Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 416 · 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.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 7225 (b) 9035 (c) 9025 (d) 8125
2. 2.A bag has 10 yellow balls and 3 red 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) 13 (c) 11 (d) 4
3. 3.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
4. 4.In a class of 43 children, 24 like maths, 18 like science and 7 like both. How many like neither? (a) 1 (b) 8 (c) 7 (d) 15
5. 5.In a class of 38 children, 22 like tea, 15 like coffee and 9 like neither. How many like both? (a) 9 (b) 7 (c) 29 (d) 8
6. 6.Which is the correct factorisation of x² + 7x + 10? (a) (x + 2)(x + 5) (b) (x − 2)(x − 5) (c) (x + 1)(x + 6) (d) (x + 1)(x + 10)
7. 7.A cuboid is 6 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 129 sq cm (b) 270 sq cm (c) 258 sq cm (d) 516 sq cm
8. 8.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
9. 9.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 50°
10. 10.A bag has 8 yellow balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 19 (c) 10 (d) 9
11. 11.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
12. 12.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 24 (c) 12 (d) 16
13. 13.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
14. 14.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 216 sq cm (c) 36 sq cm (d) 144 sq cm
15. 15.The mean of 9 numbers is 32. When the number 72 is added to them, what is the new mean? (a) 32 (b) 37 (c) 52 (d) 36
16. 16.What is the 39th term of the AP 4, 9, 14, 19, …? (a) 190 (b) 194 (c) 199 (d) 195
17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
18. 18.If a + b = 17 and ab = 60, what is (a − b)²? (a) 49 (b) 7 (c) 169 (d) 289
19. 19.How many factors does 87 have? (a) 5 (b) 2 (c) 3 (d) 4
20. 20.In a class of 43 children, 29 like tea, 24 like coffee and 11 like both. How many like only tea? (a) 19 (b) 13 (c) 29 (d) 18
21. 21.In a class of 32 children, 23 like tea, 12 like coffee and 4 like both. How many like only tea? (a) 23 (b) 20 (c) 19 (d) 8
22. 22.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 145° (b) 160° (c) 20° (d) 55°
23. 23.What is the mean of 13, 7, 7 and 9? (a) 9 (b) 10 (c) 8 (d) 12
24. 24.If a + b = 17 and ab = 72, what is (a − b)²? (a) 289 (b) 1 (c) 217 (d) 145
25. 25.What is the distance between the points (4, 17) and (19, 9)? (a) 18 (b) 23 (c) 289 (d) 17
26. 26.What is the 22nd term of the AP 17, 19, 21, 23, …? (a) 44 (b) 59 (c) 42 (d) 61
27. 27.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/8 (c) 3/5 (d) 5/8
28. 28.In a class of 34 children, 20 like cricket, 16 like football and 7 like both. How many like only cricket? (a) 13 (b) 20 (c) 9 (d) 18
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 18 (b) 20 (c) 8 (d) 19
30. 30.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) 75 (d) 24
31. 31.What is the 19th term of the AP 5, 7, 9, 11, …? (a) 36 (b) 41 (c) 38 (d) 43
32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
33. 33.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 22 (c) 21 (d) 29
34. 34.If a + b = 19 and ab = 84, what is (a − b)²? (a) 193 (b) 5 (c) 25 (d) 361
35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
36. 36.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
37. 37.A drawer has lots of black and white 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) 3 (c) 5 (d) 4
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
39. 39.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
40. 40.What is the sum of the first 12 terms of the AP 3, 8, 13, …? (a) 732 (b) 396 (c) 366 (d) 58

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