Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 869 · 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.In a class of 32 children, 10 like maths, 16 like science and 2 like both. How many like at least one of the two? (a) 26 (b) 22 (c) 24 (d) 32
2. 2.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 48 (c) 24 (d) 11
3. 3.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
4. 4.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 55° (c) 110° (d) 35°
5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 55 (c) 22 (d) 121
6. 6.What is the mean of 7, 7, 12, 2, 7 and 7? (a) 9 (b) 8 (c) 6 (d) 7
7. 7.In a class of 27 children, 11 like tea, 21 like coffee and 7 like both. How many like neither? (a) 9 (b) 3 (c) 2 (d) 7
8. 8.What is the midpoint of the line joining (0, 8) and (6, 20)? (a) (3, 14) (b) (14, 3) (c) (3, 6) (d) (6, 28)
9. 9.What is the sum of the first 12 terms of the AP 9, 14, 19, …? (a) 468 (b) 876 (c) 64 (d) 438
10. 10.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 30 (c) 18 (d) 15
11. 11.What is the missing term in the AP 3, 5, 7, ?, 11? (a) 9 (b) 8 (c) 11 (d) 10
12. 12.If a + b = 9 and ab = 18, what is a² + b²? (a) 63 (b) 81 (c) 117 (d) 45
13. 13.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 16 (c) 72 (d) 18
14. 14.What is the median of 17, 23, 31, 36 and 8? (a) 17 (b) 31 (c) 24 (d) 23
15. 15.What is the 30th term of the AP 7, 9, 11, 13, …? (a) 65 (b) 60 (c) 58 (d) 67
16. 16.How many prime numbers are there between 10 and 40? (a) 10 (b) 9 (c) 8 (d) 7
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
18. 18.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 310° (c) 40° (d) 50°
19. 19.In a class of 23 children, 15 like cricket, 6 like football and 5 like neither. How many like both? (a) 18 (b) 5 (c) 3 (d) 4
20. 20.Which is the correct factorisation of x² + 11x + 24? (a) (x + 3)(x + 8) (b) (x + 1)(x + 10) (c) (x − 3)(x − 8) (d) (x + 1)(x + 24)
21. 21.What is the sum of all the whole numbers from 1 to 76? (a) 2850 (b) 2926 (c) 2888 (d) 5852
22. 22.What is the sum of the first 12 terms of the AP 5, 8, 11, …? (a) 38 (b) 276 (c) 258 (d) 516
23. 23.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 8 (d) 5
24. 24.What is the distance between the points (0, 17) and (12, 8)? (a) 21 (b) 15 (c) 225 (d) 16
25. 25.If a + b = 14 and ab = 48, what is a² + b²? (a) 196 (b) 100 (c) 148 (d) 292
26. 26.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 232 (b) 208 (c) 47 (d) 416
27. 27.What is the 40th term of the AP 13, 16, 19, 22, …? (a) 130 (b) 133 (c) 117 (d) 120
28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
29. 29.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
30. 30.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 70° (c) 110° (d) 100°
31. 31.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 145° (d) 95°
32. 32.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) 22 (b) 21 (c) 29 (d) 28
33. 33.In a class of 20 children, 11 like dance, 10 like music and 3 like neither. How many like both? (a) 17 (b) 4 (c) 3 (d) 1
34. 34.In a class of 34 children, 11 like cricket, 24 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 35 (d) 31
35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
36. 36.A drawer has lots of red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 5 (d) 4
37. 37.In which quadrant does the point (−1, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
38. 38.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 5 (b) 14 (c) 15 (d) 16

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