Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 764 · 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 29th term of the AP 19, 25, 31, 37, …? (a) 193 (b) 174 (c) 168 (d) 187
2. 2.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/3 (c) 1/6 (d) 1/5
3. 3.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 5 (b) 6 (c) 12 (d) 9
4. 4.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 20 (d) 25
5. 5.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 65° (d) 115°
6. 6.A bag has 8 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 10 (c) 17 (d) 2
7. 7.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 320° (c) 140° (d) 20°
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 48 (d) 12
9. 9.A drawer has lots of red, blue, white, black 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) 5 (b) 10 (c) 6 (d) 2
10. 10.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
12. 12.If a + b = 13 and ab = 42, what is a² + b²? (a) 253 (b) 169 (c) 127 (d) 85
13. 13.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
14. 14.A bag has 2 green, 8 blue and 9 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 17/19 (b) 2/17 (c) 2/19 (d) 1/3
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 7 (b) 5 (c) 6 (d) 4
16. 16.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4465 (c) 4418 (d) 8930
17. 17.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 86° (c) 85° (d) 170°
18. 18.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) 24 (b) 36 (c) 37 (d) 25
19. 19.What is the smallest prime factor of 403? (a) 31 (b) 1 (c) 2 (d) 13
20. 20.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
21. 21.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 1 (d) 2
22. 22.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 140° (b) 170° (c) 50° (d) 10°
23. 23.What is the sum of the first 5 terms of the AP 4, 7, 10, …? (a) 16 (b) 53 (c) 50 (d) 100
24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
25. 25.In a class of 54 children, 29 like cricket, 29 like football and 10 like both. How many like only cricket? (a) 25 (b) 10 (c) 19 (d) 29
26. 26.A bag has 6 blue, 2 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/8 (b) 1/3 (c) 15/16 (d) 7/8
27. 27.If a + b = 9 and ab = 18, what is (a − b)²? (a) 3 (b) 9 (c) 45 (d) 81
28. 28.How many factors does 86 have? (a) 4 (b) 3 (c) 5 (d) 2
29. 29.The mean of 3 numbers is 18. When the number 14 is added to them, what is the new mean? (a) 18 (b) 16 (c) 17 (d) 19
30. 30.A bag has 9 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 2 (c) 10 (d) 16
31. 31.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 15 (c) 22 (d) 21
32. 32.The mean of 3 numbers is 12. When the number 8 is added to them, what is the new mean? (a) 13 (b) 11 (c) 12 (d) 10
33. 33.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 72 (c) 16 (d) 18
34. 34.What is the prime factorisation of 36? (a) 2² × 3² (b) 2 × 3² (c) 2² × 3³ (d) 2³ × 3²
35. 35.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 5625 (b) 7235 (c) 6425 (d) 7225
36. 36.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
38. 38.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/8 (d) 3/5
39. 39.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 6 times (d) 2 times

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