Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 742 · 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.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
2. 2.If a + b = 12 and ab = 35, what is a² + b²? (a) 74 (b) 144 (c) 214 (d) 109
3. 3.What is the 10th term of the AP 5, 8, 11, 14, …? (a) 30 (b) 32 (c) 35 (d) 27
4. 4.What is the sum of all the whole numbers from 1 to 24? (a) 288 (b) 600 (c) 276 (d) 300
5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 14 (b) 16 (c) 5 (d) 15
6. 6.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
7. 7.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 60 (c) 63 (d) 180
8. 8.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
11. 11.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 3 (d) 1
12. 12.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 346 (b) 56 (c) 341 (d) 682
13. 13.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
14. 14.The mean of 8 numbers is 23. When the number 50 is added to them, what is the new mean? (a) 26 (b) 23 (c) 27 (d) 25
15. 15.Using (a − b)² = a² − 2ab + b², what is 98²? (a) 9614 (b) 9604 (c) 10404 (d) 9996
16. 16.The mean of 9 numbers is 38. When the number 78 is added to them, what is the new mean? (a) 58 (b) 43 (c) 42 (d) 38
17. 17.The mean of 9 numbers is 21. When the number 1 is added to them, what is the new mean? (a) 11 (b) 19 (c) 20 (d) 21
18. 18.How many factors does 18 have? (a) 7 (b) 4 (c) 5 (d) 6
19. 19.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 132 (c) 144 (d) 66
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/11 (d) 1/6
21. 21.What is the midpoint of the line joining (2, 10) and (14, 12)? (a) (11, 8) (b) (8, 11) (c) (6, 1) (d) (16, 22)
22. 22.How many factors does 24 have? (a) 9 (b) 6 (c) 8 (d) 7
23. 23.A bag has 4 red balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 16 (b) 6 (c) 2 (d) 5
24. 24.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
25. 25.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
26. 26.In a class of 41 children, 25 like cricket, 11 like football and 5 like both. How many like at least one of the two? (a) 36 (b) 26 (c) 31 (d) 41
27. 27.A bag has 7 blue, 7 green and 6 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 13/20 (c) 7/20 (d) 7/13
28. 28.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
29. 29.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
30. 30.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 50° (b) 51° (c) 230° (d) 130°
31. 31.If a + b = 13 and ab = 30, what is a² + b²? (a) 139 (b) 169 (c) 229 (d) 109
32. 32.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 13 (b) 152 (c) 80 (d) 76
33. 33.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) 8 (d) 7
34. 34.What is the midpoint of the line joining (5, 4) and (13, 6)? (a) (4, 1) (b) (18, 10) (c) (5, 9) (d) (9, 5)
35. 35.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3
36. 36.What is the sum of all the whole numbers from 1 to 80? (a) 3160 (b) 3240 (c) 6480 (d) 3200
37. 37.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
38. 38.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
39. 39.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
40. 40.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 5 times (c) 8 times (d) 2 times

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