Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 375 · 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 angles of a triangle are 30° and 110°. What is the third angle? (a) 140° (b) 150° (c) 70° (d) 40°
2. 2.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 1 and 16 (c) 1 and 72 (d) 2 and 36
3. 3.A bag has 3 yellow balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 4 (b) 2 (c) 13 (d) 5
4. 4.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 145° (b) 120° (c) 95° (d) 85°
5. 5.Two angles of a triangle are 40° and 50°. What is the third angle? (a) 270° (b) 130° (c) 90° (d) 140°
6. 6.A bag has 8 white, 8 red and 8 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 1/3 (c) 1/2 (d) 3/8
7. 7.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 125° (b) 155° (c) 80° (d) 100°
8. 8.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) 2 times (d) 8 times
9. 9.What is the mean of 5, 6, 20, 8, 8 and 19? (a) 11 (b) 13 (c) 10 (d) 12
10. 10.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 35° (c) 145° (d) 55°
11. 11.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 115°
12. 12.In a class of 34 children, 15 like cricket, 20 like football and 5 like neither. How many like both? (a) 6 (b) 29 (c) 5 (d) 1
13. 13.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 1)(x + 15) (c) (x − 7)(x − 9) (d) (x + 7)(x + 9)
14. 14.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 5)(x + 8) (c) (x + 1)(x + 12) (d) (x − 5)(x − 8)
15. 15.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 8742 (c) 4371 (d) 4278
16. 16.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 145° (c) 70° (d) 110°
17. 17.What is the mean of 16, 12, 15 and 9? (a) 15 (b) 13 (c) 14 (d) 12
18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 120 (c) 240 (d) 20
19. 19.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 15 (d) 12
20. 20.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
21. 21.What is the mode of 7, 2, 15, 10, 10, 10 and 15? (a) 2 (b) 7 (c) 10 (d) 15
22. 22.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 306 (c) 289 (d) 153
23. 23.What is the sum of the first 5 terms of the AP 6, 8, 10, …? (a) 50 (b) 14 (c) 55 (d) 100
24. 24.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 9216 (b) 10016 (c) 10826 (d) 10816
25. 25.A bag has 11 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 12 (d) 17
26. 26.What is the smallest prime factor of 133? (a) 2 (b) 7 (c) 19 (d) 1
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
28. 28.What is the midpoint of the line joining (5, 3) and (13, 9)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (4, 3)
29. 29.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 27 cu cm (c) 324 cu cm (d) 729 cu cm
30. 30.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
31. 31.A drawer has lots of yellow 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) 2 (b) 5 (c) 3 (d) 4
32. 32.What is the mode of 17, 17, 10, 20, 20, 18 and 20? (a) 17 (b) 20 (c) 10 (d) 18
33. 33.What is the mean of 8, 2, 7, 6, 19 and 6? (a) 8 (b) 10 (c) 9 (d) 7
34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 4 (d) 16
35. 35.What is the product of the roots of x² − 15x + 56 = 0? (a) 57 (b) 55 (c) 15 (d) 56
36. 36.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 30 (d) 10
37. 37.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 3/8 (d) 7/8
38. 38.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 196 (b) 27 (c) 210 (d) 105
39. 39.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
40. 40.If a + b = 17 and ab = 70, what is (a − b)²? (a) 289 (b) 3 (c) 9 (d) 149

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