Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 935 · 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 product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 15 (c) 54 (d) 55
2. 2.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 110° (c) 85° (d) 95°
3. 3.A bag has 3 yellow, 4 red and 5 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 5/6 (b) 1/4 (c) 3/4 (d) 1/3
4. 4.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
5. 5.In a class of 42 children, 16 like cricket, 25 like football and 8 like both. How many like only cricket? (a) 16 (b) 8 (c) 9 (d) 17
6. 6.A bag has 7 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 8 (c) 14 (d) 9
7. 7.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
8. 8.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 115° (b) 90° (c) 65° (d) 155°
9. 9.What is the median of 3, 12, 22, 28 and 37? (a) 23 (b) 28 (c) 22 (d) 12
10. 10.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/4 (c) 5/6 (d) 1/3
11. 11.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x + 1)(x + 14)
12. 12.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 48 (c) 12 (d) 16
13. 13.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 298 (c) 340 (d) 330
14. 14.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 9 (d) 3
15. 15.In which quadrant does the point (−7, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.A bag has 7 red, 8 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/13 (b) 7/20 (c) 13/20 (d) 1/3
17. 17.What is the prime factorisation of 15? (a) 3 × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3² × 5
18. 18.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 35° (b) 60° (c) 155° (d) 145°
19. 19.A bag has 11 red balls and 12 black 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) 23 (d) 12
20. 20.What is the distance between the points (3, 1) and (6, 5)? (a) 25 (b) 7 (c) 6 (d) 5
21. 21.Which term of the AP 1, 4, 7, 10, … is 58? (a) 22nd (b) 19th (c) 20th (d) 21st
22. 22.In a class of 25 children, 15 like maths, 10 like science and 2 like neither. How many like both? (a) 3 (b) 1 (c) 2 (d) 23
23. 23.A bag has 8 blue, 3 yellow and 4 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/15 (b) 1/3 (c) 8/15 (d) 3/5
24. 24.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 192 (c) 206 (d) 202
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
26. 26.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 24 (c) 28 (d) 48
27. 27.What is the median of 10, 12, 2, 31, 27, 19 and 23? (a) 31 (b) 23 (c) 19 (d) 12
28. 28.What is the smallest prime factor of 121? (a) 2 (b) 1 (c) 3 (d) 11
29. 29.How many factors does 37 have? (a) 2 (b) 3 (c) 1 (d) 4
30. 30.What is the distance between the points (7, 9) and (15, 24)? (a) 289 (b) 18 (c) 23 (d) 17
31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
32. 32.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 24 (c) 7 (d) 21
33. 33.What is the sum of the first 7 terms of the AP 7, 11, 15, …? (a) 266 (b) 133 (c) 31 (d) 147
34. 34.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 516 (c) 525 (d) 422
35. 35.A bag has 2 red, 8 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 8/13 (b) 5/13 (c) 1/3 (d) 5/8
36. 36.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
37. 37.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
38. 38.What is the midpoint of the line joining (8, 17) and (14, 9)? (a) (13, 11) (b) (3, 4) (c) (22, 26) (d) (11, 13)
39. 39.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 225 (b) 635 (c) 625 (d) 425
40. 40.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°

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