Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 883 · 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.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°
2. 2.What is the 28th term of the AP 1, 6, 11, 16, …? (a) 135 (b) 140 (c) 136 (d) 141
3. 3.In a class of 46 children, 28 like maths, 19 like science and 8 like both. How many like only maths? (a) 28 (b) 11 (c) 20 (d) 27
4. 4.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) 72 (b) 27 (c) 8 (d) 24
5. 5.How many factors does 19 have? (a) 4 (b) 1 (c) 3 (d) 2
6. 6.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 12 (d) 25
7. 7.A bag has 9 yellow balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 6 (d) 14
8. 8.What is the midpoint of the line joining (0, 3) and (2, 13)? (a) (8, 1) (b) (1, 8) (c) (1, 5) (d) (2, 16)
9. 9.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 190° (c) 10° (d) 95°
10. 10.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
11. 11.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 3)(x + 5) (c) (x + 1)(x + 15) (d) (x + 1)(x + 7)
12. 12.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 35 (c) 56 (d) 28
13. 13.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
14. 14.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
15. 15.The mean of 3 numbers is 12. When the number 16 is added to them, what is the new mean? (a) 14 (b) 12 (c) 15 (d) 13
16. 16.What are the roots of x² − 13x + 42 = 0? (a) 2 and 21 (b) 6 and 7 (c) 1 and 42 (d) 1 and 12
17. 17.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
18. 18.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 864 sq cm (c) 576 sq cm (d) 144 sq cm
19. 19.What is the mode of 6, 1, 6, 3, 1, 1 and 18? (a) 6 (b) 3 (c) 1 (d) 18
20. 20.In a class of 42 children, 12 like tea, 24 like coffee and 4 like both. How many like only tea? (a) 18 (b) 20 (c) 8 (d) 12
21. 21.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 321 (c) 322 (d) 286
22. 22.How many factors does 98 have? (a) 4 (b) 7 (c) 6 (d) 5
23. 23.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
24. 24.Using (a − b)² = a² − 2ab + b², what is 17²? (a) 299 (b) 529 (c) 289 (d) 391
25. 25.Which term of the AP 14, 16, 18, 20, … is 56? (a) 22nd (b) 21st (c) 28th (d) 23rd
26. 26.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 30° (c) 150° (d) 210°
27. 27.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 18 (c) 16 (d) 17
28. 28.A drawer has lots of black, yellow, blue 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) 2 (b) 8 (c) 4 (d) 5
29. 29.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 9 (c) 12 (d) 18
30. 30.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 115° (d) 25°
31. 31.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/8 (d) 3/5
32. 32.What is the distance between the points (1, 5) and (5, 8)? (a) 6 (b) 7 (c) 25 (d) 5
33. 33.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
34. 34.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x − 5)(x − 7) (c) (x + 1)(x + 35) (d) (x + 1)(x + 11)
35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
36. 36.What is the mode of 18, 20, 12, 12, 12, 6 and 18? (a) 6 (b) 20 (c) 18 (d) 12
37. 37.A drawer has lots of blue, white and yellow 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) 6 (c) 4 (d) 3
38. 38.What is the sum of the first 9 terms of the AP 5, 10, 15, …? (a) 225 (b) 450 (c) 230 (d) 45
39. 39.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
40. 40.A drawer has lots of red, yellow, 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) 2 (b) 4 (c) 8 (d) 5

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