Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 943 · 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 area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11
3. 3.What is the 33rd term of the AP 5, 14, 23, 32, …? (a) 302 (b) 297 (c) 288 (d) 293
4. 4.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 55 (c) 110 (d) 121
6. 6.In a class of 32 children, 18 like cricket, 22 like football and 10 like both. How many like neither? (a) 12 (b) 3 (c) 10 (d) 2
7. 7.What is the prime factorisation of 20? (a) 2 × 5 (b) 2³ × 5 (c) 2 × 5² (d) 2² × 5
8. 8.What is the smallest prime factor of 121? (a) 3 (b) 1 (c) 2 (d) 11
9. 9.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 13 (d) 23
10. 10.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 2 (d) 7
11. 11.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
12. 12.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 72 (c) 45 (d) 81
14. 14.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
15. 15.A bag has 12 black balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 13 (c) 14 (d) 15
16. 16.What is the distance between the points (5, 4) and (13, 10)? (a) 14 (b) 11 (c) 100 (d) 10
17. 17.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 625 (c) 635 (d) 225
18. 18.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 1 and 16 (c) 2 and 36 (d) 8 and 9
19. 19.In a class of 20 children, 12 like cricket, 13 like football and 7 like both. How many like at least one of the two? (a) 11 (b) 25 (c) 20 (d) 18
20. 20.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 4 times (d) 8 times
23. 23.What is the 28th term of the AP 17, 26, 35, 44, …? (a) 243 (b) 252 (c) 260 (d) 269
24. 24.What is the midpoint of the line joining (8, 14) and (14, 4)? (a) (9, 11) (b) (11, 9) (c) (22, 18) (d) (3, 5)
25. 25.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
26. 26.What is the distance between the points (3, 0) and (19, 12)? (a) 20 (b) 21 (c) 400 (d) 28
27. 27.A bag has 8 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 10 (c) 2 (d) 9
28. 28.A bag has 8 blue, 8 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 5/9 (b) 11/18 (c) 4/9 (d) 1/3
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
30. 30.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 105° (c) 75° (d) 155°
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
32. 32.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
33. 33.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5
34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
35. 35.What is the sum of all the whole numbers from 1 to 100? (a) 5050 (b) 10100 (c) 5000 (d) 4950
36. 36.What is the product of the roots of x² − 11x + 24 = 0? (a) 11 (b) 24 (c) 25 (d) 23
37. 37.What is the mode of 10, 18, 5, 5, 13, 10 and 10? (a) 10 (b) 5 (c) 18 (d) 13
38. 38.If a + b = 5 and ab = 4, what is (a − b)²? (a) 25 (b) 17 (c) 3 (d) 9
39. 39.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 21 (d) 28
40. 40.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100

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