Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 130 · 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 sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
2. 2.In a class of 30 children, 10 like maths, 16 like science and 2 like both. How many like only maths? (a) 14 (b) 10 (c) 2 (d) 8
3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 37 (d) 25
4. 4.A bag has 4 red, 8 white and 8 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/5 (b) 17/20 (c) 4/5 (d) 1/3
5. 5.What is the 28th term of the AP 20, 26, 32, 38, …? (a) 162 (b) 188 (c) 168 (d) 182
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
7. 7.What is the median of 8, 11, 22, 10, 34, 30 and 9? (a) 22 (b) 12 (c) 11 (d) 10
8. 8.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
9. 9.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 10° (d) 20°
10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
12. 12.In which quadrant does the point (−7, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the sum of all the whole numbers from 1 to 77? (a) 3004 (b) 2926 (c) 6006 (d) 3003
14. 14.What is the sum of the first 6 terms of the AP 7, 13, 19, …? (a) 150 (b) 264 (c) 37 (d) 132
15. 15.What is the missing term in the AP 12, 18, 24, ?, 36? (a) 30 (b) 29 (c) 36 (d) 31
16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
17. 17.What is the distance between the points (7, 0) and (13, 8)? (a) 10 (b) 100 (c) 14 (d) 11
18. 18.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 36 (d) 39
19. 19.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
20. 20.What is the 36th term of the AP 6, 9, 12, 15, …? (a) 108 (b) 114 (c) 111 (d) 105
21. 21.What is the median of 38, 25, 32, 2, 3, 10 and 8? (a) 25 (b) 10 (c) 2 (d) 8
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
23. 23.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
24. 24.A bag has 7 green, 3 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 11/14 (c) 6/7 (d) 3/14
25. 25.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
26. 26.6 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) 18 (b) 24 (c) 12 (d) 8
27. 27.In which quadrant does the point (4, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.What is the distance between the points (5, 0) and (10, 12)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.In a class of 26 children, 13 like mangoes, 10 like bananas and 6 like neither. How many like both? (a) 20 (b) 6 (c) 4 (d) 3
30. 30.What is the sum of the roots of x² − 13x + 40 = 0? (a) 12 (b) 14 (c) 13 (d) 40
31. 31.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
32. 32.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 84 (b) 42 (c) 13 (d) 48
33. 33.4 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 20 (c) 24 (d) 9
34. 34.In a class of 34 children, 12 like maths, 23 like science and 8 like both. How many like only maths? (a) 11 (b) 12 (c) 4 (d) 15
35. 35.Two angles of a triangle are 45° and 70°. What is the third angle? (a) 110° (b) 65° (c) 135° (d) 115°
36. 36.What is the mode of 11, 8, 7, 7, 8, 20 and 8? (a) 8 (b) 7 (c) 20 (d) 11
37. 37.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 21 (c) 24 (d) 42
38. 38.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) 28 (b) 22 (c) 21 (d) 29
39. 39.What is the 40th term of the AP 3, 12, 21, 30, …? (a) 360 (b) 351 (c) 363 (d) 354
40. 40.Two angles of a triangle are 35° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 145° (d) 65°

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