Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 991 · 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 median of 32, 6, 2, 5 and 12? (a) 12 (b) 6 (c) 2 (d) 5
2. 2.What is the 18th term of the AP 1, 4, 7, 10, …? (a) 55 (b) 51 (c) 52 (d) 54
3. 3.What is the mean of 5, 9, 15, 13 and 8? (a) 11 (b) 12 (c) 9 (d) 10
4. 4.In a class of 49 children, 29 like cricket, 27 like football and 2 like neither. How many like both? (a) 47 (b) 2 (c) 9 (d) 7
5. 5.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
6. 6.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12
8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 3 (c) 6 (d) 4
9. 9.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 36° (c) 35° (d) 145°
10. 10.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 468 (c) 384 (d) 469
11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
12. 12.What is the 26th term of the AP 19, 21, 23, 25, …? (a) 71 (b) 50 (c) 52 (d) 69
13. 13.A bag has 7 yellow, 6 red and 5 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/3 (b) 7/18 (c) 1/3 (d) 11/18
14. 14.A cuboid is 11 cm long, 6 cm wide and 10 cm high. What is its total surface area? (a) 236 sq cm (b) 660 sq cm (c) 944 sq cm (d) 472 sq cm
15. 15.What is the missing term in the AP 14, 17, ?, 23, 26? (a) 20 (b) 21 (c) 19 (d) 23
16. 16.A bag has 9 yellow balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 11 (c) 14 (d) 10
17. 17.What are the roots of x² − 15x + 56 = 0? (a) 1 and 56 (b) 2 and 28 (c) 7 and 8 (d) 1 and 14
18. 18.In a class of 43 children, 30 like cricket, 24 like football and 12 like both. How many like at least one of the two? (a) 42 (b) 30 (c) 43 (d) 54
19. 19.What is the distance between the points (5, 0) and (12, 24)? (a) 26 (b) 625 (c) 31 (d) 25
20. 20.How many factors does 52 have? (a) 6 (b) 5 (c) 4 (d) 7
21. 21.What is the 12th term of the AP 18, 27, 36, 45, …? (a) 108 (b) 117 (c) 126 (d) 99
22. 22.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 3 (d) 4
23. 23.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
24. 24.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
25. 25.What are the roots of x² − 13x + 42 = 0? (a) 1 and 12 (b) 1 and 42 (c) 2 and 21 (d) 6 and 7
26. 26.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
27. 27.What is the mean of 17, 7, 10 and 22? (a) 14 (b) 13 (c) 15 (d) 16
28. 28.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2116 (b) 2926 (c) 2516 (d) 2916
29. 29.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm
30. 30.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
31. 31.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
32. 32.The mean of 3 numbers is 15. When the number 31 is added to them, what is the new mean? (a) 15 (b) 20 (c) 23 (d) 19
33. 33.If a + b = 19 and ab = 84, what is (a − b)²? (a) 361 (b) 5 (c) 25 (d) 193
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 1/6 (c) 6/11 (d) 7/36
35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
36. 36.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 100° (d) 110°
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/11 (c) 2/11 (d) 1/18
38. 38.Two angles of a triangle are 70° and 30°. What is the third angle? (a) 110° (b) 150° (c) 80° (d) 100°
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 5 (c) 4 (d) 2
40. 40.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°

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