Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 66 · 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.A drawer has lots of red, green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 6 (d) 4
2. 2.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
3. 3.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
4. 4.How many factors does 72 have? (a) 10 (b) 11 (c) 12 (d) 13
5. 5.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) 40 (b) 64 (c) 12 (d) 32
6. 6.The mean of 7 numbers is 26. When the number 50 is added to them, what is the new mean? (a) 26 (b) 29 (c) 30 (d) 38
7. 7.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 76° (d) 75°
8. 8.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 270° (c) 135° (d) 90°
9. 9.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 909 (b) 1099 (c) 729 (d) 1089
10. 10.What is the mode of 13, 13, 2, 13, 10, 10 and 8? (a) 8 (b) 10 (c) 2 (d) 13
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
12. 12.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 45 (c) 135 (d) 15
13. 13.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 144 (c) 134 (d) 143
14. 14.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 8 (d) 15
16. 16.How many prime numbers are there between 90 and 110? (a) 7 (b) 6 (c) 4 (d) 5
17. 17.What is the 16th term of the AP 14, 23, 32, 41, …? (a) 158 (b) 144 (c) 135 (d) 149
18. 18.In a class of 31 children, 20 like mangoes, 12 like bananas and 3 like both. How many like neither? (a) 5 (b) 1 (c) 2 (d) 3
19. 19.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 99 (d) 36
20. 20.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 12 (c) 8 (d) 24
21. 21.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
22. 22.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 258 (b) 276 (c) 38 (d) 516
23. 23.In a class of 38 children, 21 like cricket, 16 like football and 3 like both. How many like at least one of the two? (a) 38 (b) 34 (c) 37 (d) 31
24. 24.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
25. 25.What is the midpoint of the line joining (5, 11) and (15, 7)? (a) (10, 9) (b) (9, 10) (c) (5, 2) (d) (20, 18)
26. 26.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 35 (b) 56 (c) 11 (d) 28
27. 27.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2048 (c) 2016 (d) 2080
28. 28.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 16 (b) 126 (c) 132 (d) 252
29. 29.How many factors does 69 have? (a) 4 (b) 3 (c) 5 (d) 2
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
31. 31.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 155° (c) 25° (d) 26°
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
33. 33.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x + 1)(x + 20) (c) (x + 1)(x + 8) (d) (x − 4)(x − 5)
34. 34.In a class of 25 children, 12 like cricket, 13 like football and 6 like neither. How many like both? (a) 5 (b) 19 (c) 7 (d) 6
35. 35.If a + b = 6 and ab = 8, what is (a − b)²? (a) 20 (b) 4 (c) 2 (d) 36
36. 36.What is the median of 29, 26, 13, 32, 33, 2 and 34? (a) 26 (b) 29 (c) 30 (d) 32
37. 37.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 138 (c) 120 (d) 130
38. 38.How many factors does 39 have? (a) 4 (b) 3 (c) 5 (d) 2
39. 39.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
40. 40.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3

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