Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 509 · 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.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 7 (d) 9
2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
3. 3.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 75° (c) 145° (d) 105°
4. 4.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.In a class of 25 children, 10 like tea, 20 like coffee and 6 like both. How many like neither? (a) 2 (b) 6 (c) 7 (d) 1
6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
7. 7.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 103 (d) 94
8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
9. 9.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 343 cu cm (c) 294 cu cm (d) 196 cu cm
10. 10.A bag has 9 blue, 3 red and 5 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 12/17 (b) 1/3 (c) 5/12 (d) 5/17
11. 11.What is the product of the roots of x² − 13x + 42 = 0? (a) 13 (b) 41 (c) 42 (d) 43
12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
13. 13.If a + b = 21 and ab = 108, what is a² + b²? (a) 441 (b) 225 (c) 657 (d) 333
14. 14.The mean of 6 numbers is 39. When the number 32 is added to them, what is the new mean? (a) 40 (b) 37 (c) 38 (d) 39
15. 15.What is the midpoint of the line joining (0, 14) and (8, 4)? (a) (4, 5) (b) (9, 4) (c) (8, 18) (d) (4, 9)
16. 16.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 6 (d) 4
17. 17.In a league, 6 teams each play every other team once. How many matches are played? (a) 15 (b) 36 (c) 21 (d) 30
18. 18.A drawer has lots of red and green 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) 5 (d) 2
19. 19.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
20. 20.What is the 25th term of the AP 15, 21, 27, 33, …? (a) 144 (b) 165 (c) 159 (d) 150
21. 21.If a + b = 14 and ab = 48, what is a² + b²? (a) 292 (b) 148 (c) 196 (d) 100
22. 22.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
23. 23.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
24. 24.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) 7 (b) 15 (c) 8 (d) 14
25. 25.A bag has 8 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 9 (c) 2 (d) 10
26. 26.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 61 (c) 52 (d) 62
27. 27.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 202 (c) 192 (d) 206
28. 28.A drawer has lots of red, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 4 (d) 3
29. 29.A bag has 6 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 8 (d) 7
30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
31. 31.Which term of the AP 10, 13, 16, 19, … is 127? (a) 41st (b) 42nd (c) 39th (d) 40th
32. 32.A bag has 8 yellow balls and 5 white 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) 9 (c) 6 (d) 13
33. 33.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 25 (c) 10 (d) 20
34. 34.How many factors does 72 have? (a) 10 (b) 13 (c) 12 (d) 11
35. 35.The mean of 4 numbers is 34. When the number 24 is added to them, what is the new mean? (a) 34 (b) 29 (c) 32 (d) 33
36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
37. 37.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
38. 38.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) 21 (b) 22 (c) 14 (d) 15
39. 39.How many factors does 22 have? (a) 5 (b) 4 (c) 3 (d) 2
40. 40.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm

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