Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 233 · 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.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
3. 3.If a + b = 20 and ab = 96, what is (a − b)²? (a) 4 (b) 400 (c) 208 (d) 16
4. 4.In which quadrant does the point (−7, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
5. 5.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) 162 (b) 54 (c) 57 (d) 18
6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
7. 7.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
8. 8.What are the roots of x² − 15x + 56 = 0? (a) 1 and 56 (b) 1 and 14 (c) 2 and 28 (d) 7 and 8
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 59 (d) 930
11. 11.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
12. 12.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 8084 (b) 8836 (c) 7406 (d) 7396
13. 13.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 14 (d) 42
14. 14.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
15. 15.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 55° (b) 90° (c) 125° (d) 145°
16. 16.A drawer has lots of red, white, black, green 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) 10 (b) 5 (c) 6 (d) 2
17. 17.In a class of 40 children, 27 like cricket, 19 like football and 3 like neither. How many like both? (a) 3 (b) 9 (c) 6 (d) 37
18. 18.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 42 (b) 9 (c) 78 (d) 39
19. 19.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 100° (c) 120° (d) 140°
20. 20.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 105° (b) 150° (c) 75° (d) 135°
21. 21.In a class of 26 children, 21 like dance, 10 like music and 6 like both. How many like only dance? (a) 15 (b) 16 (c) 4 (d) 21
22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
23. 23.What is the median of 25, 12, 9, 26, 36, 14 and 5? (a) 26 (b) 12 (c) 14 (d) 25
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
25. 25.In a class of 32 children, 15 like cricket, 18 like football and 10 like neither. How many like both? (a) 22 (b) 11 (c) 10 (d) 1
26. 26.The mean of 4 numbers is 16. When the number 26 is added to them, what is the new mean? (a) 21 (b) 19 (c) 16 (d) 18
27. 27.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
28. 28.In a class of 36 children, 27 like dance, 15 like music and 9 like both. How many like only dance? (a) 27 (b) 21 (c) 6 (d) 18
29. 29.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
30. 30.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
31. 31.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
32. 32.What is the median of 34, 21, 2, 17 and 10? (a) 21 (b) 2 (c) 10 (d) 17
33. 33.A bag has 5 blue, 3 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 5/17 (b) 13/17 (c) 12/17 (d) 1/3
34. 34.Which term of the AP 2, 4, 6, 8, … is 28? (a) 14th (b) 16th (c) 15th (d) 13th
35. 35.What is the midpoint of the line joining (10, 8) and (22, 10)? (a) (9, 16) (b) (32, 18) (c) (6, 1) (d) (16, 9)
36. 36.A drawer has lots of green, yellow, white 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) 4 (b) 8 (c) 2 (d) 5
37. 37.A cuboid is 8 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 134 sq cm (b) 536 sq cm (c) 268 sq cm (d) 240 sq cm
38. 38.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x − 8)(x − 9)
39. 39.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 10° (b) 170° (c) 65° (d) 125°
40. 40.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2714 (b) 2304 (c) 2704 (d) 2504

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