Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 919 · 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.Which term of the AP 4, 13, 22, 31, … is 229? (a) 25th (b) 26th (c) 28th (d) 27th
2. 2.In a class of 38 children, 21 like dance, 20 like music and 10 like both. How many like at least one of the two? (a) 21 (b) 38 (c) 41 (d) 31
3. 3.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
4. 4.What is the smallest prime factor of 217? (a) 7 (b) 1 (c) 2 (d) 31
5. 5.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
6. 6.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 7)(x + 8) (c) (x + 1)(x + 56) (d) (x + 1)(x + 14)
7. 7.What is the mean of 17, 4, 6, 19, 10 and 10? (a) 12 (b) 13 (c) 10 (d) 11
8. 8.In a class of 35 children, 18 like maths, 22 like science and 11 like both. How many like at least one of the two? (a) 35 (b) 40 (c) 29 (d) 18
9. 9.What is the median of 19, 38, 30, 9, 11, 7 and 37? (a) 19 (b) 11 (c) 30 (d) 9
10. 10.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 30 (c) 36 (d) 11
11. 11.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 105°
12. 12.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 36 cu cm (c) 1728 cu cm (d) 576 cu cm
13. 13.In which quadrant does the point (8, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
14. 14.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 18 (c) 14 (d) 16
15. 15.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
16. 16.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
18. 18.Which is the correct factorisation of x² + 10x + 21? (a) (x − 3)(x − 7) (b) (x + 1)(x + 9) (c) (x + 3)(x + 7) (d) (x + 1)(x + 21)
19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 4 (d) 14
20. 20.In a class of 24 children, 11 like tea, 14 like coffee and 4 like both. How many like only tea? (a) 4 (b) 11 (c) 7 (d) 10
21. 21.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7
22. 22.In a class of 31 children, 12 like cricket, 11 like football and 2 like both. How many like only cricket? (a) 12 (b) 10 (c) 9 (d) 20
23. 23.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 70° (c) 71° (d) 250°
24. 24.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 20° (c) 10° (d) 80°
25. 25.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
26. 26.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 379 (c) 324 (d) 369
27. 27.What is the sum of the first 9 terms of the AP 5, 11, 17, …? (a) 522 (b) 288 (c) 53 (d) 261
28. 28.If a + b = 8 and ab = 7, what is a² + b²? (a) 50 (b) 64 (c) 78 (d) 57
29. 29.What is the median of 13, 1, 12, 34, 23, 30 and 11? (a) 12 (b) 23 (c) 34 (d) 13
30. 30.What is the 16th term of the AP 7, 12, 17, 22, …? (a) 75 (b) 80 (c) 82 (d) 87
31. 31.If a + b = 8 and ab = 15, what is (a − b)²? (a) 4 (b) 34 (c) 2 (d) 64
32. 32.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 60° (d) 120°
33. 33.What is the smallest prime factor of 35? (a) 7 (b) 5 (c) 1 (d) 2
34. 34.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 4)(x + 5) (c) (x − 4)(x − 5) (d) (x + 1)(x + 8)
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 6 (d) 12
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
37. 37.The mean of 9 numbers is 30. When the number 10 is added to them, what is the new mean? (a) 30 (b) 28 (c) 29 (d) 20
38. 38.A bag has 11 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 18 (c) 13 (d) 12
39. 39.Two angles of a triangle are 45° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 100° (d) 135°
40. 40.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 70 (c) 65 (d) 130

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