Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 225 · 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.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
2. 2.Which is the correct factorisation of x² + 11x + 30? (a) (x + 5)(x + 6) (b) (x − 5)(x − 6) (c) (x + 1)(x + 10) (d) (x + 1)(x + 30)
3. 3.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁴ × 3 × 5
4. 4.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
5. 5.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 9 (d) 12
6. 6.What is the midpoint of the line joining (10, 8) and (22, 18)? (a) (13, 16) (b) (6, 5) (c) (16, 13) (d) (32, 26)
7. 7.How many factors does 88 have? (a) 7 (b) 6 (c) 8 (d) 9
8. 8.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
9. 9.In a class of 44 children, 20 like tea, 24 like coffee and 6 like both. How many like neither? (a) 12 (b) 0 (c) 7 (d) 6
10. 10.How many prime numbers are there between 30 and 60? (a) 9 (b) 6 (c) 8 (d) 7
11. 11.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1296 (b) 1306 (c) 1936 (d) 1584
12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
13. 13.A cuboid is 11 cm long, 3 cm wide and 10 cm high. What is its volume? (a) 33 cu cm (b) 24 cu cm (c) 346 cu cm (d) 330 cu cm
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
15. 15.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 19 (d) 7
17. 17.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 160° (c) 340° (d) 20°
18. 18.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 145° (b) 155° (c) 120° (d) 60°
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 17 (c) 15 (d) 16
21. 21.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 100° (c) 120° (d) 140°
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
23. 23.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
25. 25.What is the midpoint of the line joining (4, 14) and (10, 4)? (a) (7, 9) (b) (9, 7) (c) (3, 5) (d) (14, 18)
26. 26.What is the mode of 4, 16, 16, 3, 1, 1 and 16? (a) 3 (b) 4 (c) 16 (d) 1
27. 27.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 24 (d) 144
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 4 (d) 3
29. 29.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 971 (c) 841 (d) 901
30. 30.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 3 (d) 441
31. 31.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 104 (c) 192 (d) 19
32. 32.How many factors does 23 have? (a) 3 (b) 1 (c) 2 (d) 4
33. 33.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 36 (d) 15
34. 34.What is the midpoint of the line joining (2, 0) and (14, 2)? (a) (16, 2) (b) (6, 1) (c) (8, 1) (d) (1, 8)
35. 35.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 72 (c) 36 (d) 12
36. 36.What is the mode of 16, 1, 16, 6, 9, 16 and 1? (a) 9 (b) 16 (c) 1 (d) 6
37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 171 (d) 57
38. 38.A bag has 3 red, 2 green and 4 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 4/5 (b) 4/9 (c) 1/3 (d) 5/9
39. 39.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
40. 40.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm

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