Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 142 · 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.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 32 (b) 234 (c) 132 (d) 117
2. 2.What is the smallest prime factor of 403? (a) 31 (b) 13 (c) 2 (d) 1
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/36 (d) 1/11
4. 4.What is the mean of 3, 7, 4, 18, 6 and 16? (a) 9 (b) 11 (c) 8 (d) 10
5. 5.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 230° (b) 100° (c) 130° (d) 50°
6. 6.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
7. 7.What is the mode of 19, 5, 19, 19, 5, 15 and 13? (a) 15 (b) 13 (c) 5 (d) 19
8. 8.In a class of 50 children, 30 like dance, 23 like music and 11 like both. How many like at least one of the two? (a) 31 (b) 42 (c) 53 (d) 50
9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
10. 10.A cuboid is 4 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 328 sq cm (b) 120 sq cm (c) 164 sq cm (d) 82 sq cm
11. 11.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 90° (b) 110° (c) 160° (d) 270°
12. 12.A bag has 4 blue, 8 white and 5 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/17 (b) 8/9 (c) 1/3 (d) 8/17
13. 13.What is the 11th term of the AP 11, 17, 23, 29, …? (a) 60 (b) 71 (c) 66 (d) 77
14. 14.A bag has 9 blue balls and 4 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) 13 (c) 5 (d) 10
15. 15.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
16. 16.A bag has 3 green balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 11 (c) 9 (d) 2
17. 17.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 36 cu cm (b) 144 cu cm (c) 176 cu cm (d) 17 cu cm
18. 18.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 192 (c) 19 (d) 96
19. 19.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
20. 20.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 320° (c) 140° (d) 50°
21. 21.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 66 (d) 198
22. 22.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 12 (c) 7 (d) 15
23. 23.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
24. 24.A bag has 9 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 10 (c) 2 (d) 13
25. 25.A bag has 3 red, 3 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 7/9 (b) 1/3 (c) 2/3 (d) 1/9
26. 26.What is the midpoint of the line joining (1, 5) and (9, 7)? (a) (4, 1) (b) (6, 5) (c) (5, 6) (d) (10, 12)
27. 27.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 1 (d) 2
28. 28.In a class of 31 children, 11 like maths, 24 like science and 6 like both. How many like at least one of the two? (a) 35 (b) 23 (c) 29 (d) 31
29. 29.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 55° (d) 95°
30. 30.If a + b = 14 and ab = 24, what is a² + b²? (a) 244 (b) 148 (c) 172 (d) 196
31. 31.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2² × 3
32. 32.What is the sum of the first 5 terms of the AP 4, 9, 14, …? (a) 24 (b) 75 (c) 70 (d) 140
33. 33.How many factors does 30 have? (a) 7 (b) 8 (c) 9 (d) 6
34. 34.What is the mode of 4, 19, 4, 12, 4, 19 and 9? (a) 9 (b) 4 (c) 19 (d) 12
35. 35.What is the mean of 15, 13, 20, 19, 14 and 21? (a) 19 (b) 16 (c) 17 (d) 18
36. 36.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 100° (d) 80°
37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
38. 38.The mean of 3 numbers is 11. When the number 7 is added to them, what is the new mean? (a) 9 (b) 10 (c) 12 (d) 11
39. 39.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 4)(x + 6) (c) (x − 4)(x − 6) (d) (x + 1)(x + 24)
40. 40.What is the mean of 8, 13, 20, 7 and 17? (a) 15 (b) 12 (c) 14 (d) 13

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