Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 192 · 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 fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
2. 2.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
3. 3.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 59° (b) 60° (c) 61° (d) 120°
4. 4.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) 42 (d) 49
5. 5.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
6. 6.In a class of 21 children, 14 like mangoes, 12 like bananas and 6 like both. How many like only mangoes? (a) 14 (b) 6 (c) 9 (d) 8
7. 7.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
8. 8.The mean of 4 numbers is 39. When the number 59 is added to them, what is the new mean? (a) 39 (b) 44 (c) 43 (d) 49
9. 9.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 130° (d) 85°
10. 10.The mean of 7 numbers is 37. When the number 13 is added to them, what is the new mean? (a) 25 (b) 37 (c) 35 (d) 34
11. 11.If a + b = 13 and ab = 42, what is a² + b²? (a) 169 (b) 253 (c) 127 (d) 85
12. 12.If a + b = 17 and ab = 72, what is (a − b)²? (a) 289 (b) 1 (c) 145 (d) 217
13. 13.What is the sum of the first 6 terms of the AP 10, 14, 18, …? (a) 30 (b) 120 (c) 240 (d) 132
14. 14.If a + b = 17 and ab = 72, what is a² + b²? (a) 289 (b) 145 (c) 433 (d) 217
15. 15.What is the mode of 19, 19, 6, 1, 2, 19 and 6? (a) 19 (b) 6 (c) 2 (d) 1
16. 16.A bag has 2 red, 2 blue and 6 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/5 (b) 4/5 (c) 1/3 (d) 9/10
17. 17.A bag has 6 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 2 (c) 10 (d) 8
18. 18.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 7 (d) 6
19. 19.In a class of 15 children, 10 like mangoes, 8 like bananas and 4 like both. How many like neither? (a) 5 (b) 4 (c) 2 (d) 1
20. 20.A bag has 5 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 16 (b) 7 (c) 2 (d) 6
21. 21.What is the mode of 6, 13, 6, 6, 7, 18 and 7? (a) 18 (b) 13 (c) 6 (d) 7
22. 22.What is the mean of 6, 5, 3, 18 and 8? (a) 9 (b) 10 (c) 7 (d) 8
23. 23.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) 15 (d) 14
24. 24.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 35° (c) 130° (d) 50°
25. 25.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 35° (c) 105° (d) 110°
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
27. 27.A bag has 2 red, 5 green and 8 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/15 (b) 14/15 (c) 2/15 (d) 1/3
28. 28.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2⁴ × 3 × 7
29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
30. 30.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 1)(x + 42) (c) (x + 1)(x + 12) (d) (x + 6)(x + 7)
31. 31.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 35° (d) 160°
32. 32.A bag has 4 blue balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 5 (c) 2 (d) 13
33. 33.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
34. 34.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) 25 (b) 24 (c) 12 (d) 13
35. 35.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 210° (b) 105° (c) 30° (d) 150°
36. 36.In a class of 41 children, 13 like cricket, 26 like football and 8 like both. How many like at least one of the two? (a) 41 (b) 39 (c) 31 (d) 23
37. 37.Which term of the AP 14, 23, 32, 41, … is 113? (a) 12th (b) 11th (c) 13th (d) 14th
38. 38.In a class of 39 children, 21 like dance, 21 like music and 12 like both. How many like only dance? (a) 12 (b) 21 (c) 18 (d) 9
39. 39.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 39 (c) 108 (d) 36
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17

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