Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 599 · 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 10th term of the AP 4, 11, 18, 25, …? (a) 63 (b) 67 (c) 74 (d) 70
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
5. 5.What is the sum of the first 11 terms of the AP 4, 5, 6, …? (a) 14 (b) 198 (c) 100 (d) 99
6. 6.A bag has 7 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 8 (d) 6
7. 7.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
8. 8.What is the product of the roots of x² − 11x + 18 = 0? (a) 11 (b) 19 (c) 17 (d) 18
9. 9.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
10. 10.Which term of the AP 2, 9, 16, 23, … is 142? (a) 21st (b) 20th (c) 22nd (d) 23rd
11. 11.How many factors does 26 have? (a) 2 (b) 4 (c) 5 (d) 3
12. 12.There are 6 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) 36 (b) 9 (c) 18 (d) 24
13. 13.If a + b = 11 and ab = 10, what is (a − b)²? (a) 81 (b) 101 (c) 9 (d) 121
14. 14.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/4 (c) 1/8 (d) 7/8
15. 15.Two angles of a triangle are 20° and 130°. What is the third angle? (a) 150° (b) 160° (c) 30° (d) 50°
16. 16.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
17. 17.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 150 sq cm (c) 25 sq cm (d) 100 sq cm
18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
19. 19.What is the mode of 20, 1, 20, 16, 6, 20 and 16? (a) 1 (b) 16 (c) 20 (d) 6
20. 20.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 448 (c) 370 (d) 447
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 6 (b) 10 (c) 12 (d) 13
22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
23. 23.How many factors does 119 have? (a) 5 (b) 3 (c) 4 (d) 2
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 2464 cm (d) 352 cm
25. 25.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 20 (d) 25
26. 26.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 48 (d) 16
27. 27.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1691 (b) 1521 (c) 1601 (d) 1681
28. 28.What is the mean of 20, 13, 4, 13 and 15? (a) 13 (b) 14 (c) 12 (d) 15
29. 29.What are the roots of x² − 15x + 56 = 0? (a) 2 and 28 (b) 1 and 56 (c) 1 and 14 (d) 7 and 8
30. 30.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 12 (c) 40 (d) 32
31. 31.What is the distance between the points (6, 15) and (30, 8)? (a) 625 (b) 26 (c) 25 (d) 31
32. 32.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 48 (c) 24 (d) 32
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
34. 34.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8474 (b) 8464 (c) 7744 (d) 8104
35. 35.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
36. 36.In a class of 36 children, 9 like cricket, 21 like football and 2 like both. How many like neither? (a) 6 (b) 10 (c) 2 (d) 8
37. 37.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2³ × 3² × 5
38. 38.In a class of 36 children, 22 like maths, 15 like science and 8 like both. How many like at least one of the two? (a) 37 (b) 21 (c) 36 (d) 29
39. 39.What is the mode of 15, 7, 15, 7, 20, 6 and 7? (a) 20 (b) 6 (c) 7 (d) 15
40. 40.What is the median of 12, 1, 30, 17, 8, 33 and 5? (a) 17 (b) 13 (c) 8 (d) 12

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