Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 932 · 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.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 10 (d) 8
2. 2.In a class of 28 children, 11 like cricket, 18 like football and 7 like both. How many like at least one of the two? (a) 28 (b) 29 (c) 22 (d) 15
3. 3.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x + 1)(x + 24) (c) (x − 4)(x − 6) (d) (x + 1)(x + 9)
4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
5. 5.Using (a − b)² = a² − 2ab + b², what is 68²? (a) 4896 (b) 5184 (c) 4634 (d) 4624
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
7. 7.What is the distance between the points (0, 7) and (12, 2)? (a) 14 (b) 13 (c) 169 (d) 17
8. 8.If a + b = 12 and ab = 20, what is (a − b)²? (a) 8 (b) 104 (c) 64 (d) 144
9. 9.The mean of 4 numbers is 40. When the number 55 is added to them, what is the new mean? (a) 42 (b) 43 (c) 44 (d) 40
10. 10.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 115° (b) 40° (c) 105° (d) 140°
11. 11.What is the mode of 3, 1, 7, 1, 6, 1 and 3? (a) 1 (b) 6 (c) 7 (d) 3
12. 12.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 41 (b) 312 (c) 294 (d) 588
13. 13.Which term of the AP 14, 18, 22, 26, … is 122? (a) 30th (b) 29th (c) 28th (d) 27th
14. 14.The mean of 8 numbers is 23. When the number 32 is added to them, what is the new mean? (a) 25 (b) 24 (c) 26 (d) 23
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 18 (b) 16 (c) 6 (d) 17
16. 16.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 9 (c) 14 (d) 28
17. 17.What is the mean of 9, 4, 9 and 18? (a) 9 (b) 8 (c) 10 (d) 11
18. 18.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 48 (c) 24 (d) 12
19. 19.What is the median of 30, 33, 29, 7 and 24? (a) 29 (b) 28 (c) 24 (d) 30
20. 20.What is the median of 29, 4, 3, 37 and 1? (a) 3 (b) 29 (c) 5 (d) 4
21. 21.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
22. 22.The mean of 9 numbers is 40. When the number 60 is added to them, what is the new mean? (a) 50 (b) 40 (c) 43 (d) 42
23. 23.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 120° (c) 90° (d) 270°
24. 24.What is the mean of 4, 3, 3, 13, 16 and 21? (a) 12 (b) 9 (c) 10 (d) 11
25. 25.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 13 (d) 11
26. 26.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 6 (d) 18
27. 27.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
28. 28.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 25° (c) 125° (d) 155°
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
30. 30.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 60 sq cm (b) 224 sq cm (c) 56 sq cm (d) 112 sq cm
31. 31.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 142 (c) 160 (d) 152
32. 32.What is the sum of all the whole numbers from 1 to 99? (a) 4851 (b) 4950 (c) 4951 (d) 9900
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
34. 34.A bag has 11 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 13 (c) 12 (d) 22
35. 35.What is the 37th term of the AP 4, 11, 18, 25, …? (a) 256 (b) 259 (c) 263 (d) 252
36. 36.A bag has 8 red balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 10 (c) 9 (d) 2
37. 37.In a class of 24 children, 11 like cricket, 12 like football and 8 like both. How many like at least one of the two? (a) 23 (b) 15 (c) 7 (d) 24
38. 38.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
39. 39.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 5 (d) 6
40. 40.What is the mean of 13, 16, 19 and 16? (a) 17 (b) 18 (c) 15 (d) 16

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