Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 858 · 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. 1.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81
2. 2.If a + b = 14 and ab = 48, what is (a − b)²? (a) 4 (b) 2 (c) 100 (d) 196
3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
4. 4.Which is the correct factorisation of x² + 16x + 63? (a) (x + 7)(x + 9) (b) (x + 1)(x + 63) (c) (x − 7)(x − 9) (d) (x + 1)(x + 15)
5. 5.If a + b = 12 and ab = 35, what is a² + b²? (a) 144 (b) 109 (c) 214 (d) 74
6. 6.A bag has 9 white, 2 red and 8 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/10 (b) 10/19 (c) 9/19 (d) 1/3
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 5/36 (c) 1/11 (d) 4/11
8. 8.What is the distance between the points (1, 10) and (7, 2)? (a) 10 (b) 14 (c) 11 (d) 100
9. 9.Two angles of a triangle are 45° and 55°. What is the third angle? (a) 80° (b) 125° (c) 100° (d) 135°
10. 10.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
11. 11.What are the roots of x² − 9x + 18 = 0? (a) 1 and 8 (b) 1 and 18 (c) 2 and 9 (d) 3 and 6
12. 12.In a class of 45 children, 22 like mangoes, 21 like bananas and 5 like both. How many like at least one of the two? (a) 33 (b) 45 (c) 38 (d) 43
13. 13.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 320° (d) 50°
14. 14.A bag has 2 blue, 7 white and 4 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 6/7 (b) 1/3 (c) 7/13 (d) 6/13
15. 15.What is the 39th term of the AP 17, 20, 23, 26, …? (a) 117 (b) 131 (c) 134 (d) 114
16. 16.A bag has 9 white, 3 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/4 (b) 1/3 (c) 4/5 (d) 1/5
17. 17.A bag has 2 green, 2 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
18. 18.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 140° (c) 70° (d) 110°
19. 19.In a class of 28 children, 16 like dance, 17 like music and 7 like both. How many like neither? (a) 7 (b) 2 (c) 3 (d) 9
20. 20.What is the mode of 2, 2, 4, 19, 4, 5 and 4? (a) 19 (b) 5 (c) 2 (d) 4
21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 22 (c) 29 (d) 21
22. 22.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
23. 23.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 8) (b) (x + 1)(x + 20) (c) (x + 4)(x + 5) (d) (x − 4)(x − 5)
24. 24.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
25. 25.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) 24 (b) 7 (c) 63 (d) 21
26. 26.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4771 (b) 4899 (c) 5041 (d) 4761
27. 27.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 4 (d) 6
28. 28.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 43 (b) 408 (c) 204 (d) 224
29. 29.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 35°
30. 30.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2² × 3² × 5
31. 31.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.In a class of 28 children, 18 like dance, 5 like music and 2 like both. How many like neither? (a) 7 (b) 9 (c) 2 (d) 5
33. 33.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
34. 34.How many factors does 115 have? (a) 4 (b) 5 (c) 2 (d) 3
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
37. 37.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 110°
38. 38.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 9 sq cm (c) 27 sq cm (d) 54 sq cm
39. 39.If a + b = 13 and ab = 12, what is (a − b)²? (a) 121 (b) 11 (c) 169 (d) 145
40. 40.A cuboid is 8 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 19 cu cm (b) 24 cu cm (c) 192 cu cm (d) 224 cu cm

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