Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 504 · 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 is the correct factorisation of x² + 7x + 10? (a) (x + 2)(x + 5) (b) (x + 1)(x + 6) (c) (x − 2)(x − 5) (d) (x + 1)(x + 10)
2. 2.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 2025 (c) 1575 (d) 1235
3. 3.In a class of 22 children, 13 like tea, 12 like coffee and 6 like both. How many like only tea? (a) 13 (b) 6 (c) 10 (d) 7
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
5. 5.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
6. 6.In a class of 28 children, 9 like mangoes, 17 like bananas and 3 like both. How many like at least one of the two? (a) 20 (b) 26 (c) 28 (d) 23
7. 7.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
8. 8.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 20 (c) 40 (d) 9
9. 9.In a class of 56 children, 30 like tea, 32 like coffee and 12 like both. How many like neither? (a) 12 (b) 6 (c) 7 (d) 18
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
11. 11.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
12. 12.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 20
14. 14.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 91 (c) 196 (d) 105
15. 15.The mean of 4 numbers is 35. When the number 50 is added to them, what is the new mean? (a) 39 (b) 37 (c) 35 (d) 38
16. 16.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
17. 17.A bag has 10 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 7 (c) 11 (d) 2
18. 18.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 3 (b) 4 (c) 6 (d) 5
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 1/11 (c) 5/36 (d) 1/6
22. 22.What is the 35th term of the AP 14, 22, 30, 38, …? (a) 286 (b) 280 (c) 272 (d) 294
23. 23.In a class of 32 children, 12 like dance, 24 like music and 5 like both. How many like only dance? (a) 12 (b) 8 (c) 7 (d) 19
24. 24.A bag has 7 yellow balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 2 (c) 8 (d) 10
25. 25.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 28) (b) (x + 1)(x + 10) (c) (x − 4)(x − 7) (d) (x + 4)(x + 7)
26. 26.In a class of 38 children, 29 like cricket, 15 like football and 9 like both. How many like at least one of the two? (a) 38 (b) 44 (c) 26 (d) 35
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 44 sq cm (d) 616 sq cm
28. 28.If a + b = 13 and ab = 36, what is (a − b)²? (a) 97 (b) 5 (c) 25 (d) 169
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
30. 30.If a + b = 12 and ab = 27, what is (a − b)²? (a) 144 (b) 90 (c) 6 (d) 36
31. 31.How many factors does 12 have? (a) 5 (b) 6 (c) 7 (d) 4
32. 32.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 250 (c) 238 (d) 249
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 2 times (d) 4 times
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
35. 35.What is the 25th term of the AP 17, 20, 23, 26, …? (a) 72 (b) 89 (c) 75 (d) 92
36. 36.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
37. 37.There are 4 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) 7 (b) 12 (c) 16 (d) 24
38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
39. 39.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 126 (d) 136
40. 40.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 120 (c) 240 (d) 25

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