science and 8 like both. How many like neither? (a) 2 (b) 10 (c) 8 (d) 3
13. 13.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
14. 14.What is the midpoint of the line joining (1, 8) and (3, 16)? (a) (4, 24) (b) (2, 12) (c) (1, 4) (d) (12, 2)
15. 15.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x + 1)(x + 42) (c) (x − 6)(x − 7) (d) (x + 1)(x + 12)
16. 16.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2³ × 3 × 5
17. 17.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 240 (b) 30 (c) 120 (d) 132
18. 18.In a class of 19 children, 6 like mangoes, 6 like bananas and 3 like both. How many like neither? (a) 7 (b) 3 (c) 10 (d) 13
19. 19.What is the distance between the points (2, 2) and (9, 26)? (a) 625 (b) 31 (c) 26 (d) 25
20. 20.In a class of 47 children, 29 like maths, 21 like science and 7 like neither. How many like both? (a) 3 (b) 10 (c) 7 (d) 40
21. 21.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 15 (d) 8
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 18 (b) 17 (c) 6 (d) 16
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
24. 24.In a class of 37 children, 26 like maths, 15 like science and 3 like neither. How many like both? (a) 34 (b) 3 (c) 4 (d) 7
25. 25.What is the mean of 18, 14, 20 and 16? (a) 19 (b) 18 (c) 16 (d) 17
26. 26.A cuboid is 7 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 376 sq cm (b) 168 sq cm (c) 94 sq cm (d) 188 sq cm
27. 27.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 4 times (d) 5 times
28. 28.What is the distance between the points (9, 3) and (14, 15)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.What is the distance between the points (0, 3) and (6, 11)? (a) 100 (b) 14 (c) 11 (d) 10
30. 30.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
31. 31.A bag has 8 white balls and 5 blue 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) 9 (c) 6 (d) 2
32. 32.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 110° (d) 40°
33. 33.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
34. 34.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 48 sq cm (b) 40 sq cm (c) 80 sq cm (d) 160 sq cm
35. 35.A drawer has lots of blue, green, black 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) 5 (b) 4 (c) 8 (d) 2
36. 36.What is the mode of 16, 16, 18, 16, 6, 6 and 1? (a) 16 (b) 6 (c) 1 (d) 18
37. 37.What is the mean of 19, 18, 4, 9 and 15? (a) 13 (b) 14 (c) 12 (d) 15
38. 38.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 75 (c) 72 (d) 216
39. 39.What is the midpoint of the line joining (9, 18) and (21, 8)? (a) (30, 26) (b) (13, 15) (c) (6, 5) (d) (15, 13)
40. 40.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 21 (c) 15 (d) 36

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