Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 683 · 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 prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2⁵ × 7
2. 2.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
3. 3.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 90°
4. 4.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 198 (c) 66 (d) 22
5. 5.A bag has 11 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 12 (c) 2 (d) 14
6. 6.A bag has 4 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 13 (c) 6 (d) 5
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
8. 8.What is the mean of 13, 5, 13 and 13? (a) 11 (b) 13 (c) 12 (d) 10
9. 9.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 153 (c) 289 (d) 33
11. 11.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
12. 12.What is the 23rd term of the AP 9, 12, 15, 18, …? (a) 69 (b) 78 (c) 66 (d) 75
13. 13.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 105° (d) 145°
14. 14.How many factors does 28 have? (a) 4 (b) 5 (c) 7 (d) 6
15. 15.A bag has 11 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 23 (b) 12 (c) 13 (d) 2
16. 16.Using (a − b)² = a² − 2ab + b², what is 88²? (a) 8464 (b) 8096 (c) 7744 (d) 7754
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 17 (d) 15
18. 18.A bag has 5 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 11 (d) 6
19. 19.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) 15 (b) 14 (c) 7 (d) 8
20. 20.In a class of 35 children, 20 like tea, 18 like coffee and 4 like both. How many like only tea? (a) 14 (b) 16 (c) 17 (d) 20
21. 21.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 13 (c) 49 (d) 84
22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
23. 23.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
24. 24.What is the median of 4, 12, 24, 5 and 7? (a) 7 (b) 5 (c) 12 (d) 24
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
26. 26.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
27. 27.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
28. 28.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7²
29. 29.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 42 (d) 39
30. 30.In a class of 47 children, 26 like maths, 27 like science and 7 like both. How many like only maths? (a) 26 (b) 19 (c) 20 (d) 7
31. 31.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 61° (c) 120° (d) 30°
32. 32.In a class of 26 children, 11 like tea, 12 like coffee and 6 like both. How many like neither? (a) 3 (b) 15 (c) 6 (d) 9
33. 33.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 58 (d) 49
34. 34.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 100° (d) 140°
35. 35.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 55° (d) 125°
36. 36.In a class of 31 children, 18 like cricket, 13 like football and 8 like both. How many like neither? (a) 16 (b) 9 (c) 0 (d) 8
37. 37.The mean of 8 numbers is 39. When the number 21 is added to them, what is the new mean? (a) 39 (b) 38 (c) 30 (d) 37
38. 38.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 45 (c) 529 (d) 276
39. 39.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 25° (d) 65°
40. 40.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 105° (c) 65° (d) 140°

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