Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 827 · 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 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 435 (c) 841 (d) 57
2. 2.What is the mean of 2, 13, 19, 9 and 17? (a) 10 (b) 13 (c) 15 (d) 12
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
4. 4.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 7 (d) 5
5. 5.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
6. 6.A bag has 11 white balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 21 (b) 12 (c) 2 (d) 13
7. 7.What is the sum of the roots of x² − 13x + 42 = 0? (a) 12 (b) 13 (c) 14 (d) 42
8. 8.What is the midpoint of the line joining (8, 16) and (18, 4)? (a) (26, 20) (b) (13, 10) (c) (5, 6) (d) (10, 13)
9. 9.What is the missing term in the AP 18, ?, 36, 45, 54? (a) 27 (b) 28 (c) 36 (d) 26
10. 10.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 25 (c) 20 (d) 240
11. 11.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 1034 (b) 1024 (c) 904 (d) 784
12. 12.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 1682 (d) 3422
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/18 (d) 1/12
15. 15.How many factors does 43 have? (a) 2 (b) 4 (c) 1 (d) 3
16. 16.A bag has 7 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 8 (c) 9 (d) 13
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm
18. 18.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2314 (b) 2496 (c) 2704 (d) 2304
19. 19.A bag has 8 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 13 (d) 10
20. 20.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 135° (b) 85° (c) 45° (d) 140°
21. 21.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 42 (c) 49 (d) 13
22. 22.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) 40 (c) 20 (d) 9
23. 23.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
24. 24.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1444 (b) 1774 (c) 1764 (d) 1604
25. 25.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 6)(x + 7)
26. 26.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
27. 27.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 51 (c) 16 (d) 48
28. 28.8 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) 13 (b) 40 (c) 80 (d) 48
29. 29.What is the mode of 13, 19, 13, 12, 13, 19 and 3? (a) 3 (b) 19 (c) 13 (d) 12
30. 30.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 8 (d) 6
31. 31.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 145°
32. 32.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 144 (c) 66 (d) 132
33. 33.What is the mean of 11, 6, 14, 2 and 22? (a) 11 (b) 12 (c) 13 (d) 10
34. 34.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 146 (c) 145 (d) 136
35. 35.In a class of 35 children, 16 like maths, 24 like science and 1 like neither. How many like both? (a) 5 (b) 1 (c) 6 (d) 34
36. 36.The mean of 3 numbers is 23. When the number 39 is added to them, what is the new mean? (a) 23 (b) 28 (c) 31 (d) 27
37. 37.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
38. 38.A drawer has lots of blue 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) 4 (b) 3 (c) 2 (d) 5
39. 39.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
40. 40.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad