Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 41 · 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.How many factors does 22 have? (a) 2 (b) 5 (c) 3 (d) 4
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
3. 3.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 16 (c) 48 (d) 24
4. 4.In a class of 29 children, 14 like cricket, 13 like football and 2 like both. How many like at least one of the two? (a) 29 (b) 27 (c) 23 (d) 25
5. 5.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
6. 6.If a + b = 15 and ab = 36, what is a² + b²? (a) 153 (b) 225 (c) 297 (d) 189
7. 7.The mean of 7 numbers is 18. When the number 10 is added to them, what is the new mean? (a) 18 (b) 16 (c) 17 (d) 14
8. 8.A bag has 7 yellow, 8 red and 6 green balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/21 (b) 5/7 (c) 1/3 (d) 2/3
9. 9.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 7 (d) 5
10. 10.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 110° (d) 140°
11. 11.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
12. 12.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 14 (d) 15
13. 13.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
14. 14.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 50° (b) 160° (c) 130° (d) 70°
15. 15.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2² × 7 (c) 2 × 7³ (d) 2³ × 7
16. 16.In a class of 30 children, 10 like dance, 13 like music and 10 like neither. How many like both? (a) 4 (b) 3 (c) 10 (d) 20
17. 17.The mean of 5 numbers is 25. When the number 1 is added to them, what is the new mean? (a) 25 (b) 22 (c) 21 (d) 13
18. 18.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
19. 19.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 60° (c) 30° (d) 70°
20. 20.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 256 cu cm (c) 512 cu cm (d) 24 cu cm
21. 21.A bag has 3 green, 8 white and 8 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 17/19 (b) 3/19 (c) 1/3 (d) 16/19
22. 22.What is the median of 4, 17, 12, 33 and 25? (a) 18 (b) 17 (c) 25 (d) 12
23. 23.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
24. 24.What is the 17th term of the AP 10, 19, 28, 37, …? (a) 163 (b) 144 (c) 153 (d) 154
25. 25.What is the 21st term of the AP 4, 7, 10, 13, …? (a) 63 (b) 67 (c) 60 (d) 64
26. 26.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
27. 27.A bag has 6 blue, 3 white and 8 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 6/17 (c) 11/17 (d) 6/11
28. 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 24 (d) 25
29. 29.In a class of 29 children, 7 like dance, 20 like music and 3 like both. How many like at least one of the two? (a) 24 (b) 29 (c) 21 (d) 27
30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 361 (b) 190 (c) 37 (d) 380
31. 31.In a class of 27 children, 17 like maths, 17 like science and 3 like neither. How many like both? (a) 10 (b) 7 (c) 3 (d) 24
32. 32.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
33. 33.In a class of 39 children, 23 like dance, 10 like music and 4 like both. How many like at least one of the two? (a) 25 (b) 33 (c) 39 (d) 29
34. 34.A bag has 4 black balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 5 (d) 10
35. 35.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 12 (c) 9 (d) 3
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
37. 37.A drawer has lots of white, yellow, green 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) 8 (b) 5 (c) 4 (d) 2
38. 38.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2⁵ × 3² (d) 2² × 3⁴
39. 39.Two angles of a triangle are 20° and 130°. What is the exterior angle at the third corner? (a) 50° (b) 30° (c) 150° (d) 160°
40. 40.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225

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