Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 54 · 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.What is the distance between the points (9, 7) and (21, 12)? (a) 17 (b) 169 (c) 14 (d) 13
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
3. 3.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 12 (c) 8 (d) 24
4. 4.A drawer has lots of green, red 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) 3 (b) 2 (c) 4 (d) 6
5. 5.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 4371 (d) 8742
6. 6.What is the 37th term of the AP 15, 21, 27, 33, …? (a) 216 (b) 222 (c) 237 (d) 231
7. 7.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 130°
8. 8.What is the smallest prime factor of 85? (a) 17 (b) 5 (c) 2 (d) 1
9. 9.What is the missing term in the AP 10, ?, 14, 16, 18? (a) 11 (b) 14 (c) 13 (d) 12
10. 10.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 4225 (b) 3025 (c) 3575 (d) 3035
11. 11.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 12 (c) 18 (d) 9
12. 12.What is the median of 21, 14, 9, 33 and 2? (a) 9 (b) 14 (c) 15 (d) 21
13. 13.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
14. 14.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 31 (b) 352 (c) 176 (d) 179
15. 15.A drawer has lots of black, green, white 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) 8 (b) 4 (c) 2 (d) 5
16. 16.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 39 (c) 42 (d) 117
17. 17.What is the missing term in the AP 14, 22, 30, ?, 46? (a) 37 (b) 38 (c) 46 (d) 39
18. 18.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
19. 19.What is the mean of 18, 16, 6, 4 and 6? (a) 12 (b) 9 (c) 11 (d) 10
20. 20.What is the median of 28, 27, 2, 9, 36, 8 and 24? (a) 9 (b) 27 (c) 25 (d) 24
21. 21.What is the mean of 5, 2, 7, 7, 6 and 9? (a) 7 (b) 8 (c) 5 (d) 6
22. 22.The mean of 3 numbers is 27. When the number 19 is added to them, what is the new mean? (a) 23 (b) 25 (c) 27 (d) 26
23. 23.What is the distance between the points (2, 19) and (11, 7)? (a) 15 (b) 21 (c) 16 (d) 225
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
25. 25.What is the 37th term of the AP 8, 14, 20, 26, …? (a) 222 (b) 230 (c) 216 (d) 224
26. 26.If a + b = 20 and ab = 99, what is a² + b²? (a) 598 (b) 301 (c) 400 (d) 202
27. 27.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 20 (c) 7 (d) 15
28. 28.Which term of the AP 13, 18, 23, 28, … is 58? (a) 10th (b) 12th (c) 9th (d) 11th
29. 29.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 40° (c) 220° (d) 70°
30. 30.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 24 (d) 25
31. 31.In a class of 38 children, 14 like dance, 23 like music and 4 like neither. How many like both? (a) 2 (b) 34 (c) 4 (d) 3
32. 32.What is the sum of the first 5 terms of the AP 9, 11, 13, …? (a) 17 (b) 70 (c) 65 (d) 130
33. 33.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
34. 34.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 55 (b) 64 (c) 56 (d) 46
35. 35.What is the 24th term of the AP 4, 12, 20, 28, …? (a) 184 (b) 196 (c) 192 (d) 188
36. 36.How many factors does 37 have? (a) 3 (b) 1 (c) 4 (d) 2
37. 37.What is the midpoint of the line joining (4, 8) and (6, 10)? (a) (10, 18) (b) (9, 5) (c) (1, 1) (d) (5, 9)
38. 38.What is the mode of 10, 9, 7, 9, 7, 19 and 9? (a) 9 (b) 7 (c) 19 (d) 10
39. 39.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 135° (d) 75°
40. 40.A bag has 4 green, 8 blue and 6 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 2/3 (c) 1/18 (d) 13/18

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