Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 902 · 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.A bag has 7 green balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 2 (c) 8 (d) 9
2. 2.What is the midpoint of the line joining (5, 14) and (15, 6)? (a) (5, 4) (b) (10, 10) (c) (11, 10) (d) (20, 20)
3. 3.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
4. 4.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
5. 5.A bag has 8 black balls and 12 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) 20 (c) 13 (d) 9
6. 6.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 6 (d) 5
7. 7.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
9. 9.A bag has 8 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 14 (c) 2 (d) 9
10. 10.A bag has 9 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 10 (c) 11 (d) 14
11. 11.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 10° (c) 190° (d) 11°
12. 12.If a + b = 17 and ab = 70, what is (a − b)²? (a) 3 (b) 9 (c) 149 (d) 289
13. 13.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 140° (d) 50°
14. 14.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 400 (c) 202 (d) 301
15. 15.A bag has 3 yellow, 6 red and 5 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/7 (b) 1/3 (c) 3/4 (d) 3/7
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 5 (c) 7 (d) 8
17. 17.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/8 (d) 3/5
18. 18.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
19. 19.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 3/4 (d) 1/8
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 17 (c) 6 (d) 16
21. 21.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 28 (c) 56 (d) 11
22. 22.A bag has 8 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 10 (c) 2 (d) 9
23. 23.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) 36 (b) 24 (c) 37 (d) 25
24. 24.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 60° (b) 130° (c) 110° (d) 120°
25. 25.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 155° (b) 145° (c) 60° (d) 25°
26. 26.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 565 (c) 448 (d) 564
27. 27.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 42 (d) 21
28. 28.A bag has 10 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 11 (d) 16
29. 29.A drawer has lots of red, blue and black 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) 3 (c) 4 (d) 2
30. 30.In a class of 29 children, 16 like dance, 11 like music and 6 like both. How many like only dance? (a) 10 (b) 16 (c) 5 (d) 18
31. 31.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 50° (b) 130° (c) 310° (d) 40°
32. 32.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
33. 33.In a class of 42 children, 19 like cricket, 31 like football and 12 like both. How many like only cricket? (a) 12 (b) 19 (c) 11 (d) 7
34. 34.What are the roots of x² − 12x + 32 = 0? (a) 4 and 8 (b) 2 and 16 (c) 1 and 11 (d) 1 and 32
35. 35.Which term of the AP 6, 14, 22, 30, … is 254? (a) 33rd (b) 32nd (c) 34th (d) 31st
36. 36.What is the smallest prime factor of 95? (a) 5 (b) 2 (c) 1 (d) 19
37. 37.A drawer has lots of white, red, blue 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) 2 (b) 5 (c) 4 (d) 8
38. 38.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
39. 39.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
40. 40.How many factors does 112 have? (a) 9 (b) 10 (c) 8 (d) 11

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