Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 172 · 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.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9801 (b) 9811 (c) 10201 (d) 9999
2. 2.A drawer has lots of yellow, blue, 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) 5 (b) 10 (c) 6 (d) 2
3. 3.In a class of 46 children, 22 like mangoes, 22 like bananas and 10 like neither. How many like both? (a) 10 (b) 36 (c) 8 (d) 9
4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
5. 5.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 140° (b) 70° (c) 71° (d) 110°
6. 6.A bag has 9 red balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 2 (c) 16 (d) 11
7. 7.In a class of 51 children, 27 like mangoes, 31 like bananas and 12 like both. How many like at least one of the two? (a) 51 (b) 58 (c) 46 (d) 34
8. 8.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2² × 3² × 5
9. 9.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) 29 (c) 22 (d) 21
10. 10.What is the 40th term of the AP 9, 15, 21, 27, …? (a) 234 (b) 240 (c) 249 (d) 243
11. 11.What is the distance between the points (1, 9) and (6, 21)? (a) 169 (b) 13 (c) 17 (d) 14
12. 12.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 224 (b) 43 (c) 408 (d) 204
13. 13.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 1)(x + 10) (c) (x + 3)(x + 8) (d) (x − 3)(x − 8)
14. 14.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
15. 15.In a class of 48 children, 28 like maths, 20 like science and 10 like both. How many like at least one of the two? (a) 48 (b) 38 (c) 28 (d) 39
16. 16.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 10414 (c) 10404 (d) 9604
17. 17.What is the midpoint of the line joining (2, 4) and (8, 10)? (a) (5, 7) (b) (7, 5) (c) (3, 3) (d) (10, 14)
18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
19. 19.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 440 cm (d) 110 cm
20. 20.In a class of 48 children, 31 like cricket, 28 like football and 12 like both. How many like at least one of the two? (a) 59 (b) 35 (c) 48 (d) 47
21. 21.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
22. 22.A drawer has lots of blue 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) 3 (d) 4
23. 23.In a class of 45 children, 27 like cricket, 28 like football and 11 like both. How many like neither? (a) 11 (b) 12 (c) 1 (d) 2
24. 24.The mean of 8 numbers is 10. When the number 37 is added to them, what is the new mean? (a) 14 (b) 10 (c) 12 (d) 13
25. 25.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2³ × 3 × 7
26. 26.A bag has 4 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 9 (c) 5 (d) 6
27. 27.What is the midpoint of the line joining (5, 3) and (15, 9)? (a) (5, 3) (b) (6, 10) (c) (20, 12) (d) (10, 6)
28. 28.What is the median of 31, 4, 2, 34, 37, 21 and 16? (a) 21 (b) 34 (c) 31 (d) 16
29. 29.What is the distance between the points (0, 8) and (8, 2)? (a) 11 (b) 14 (c) 10 (d) 100
30. 30.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5⁴
31. 31.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 84 (d) 75
32. 32.A bag has 7 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 8 (d) 9
33. 33.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 160 (b) 95 (c) 80 (d) 28
34. 34.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/7 (c) 1/4 (d) 1/8
35. 35.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
36. 36.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 28 (d) 16
37. 37.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 961 (b) 899 (c) 851 (d) 841
38. 38.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2411 (b) 2401 (c) 2499 (d) 2601
39. 39.In a class of 48 children, 25 like cricket, 26 like football and 11 like both. How many like only cricket? (a) 22 (b) 14 (c) 25 (d) 15
40. 40.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15

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