Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 124 · 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 6, 11, 16, 21, … is 66? (a) 14th (b) 12th (c) 13th (d) 15th
2. 2.What is the missing term in the AP 3, ?, 11, 15, 19? (a) 11 (b) 8 (c) 7 (d) 6
3. 3.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 12 (c) 24 (d) 16
4. 4.What is the 32nd term of the AP 20, 23, 26, 29, …? (a) 116 (b) 113 (c) 93 (d) 96
5. 5.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 28 (d) 29
6. 6.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 25° (c) 110° (d) 95°
7. 7.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 15 (d) 22
8. 8.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 441 (c) 462 (d) 231
9. 9.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
10. 10.What is the sum of all the whole numbers from 1 to 22? (a) 231 (b) 253 (c) 242 (d) 506
11. 11.A bag has 5 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 6 (d) 4
12. 12.A bag has 8 green balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 19 (c) 9 (d) 2
13. 13.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 22 (c) 94 (d) 91
14. 14.Which term of the AP 7, 16, 25, 34, … is 340? (a) 40th (b) 37th (c) 39th (d) 38th
15. 15.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 64 (c) 112 (d) 56
16. 16.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
17. 17.What is the sum of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 12 (d) 10
18. 18.How many factors does 55 have? (a) 5 (b) 2 (c) 3 (d) 4
19. 19.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 57 (d) 19
20. 20.The mean of 3 numbers is 29. When the number 33 is added to them, what is the new mean? (a) 30 (b) 29 (c) 32 (d) 31
21. 21.In a class of 32 children, 13 like maths, 25 like science and 3 like neither. How many like both? (a) 3 (b) 29 (c) 9 (d) 6
22. 22.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 27 cu cm (d) 486 cu cm
23. 23.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 539 (c) 529 (d) 289
24. 24.What is the mean of 13, 13, 9, 4 and 11? (a) 12 (b) 11 (c) 9 (d) 10
25. 25.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) 25 (b) 13 (c) 24 (d) 12
26. 26.What is the median of 34, 19, 30, 5, 27, 20 and 16? (a) 27 (b) 19 (c) 20 (d) 5
27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
28. 28.In which quadrant does the point (3, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
29. 29.A drawer has lots of green, red, blue, white 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) 5 (b) 2 (c) 6 (d) 10
30. 30.In a class of 38 children, 18 like cricket, 21 like football and 8 like both. How many like at least one of the two? (a) 31 (b) 38 (c) 39 (d) 23
31. 31.What is the mean of 19, 11, 7, 19 and 14? (a) 16 (b) 14 (c) 13 (d) 15
32. 32.A bag has 7 blue, 6 white and 3 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 11/16 (b) 5/8 (c) 3/8 (d) 1/3
33. 33.How many factors does 51 have? (a) 2 (b) 3 (c) 4 (d) 5
34. 34.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
35. 35.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
36. 36.What is the mode of 18, 1, 5, 1, 10, 1 and 18? (a) 1 (b) 10 (c) 18 (d) 5
37. 37.What is the mode of 10, 11, 2, 11, 10, 6 and 10? (a) 10 (b) 11 (c) 6 (d) 2
38. 38.If a + b = 4 and ab = 3, what is (a − b)²? (a) 16 (b) 4 (c) 10 (d) 2
39. 39.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 75° (b) 40° (c) 140° (d) 145°
40. 40.What is the 30th term of the AP 8, 14, 20, 26, …? (a) 188 (b) 180 (c) 182 (d) 174

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