Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 613 · 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 50 and 70? (a) 5 (b) 3 (c) 6 (d) 4
2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
3. 3.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 115° (d) 145°
4. 4.A bag has 4 green balls and 7 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) 11 (c) 2 (d) 8
5. 5.A bag has 12 black 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) 20 (b) 13 (c) 9 (d) 2
6. 6.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁵ × 3 × 5
7. 7.What is the distance between the points (3, 4) and (15, 20)? (a) 20 (b) 28 (c) 400 (d) 21
8. 8.What is the median of 28, 38, 7, 11, 4, 10 and 23? (a) 10 (b) 23 (c) 11 (d) 12
9. 9.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 90 (d) 20
11. 11.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
12. 12.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 30 (c) 18 (d) 15
13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
14. 14.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
15. 15.What is the mode of 5, 8, 17, 8, 8, 5 and 7? (a) 7 (b) 17 (c) 8 (d) 5
16. 16.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 270° (d) 90°
17. 17.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 166 (b) 165 (c) 330 (d) 20
18. 18.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.A bag has 3 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 2 (c) 5 (d) 4
20. 20.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 66 cm (d) 132 cm
21. 21.What is the mode of 4, 1, 14, 18, 14, 14 and 18? (a) 18 (b) 1 (c) 4 (d) 14
22. 22.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 169 (d) 91
23. 23.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 70° (b) 140° (c) 30° (d) 150°
24. 24.What is the mean of 16, 13, 5, 4 and 12? (a) 12 (b) 10 (c) 9 (d) 11
25. 25.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
26. 26.In a class of 35 children, 17 like tea, 18 like coffee and 2 like both. How many like only tea? (a) 17 (b) 2 (c) 16 (d) 15
27. 27.What is the midpoint of the line joining (7, 14) and (19, 10)? (a) (26, 24) (b) (6, 2) (c) (13, 12) (d) (12, 13)
28. 28.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
29. 29.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (6, 8) (b) (16, 12) (c) (1, 6) (d) (8, 6)
30. 30.What is the median of 13, 35, 36, 21, 30, 40 and 18? (a) 21 (b) 35 (c) 30 (d) 31
31. 31.If a + b = 19 and ab = 90, what is a² + b²? (a) 181 (b) 271 (c) 541 (d) 361
32. 32.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 110° (d) 145°
33. 33.In a class of 30 children, 24 like tea, 7 like coffee and 4 like both. How many like neither? (a) 2 (b) 4 (c) 7 (d) 3
34. 34.What is the 33rd term of the AP 12, 16, 20, 24, …? (a) 132 (b) 144 (c) 140 (d) 128
35. 35.Two angles of a triangle are 50° and 45°. What is the third angle? (a) 95° (b) 130° (c) 85° (d) 135°
36. 36.What is the sum of all the whole numbers from 1 to 30? (a) 930 (b) 450 (c) 465 (d) 435
37. 37.What is the mode of 17, 10, 10, 19, 10, 9 and 19? (a) 9 (b) 19 (c) 10 (d) 17
38. 38.In a class of 30 children, 21 like maths, 14 like science and 7 like both. How many like only maths? (a) 7 (b) 16 (c) 21 (d) 14
39. 39.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 16 (c) 18 (d) 17
40. 40.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

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