Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 103 · 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.If a + b = 17 and ab = 70, what is (a − b)²? (a) 3 (b) 149 (c) 289 (d) 9
2. 2.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
4. 4.What is the sum of all the whole numbers from 1 to 14? (a) 210 (b) 91 (c) 105 (d) 98
5. 5.The mean of 6 numbers is 24. When the number 52 is added to them, what is the new mean? (a) 24 (b) 28 (c) 38 (d) 29
6. 6.In a class of 42 children, 28 like dance, 24 like music and 11 like both. How many like neither? (a) 1 (b) 2 (c) 12 (d) 11
7. 7.What is the sum of all the whole numbers from 1 to 81? (a) 3322 (b) 3321 (c) 3240 (d) 6642
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 1/6 (c) 5/11 (d) 5/36
9. 9.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
11. 11.What is the mean of 18, 17, 11 and 10? (a) 13 (b) 14 (c) 16 (d) 15
12. 12.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
13. 13.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 18 (c) 162 (d) 54
14. 14.In a class of 43 children, 24 like maths, 18 like science and 9 like both. How many like neither? (a) 19 (b) 10 (c) 9 (d) 1
15. 15.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
16. 16.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
17. 17.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 157 (c) 166 (d) 148
18. 18.What is the median of 7, 11, 36, 1, 30, 40 and 34? (a) 1 (b) 11 (c) 30 (d) 34
19. 19.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1352 (c) 1326 (d) 1378
20. 20.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 75° (d) 105°
21. 21.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 9 (d) 12
22. 22.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 2211 (c) 4422 (d) 2145
23. 23.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 150° (b) 80° (c) 100° (d) 110°
24. 24.In which quadrant does the point (1, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
25. 25.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 12 (c) 40 (d) 35
26. 26.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) 13 (b) 25 (c) 12 (d) 24
27. 27.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
28. 28.What is the median of 1, 4, 22, 37, 36, 31 and 28? (a) 28 (b) 31 (c) 22 (d) 37
29. 29.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
30. 30.What is the median of 23, 40, 12, 1, 27, 38 and 7? (a) 27 (b) 12 (c) 23 (d) 1
31. 31.What is the mean of 9, 10, 18 and 15? (a) 14 (b) 12 (c) 13 (d) 15
32. 32.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
33. 33.What is the sum of the first 12 terms of the AP 1, 7, 13, …? (a) 67 (b) 408 (c) 816 (d) 444
34. 34.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
35. 35.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
36. 36.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
37. 37.How many factors does 55 have? (a) 5 (b) 4 (c) 2 (d) 3
38. 38.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
39. 39.What is the median of 19, 21, 27, 11 and 35? (a) 22 (b) 27 (c) 19 (d) 21
40. 40.What is the sum of all the whole numbers from 1 to 30? (a) 450 (b) 435 (c) 930 (d) 465

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