Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 329 · 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 mode of 5, 10, 8, 3, 3, 3 and 8? (a) 8 (b) 5 (c) 10 (d) 3
2. 2.A bag has 9 red, 4 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/15 (b) 1/3 (c) 13/15 (d) 14/15
3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
4. 4.What is the midpoint of the line joining (5, 10) and (17, 20)? (a) (22, 30) (b) (15, 11) (c) (6, 5) (d) (11, 15)
5. 5.How many factors does 89 have? (a) 2 (b) 3 (c) 1 (d) 4
6. 6.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 115° (c) 230° (d) 130°
7. 7.What is the midpoint of the line joining (2, 1) and (10, 11)? (a) (6, 6) (b) (7, 6) (c) (12, 12) (d) (4, 5)
8. 8.In a class of 32 children, 20 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 4 (b) 25 (c) 20 (d) 17
9. 9.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 400 cu cm
10. 10.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 150° (b) 70° (c) 30° (d) 140°
11. 11.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 65° (d) 155°
12. 12.What is the sum of the first 6 terms of the AP 2, 4, 6, …? (a) 12 (b) 42 (c) 48 (d) 84
13. 13.How many factors does 81 have? (a) 4 (b) 3 (c) 6 (d) 5
14. 14.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 12 (c) 42 (d) 35
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
16. 16.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 32) (b) (x − 4)(x − 8) (c) (x + 1)(x + 11) (d) (x + 4)(x + 8)
17. 17.The mean of 9 numbers is 35. When the number 25 is added to them, what is the new mean? (a) 30 (b) 33 (c) 35 (d) 34
18. 18.What is the sum of the roots of x² − 14x + 48 = 0? (a) 13 (b) 14 (c) 48 (d) 15
19. 19.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 482 (c) 615 (d) 606
20. 20.A bag has 12 green balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 16 (b) 14 (c) 13 (d) 2
21. 21.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 160° (b) 120° (c) 80° (d) 60°
22. 22.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.In a class of 39 children, 19 like mangoes, 23 like bananas and 8 like both. How many like neither? (a) 8 (b) 6 (c) 5 (d) 13
24. 24.A bag has 4 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 5 (c) 13 (d) 2
25. 25.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 115° (d) 40°
26. 26.Which is the correct factorisation of x² + 14x + 45? (a) (x + 5)(x + 9) (b) (x + 1)(x + 13) (c) (x − 5)(x − 9) (d) (x + 1)(x + 45)
27. 27.A drawer has lots of blue, red 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) 3 (b) 2 (c) 6 (d) 4
28. 28.In a class of 30 children, 17 like cricket, 16 like football and 4 like both. How many like at least one of the two? (a) 25 (b) 30 (c) 29 (d) 33
29. 29.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
30. 30.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 100° (c) 150° (d) 130°
31. 31.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 4225 (b) 3625 (c) 4235 (d) 3025
32. 32.What is the median of 24, 13, 9, 34, 40, 18 and 23? (a) 34 (b) 24 (c) 18 (d) 23
33. 33.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
34. 34.A bag has 7 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 15 (c) 8 (d) 9
35. 35.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 48 (c) 42 (d) 13
36. 36.A drawer has lots of yellow 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) 2 (b) 4 (c) 5 (d) 3
37. 37.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2592 (c) 5256 (d) 2628
38. 38.In a class of 34 children, 13 like maths, 23 like science and 5 like neither. How many like both? (a) 7 (b) 29 (c) 2 (d) 5
39. 39.How many factors does 67 have? (a) 4 (b) 3 (c) 2 (d) 1
40. 40.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 33 (d) 36

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