Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 915 · 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 12 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 13 (c) 8 (d) 2
2. 2.In a class of 29 children, 17 like dance, 10 like music and 9 like neither. How many like both? (a) 7 (b) 9 (c) 8 (d) 20
3. 3.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x − 3)(x − 7) (c) (x + 1)(x + 21) (d) (x + 3)(x + 7)
4. 4.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 10816 (b) 9216 (c) 10016 (d) 10826
5. 5.In a class of 41 children, 23 like cricket, 20 like football and 6 like both. How many like only cricket? (a) 14 (b) 21 (c) 17 (d) 23
6. 6.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 100° (b) 145° (c) 65° (d) 115°
7. 7.A drawer has lots of red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 5 (d) 2
8. 8.In a class of 35 children, 11 like tea, 19 like coffee and 2 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 28 (d) 35
9. 9.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 404 (c) 499 (d) 489
10. 10.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 120° (d) 60°
11. 11.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 22 (c) 66 (d) 69
12. 12.Two angles of a triangle are 20° and 105°. What is the exterior angle at the third corner? (a) 55° (b) 160° (c) 125° (d) 75°
13. 13.What is the midpoint of the line joining (1, 9) and (3, 11)? (a) (10, 2) (b) (2, 10) (c) (4, 20) (d) (1, 1)
14. 14.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
15. 15.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
16. 16.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
17. 17.The mean of 8 numbers is 10. When the number 1 is added to them, what is the new mean? (a) 8 (b) 11 (c) 10 (d) 9
18. 18.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 35 (b) 11 (c) 60 (d) 30
19. 19.What is the midpoint of the line joining (7, 10) and (9, 6)? (a) (9, 8) (b) (16, 16) (c) (1, 2) (d) (8, 8)
20. 20.A bag has 4 yellow balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 2 (c) 6 (d) 13
21. 21.What are the roots of x² − 8x + 15 = 0? (a) 1 and 15 (b) 2 and 6 (c) 1 and 7 (d) 3 and 5
22. 22.In a class of 38 children, 13 like mangoes, 23 like bananas and 8 like neither. How many like both? (a) 8 (b) 7 (c) 30 (d) 6
23. 23.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
24. 24.In a class of 34 children, 17 like dance, 23 like music and 3 like neither. How many like both? (a) 3 (b) 6 (c) 31 (d) 9
25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/11 (c) 1/6 (d) 5/36
27. 27.Which term of the AP 14, 22, 30, 38, … is 134? (a) 18th (b) 16th (c) 17th (d) 15th
28. 28.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 15 (c) 7 (d) 12
29. 29.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 350 (c) 408 (d) 418
30. 30.A drawer has lots of white, red, green, black and yellow 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) 10 (c) 5 (d) 6
31. 31.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
32. 32.In a class of 26 children, 8 like tea, 16 like coffee and 4 like both. How many like only tea? (a) 8 (b) 12 (c) 10 (d) 4
33. 33.The mean of 5 numbers is 17. When the number 29 is added to them, what is the new mean? (a) 17 (b) 23 (c) 19 (d) 20
34. 34.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 3/8 (d) 1/4
35. 35.A bag has 7 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 2 (c) 8 (d) 9
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 13 (c) 3 (d) 14
37. 37.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 361 (c) 360 (d) 312
38. 38.In a class of 43 children, 20 like maths, 18 like science and 4 like both. How many like at least one of the two? (a) 34 (b) 38 (c) 43 (d) 30
39. 39.What are the roots of x² − 11x + 30 = 0? (a) 1 and 10 (b) 1 and 30 (c) 5 and 6 (d) 2 and 15
40. 40.A bag has 5 red, 3 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/3 (b) 1/3 (c) 3/4 (d) 1/12

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