Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 654 · 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.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 24 (d) 75
2. 2.In a class of 50 children, 26 like mangoes, 28 like bananas and 11 like both. How many like at least one of the two? (a) 50 (b) 32 (c) 43 (d) 54
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
4. 4.What is the median of 5, 11, 22, 13, 21, 30 and 2? (a) 11 (b) 21 (c) 13 (d) 14
5. 5.In a class of 36 children, 26 like maths, 14 like science and 8 like both. How many like neither? (a) 8 (b) 12 (c) 4 (d) 5
6. 6.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 7/8 (c) 1/7 (d) 1/4
7. 7.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 3850 cm (d) 110 cm
8. 8.In which quadrant does the point (−7, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
9. 9.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 16 times (d) 8 times
10. 10.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 7 (c) 15 (d) 8
11. 11.What is the 28th term of the AP 18, 20, 22, 24, …? (a) 74 (b) 54 (c) 56 (d) 72
12. 12.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 302 (c) 346 (d) 345
13. 13.A cuboid is 12 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 96 cu cm (b) 160 cu cm (c) 24 cu cm (d) 18 cu cm
14. 14.Which is the correct factorisation of x² + 9x + 20? (a) (x − 4)(x − 5) (b) (x + 1)(x + 8) (c) (x + 1)(x + 20) (d) (x + 4)(x + 5)
15. 15.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 441 (b) 371 (c) 361 (d) 399
16. 16.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 289 (c) 529 (d) 539
17. 17.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/11 (d) 1/12
19. 19.A bag has 5 blue, 7 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 11/15 (c) 1/15 (d) 2/3
20. 20.If a + b = 8 and ab = 15, what is (a − b)²? (a) 2 (b) 4 (c) 64 (d) 34
21. 21.In a class of 35 children, 18 like dance, 14 like music and 4 like both. How many like only dance? (a) 18 (b) 14 (c) 10 (d) 21
22. 22.A bag has 6 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 11 (c) 8 (d) 2
23. 23.What is the distance between the points (6, 8) and (9, 4)? (a) 6 (b) 5 (c) 7 (d) 25
24. 24.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 91 (b) 25 (c) 105 (d) 182
25. 25.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
26. 26.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 85° (b) 120° (c) 145° (d) 95°
27. 27.What is the median of 2, 28, 40, 25, 7, 11 and 29? (a) 28 (b) 26 (c) 11 (d) 25
28. 28.In a class of 24 children, 7 like dance, 12 like music and 9 like neither. How many like both? (a) 5 (b) 15 (c) 4 (d) 9
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
30. 30.In a class of 36 children, 15 like tea, 16 like coffee and 7 like neither. How many like both? (a) 29 (b) 3 (c) 7 (d) 2
31. 31.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 150° (d) 65°
32. 32.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 155° (b) 60° (c) 120° (d) 85°
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9
34. 34.How many factors does 37 have? (a) 4 (b) 3 (c) 1 (d) 2
35. 35.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
36. 36.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
37. 37.A bag has 9 white, 4 blue and 5 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/9 (b) 1/18 (c) 1/2 (d) 1/3
38. 38.A bag has 10 white balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 14 (c) 11 (d) 12
39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
40. 40.A drawer has lots of black, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3

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