Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 181 · 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.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
2. 2.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
3. 3.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 155° (d) 55°
4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 693 sq cm
5. 5.A drawer has lots of yellow and blue 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) 3 (c) 4 (d) 5
6. 6.What is the sum of the roots of x² − 10x + 21 = 0? (a) 21 (b) 10 (c) 11 (d) 9
7. 7.In a class of 31 children, 14 like mangoes, 19 like bananas and 4 like both. How many like only mangoes? (a) 12 (b) 15 (c) 10 (d) 14
8. 8.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
9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
10. 10.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
12. 12.In a class of 22 children, 7 like cricket, 13 like football and 2 like both. How many like at least one of the two? (a) 22 (b) 16 (c) 18 (d) 20
13. 13.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
14. 14.There are 4 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 16 (c) 8 (d) 12
15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 18 (d) 20
16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
17. 17.What is the 32nd term of the AP 6, 10, 14, 18, …? (a) 134 (b) 128 (c) 130 (d) 124
18. 18.If a + b = 19 and ab = 90, what is a² + b²? (a) 541 (b) 271 (c) 361 (d) 181
19. 19.What is the 34th term of the AP 15, 21, 27, 33, …? (a) 198 (b) 219 (c) 213 (d) 204
20. 20.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x + 1)(x + 12) (c) (x − 2)(x − 6) (d) (x + 1)(x + 7)
21. 21.A bag has 3 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 15 (b) 4 (c) 5 (d) 2
22. 22.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x − 2)(x − 8) (c) (x + 2)(x + 8) (d) (x + 1)(x + 16)
23. 23.A bag has 11 green balls and 10 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) 12 (c) 21 (d) 11
24. 24.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 18 (c) 54 (d) 21
25. 25.A cube has edges of 5 cm. What is its total surface area? (a) 100 sq cm (b) 150 sq cm (c) 125 sq cm (d) 25 sq cm
26. 26.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 135° (b) 110° (c) 155° (d) 70°
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
28. 28.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
29. 29.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
30. 30.A bag has 10 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 12 (c) 2 (d) 11
31. 31.What is the mean of 16, 6, 5, 12, 17 and 4? (a) 12 (b) 10 (c) 11 (d) 9
32. 32.In a class of 40 children, 28 like mangoes, 11 like bananas and 8 like both. How many like only mangoes? (a) 3 (b) 29 (c) 20 (d) 28
33. 33.In a class of 24 children, 14 like maths, 15 like science and 6 like both. How many like at least one of the two? (a) 29 (b) 17 (c) 24 (d) 23
34. 34.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
36. 36.A drawer has lots of yellow, red, blue 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) 5 (b) 4 (c) 8 (d) 2
37. 37.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 1/8 (d) 3/8
38. 38.In a class of 22 children, 12 like cricket, 12 like football and 4 like both. How many like neither? (a) 3 (b) 2 (c) 6 (d) 4
39. 39.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 95° (c) 86° (d) 85°
40. 40.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4

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