Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 139 · 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 an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
2. 2.What is the mode of 1, 6, 1, 1, 10, 10 and 18? (a) 18 (b) 10 (c) 1 (d) 6
3. 3.What is the mode of 9, 4, 4, 2, 4, 6 and 9? (a) 2 (b) 6 (c) 4 (d) 9
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
5. 5.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 31 (c) 136 (d) 272
6. 6.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 215° (c) 70° (d) 35°
7. 7.What is the missing term in the AP 1, 9, ?, 25, 33? (a) 16 (b) 18 (c) 17 (d) 25
8. 8.A drawer has lots of yellow, white, blue, green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 6 (d) 2
9. 9.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 140° (d) 40°
10. 10.What is the midpoint of the line joining (1, 8) and (9, 0)? (a) (4, 5) (b) (10, 8) (c) (5, 4) (d) (4, 4)
11. 11.What is the sum of all the whole numbers from 1 to 25? (a) 326 (b) 300 (c) 325 (d) 650
12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
13. 13.What is the sum of the roots of x² − 12x + 35 = 0? (a) 35 (b) 12 (c) 11 (d) 13
14. 14.What is the 16th term of the AP 13, 15, 17, 19, …? (a) 45 (b) 30 (c) 32 (d) 43
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
16. 16.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 65 cu cm (d) 96 cu cm
17. 17.What is the mode of 6, 14, 5, 14, 14, 6 and 13? (a) 6 (b) 13 (c) 5 (d) 14
18. 18.What is the sum of all the whole numbers from 1 to 70? (a) 2415 (b) 4970 (c) 2485 (d) 2450
19. 19.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 404 (b) 484 (c) 324 (d) 494
20. 20.What is the distance between the points (7, 2) and (16, 14)? (a) 21 (b) 225 (c) 16 (d) 15
21. 21.What is the mean of 10, 13, 3 and 2? (a) 9 (b) 8 (c) 7 (d) 6
22. 22.What is the midpoint of the line joining (0, 10) and (4, 16)? (a) (2, 13) (b) (13, 2) (c) (4, 26) (d) (2, 3)
23. 23.In which quadrant does the point (6, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 63 (c) 60 (d) 180
25. 25.How many factors does 105 have? (a) 6 (b) 7 (c) 8 (d) 9
26. 26.In a class of 22 children, 10 like dance, 16 like music and 7 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 19 (d) 12
27. 27.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5
28. 28.In a class of 39 children, 28 like maths, 20 like science and 12 like both. How many like at least one of the two? (a) 39 (b) 36 (c) 24 (d) 48
29. 29.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/8 (c) 1/4 (d) 3/4
30. 30.What is the distance between the points (1, 0) and (13, 9)? (a) 16 (b) 225 (c) 21 (d) 15
31. 31.How many factors does 41 have? (a) 3 (b) 4 (c) 2 (d) 1
32. 32.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 498 (d) 499
33. 33.A bag has 9 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 10 (c) 11 (d) 2
34. 34.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
35. 35.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 55° (c) 70° (d) 110°
36. 36.A bag has 9 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 10 (c) 18 (d) 11
37. 37.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 160° (c) 340° (d) 20°
38. 38.What is the distance between the points (9, 7) and (33, 0)? (a) 31 (b) 625 (c) 25 (d) 26
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
40. 40.How many factors does 48 have? (a) 11 (b) 8 (c) 10 (d) 9

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