Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 718 · 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.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1521 (b) 1531 (c) 1599 (d) 1681
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
3. 3.A bag has 4 black balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 14 (d) 5
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
5. 5.In a class of 31 children, 15 like maths, 18 like science and 3 like both. How many like at least one of the two? (a) 30 (b) 33 (c) 27 (d) 31
6. 6.What is the distance between the points (1, 16) and (25, 9)? (a) 625 (b) 26 (c) 31 (d) 25
7. 7.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 255 (c) 248 (d) 265
8. 8.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 294 cu cm (d) 21 cu cm
9. 9.What is the mean of 14, 12, 2, 11, 9 and 18? (a) 13 (b) 10 (c) 12 (d) 11
10. 10.A bag has 8 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 11 (c) 2 (d) 10
11. 11.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 90 (b) 99 (c) 18 (d) 180
12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 462 (b) 441 (c) 231 (d) 41
13. 13.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
14. 14.In a class of 34 children, 14 like dance, 17 like music and 6 like both. How many like neither? (a) 3 (b) 15 (c) 6 (d) 9
15. 15.How many factors does 70 have? (a) 8 (b) 7 (c) 6 (d) 9
16. 16.What is the distance between the points (3, 15) and (15, 6)? (a) 21 (b) 225 (c) 15 (d) 16
17. 17.What is the median of 2, 7, 11, 35 and 32? (a) 12 (b) 32 (c) 7 (d) 11
18. 18.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 144 (c) 24 (d) 66
19. 19.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 19 (b) 110 (c) 100 (d) 55
20. 20.What is the mode of 11, 11, 19, 19, 11, 15 and 18? (a) 19 (b) 18 (c) 15 (d) 11
21. 21.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
23. 23.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 555 (c) 546 (d) 556
24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
25. 25.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
26. 26.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7056 (b) 5776 (c) 6416 (d) 7066
27. 27.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.In a class of 40 children, 17 like mangoes, 29 like bananas and 11 like both. How many like at least one of the two? (a) 46 (b) 40 (c) 35 (d) 24
29. 29.What is the mean of 17, 10, 10, 4 and 4? (a) 10 (b) 11 (c) 8 (d) 9
30. 30.What is the median of 6, 10, 33, 28 and 7? (a) 7 (b) 28 (c) 33 (d) 10
31. 31.There are 8 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) 32 (b) 16 (c) 24 (d) 10
32. 32.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
33. 33.If a + b = 16 and ab = 60, what is (a − b)²? (a) 256 (b) 16 (c) 136 (d) 4
34. 34.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 3 (d) 5
35. 35.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
36. 36.What is the distance between the points (0, 21) and (5, 9)? (a) 17 (b) 13 (c) 169 (d) 14
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
38. 38.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁴ × 5 (c) 2⁵ × 5 (d) 2³ × 5
39. 39.What is the missing term in the AP 2, ?, 10, 14, 18? (a) 7 (b) 5 (c) 6 (d) 10
40. 40.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 72 (c) 78 (d) 17

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