Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 518 · 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.If a + b = 13 and ab = 12, what is a² + b²? (a) 169 (b) 193 (c) 157 (d) 145
2. 2.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 190 (d) 361
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 14 (c) 15 (d) 13
4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 95° (d) 86°
5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
6. 6.Two angles of a triangle are 50° and 105°. What is the third angle? (a) 155° (b) 75° (c) 25° (d) 130°
7. 7.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
8. 8.What is the mean of 15, 7, 19, 6, 19 and 6? (a) 13 (b) 12 (c) 14 (d) 11
9. 9.A bag has 4 red, 3 blue and 9 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/16 (b) 1/3 (c) 9/16 (d) 7/9
10. 10.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1128 (c) 2352 (d) 1152
11. 11.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 60° (b) 150° (c) 330° (d) 30°
12. 12.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
13. 13.The mean of 9 numbers is 31. When the number 51 is added to them, what is the new mean? (a) 33 (b) 31 (c) 41 (d) 34
14. 14.How many prime numbers are there between 90 and 120? (a) 6 (b) 7 (c) 8 (d) 5
15. 15.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 24 (c) 8 (d) 72
16. 16.What is the smallest prime factor of 85? (a) 1 (b) 17 (c) 5 (d) 2
17. 17.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 412 (c) 510 (d) 511
18. 18.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 125° (c) 55° (d) 56°
19. 19.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 72 (d) 18
20. 20.In a class of 19 children, 13 like cricket, 6 like football and 2 like both. How many like neither? (a) 2 (b) 3 (c) 4 (d) 0
21. 21.What is the distance between the points (0, 1) and (15, 9)? (a) 17 (b) 23 (c) 18 (d) 289
22. 22.What is the mode of 2, 2, 7, 5, 7, 15 and 7? (a) 15 (b) 5 (c) 2 (d) 7
23. 23.In a class of 20 children, 13 like cricket, 10 like football and 5 like both. How many like only cricket? (a) 13 (b) 5 (c) 8 (d) 10
24. 24.Two angles of a triangle are 45° and 40°. What is the third angle? (a) 85° (b) 135° (c) 95° (d) 140°
25. 25.What is the mean of 3, 6, 3, 3, 3 and 6? (a) 5 (b) 3 (c) 6 (d) 4
26. 26.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
27. 27.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) 14 (b) 8 (c) 15 (d) 7
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
29. 29.A drawer has lots of yellow, green, white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 4 (d) 8
30. 30.A drawer has lots of green, yellow, blue, red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 2 (d) 6
31. 31.The mean of 4 numbers is 28. When the number 43 is added to them, what is the new mean? (a) 30 (b) 28 (c) 32 (d) 31
32. 32.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 96 (c) 56 (d) 14
33. 33.In a class of 34 children, 20 like tea, 14 like coffee and 7 like both. How many like only tea? (a) 14 (b) 13 (c) 7 (d) 20
34. 34.What is the mean of 9, 15, 18 and 10? (a) 14 (b) 13 (c) 12 (d) 15
35. 35.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 4)(x + 6) (c) (x + 1)(x + 24) (d) (x − 4)(x − 6)
36. 36.If a + b = 16 and ab = 55, what is (a − b)²? (a) 146 (b) 256 (c) 6 (d) 36
37. 37.In a class of 33 children, 18 like mangoes, 14 like bananas and 3 like both. How many like neither? (a) 7 (b) 1 (c) 4 (d) 3
38. 38.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
39. 39.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 58 (b) 40 (c) 38 (d) 56
40. 40.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 100 (d) 55

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