Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 319 · 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 far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
2. 2.If a + b = 5 and ab = 4, what is a² + b²? (a) 25 (b) 21 (c) 33 (d) 17
3. 3.A cuboid is 11 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 556 cu cm (b) 880 cu cm (c) 29 cu cm (d) 88 cu cm
4. 4.What is the 28th term of the AP 10, 16, 22, 28, …? (a) 172 (b) 162 (c) 178 (d) 168
5. 5.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 1/3 (d) 5/6
6. 6.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 60° (d) 120°
7. 7.A bag has 3 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 4 (c) 5 (d) 2
8. 8.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 61° (b) 59° (c) 60° (d) 120°
9. 9.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 12 (c) 42 (d) 70
10. 10.The mean of 5 numbers is 17. When the number 29 is added to them, what is the new mean? (a) 19 (b) 23 (c) 17 (d) 20
11. 11.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 25 (b) 10 (c) 50 (d) 30
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
13. 13.What is the mean of 3, 3, 18 and 8? (a) 10 (b) 9 (c) 8 (d) 7
14. 14.In a class of 38 children, 15 like dance, 23 like music and 3 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 35 (d) 36
15. 15.In a class of 36 children, 23 like tea, 10 like coffee and 6 like both. How many like at least one of the two? (a) 21 (b) 27 (c) 36 (d) 33
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
17. 17.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x + 1)(x + 35) (c) (x + 1)(x + 11) (d) (x − 5)(x − 7)
18. 18.Using (a − b)² = a² − 2ab + b², what is 76²? (a) 6384 (b) 5776 (c) 7056 (d) 5786
19. 19.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 215 (b) 430 (c) 230 (d) 35
20. 20.The mean of 4 numbers is 16. When the number 11 is added to them, what is the new mean? (a) 17 (b) 14 (c) 16 (d) 15
21. 21.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 1 (d) 11
22. 22.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 207 (d) 69
23. 23.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) 21 (b) 18 (c) 6 (d) 54
24. 24.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 739 (b) 891 (c) 729 (d) 1089
25. 25.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 12 (c) 18 (d) 6
26. 26.A bag has 9 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 2 (c) 20 (d) 11
27. 27.In a class of 30 children, 7 like maths, 20 like science and 3 like both. How many like neither? (a) 3 (b) 7 (c) 9 (d) 6
28. 28.What is the mode of 19, 16, 16, 16, 3, 5 and 5? (a) 5 (b) 19 (c) 3 (d) 16
29. 29.A bag has 4 blue balls and 7 green 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) 11 (c) 5 (d) 8
30. 30.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 50° (c) 25° (d) 155°
31. 31.What is the sum of the roots of x² − 11x + 30 = 0? (a) 10 (b) 12 (c) 11 (d) 30
32. 32.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 11 (d) 17
33. 33.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
34. 34.What is the sum of all the whole numbers from 1 to 31? (a) 496 (b) 465 (c) 992 (d) 497
35. 35.What is the sum of the roots of x² − 5x + 6 = 0? (a) 6 (b) 4 (c) 5 (d) 7
36. 36.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
37. 37.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 4 (d) 5
39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 8)(x + 9)
40. 40.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 24 (c) 12 (d) 18

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