Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 110 · 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.In a class of 37 children, 13 like mangoes, 25 like bananas and 6 like both. How many like neither? (a) 6 (b) 5 (c) 4 (d) 11
2. 2.A bag has 5 red balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 6 (c) 17 (d) 2
3. 3.What is the median of 12, 16, 8, 21 and 25? (a) 21 (b) 12 (c) 16 (d) 8
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
5. 5.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8104 (b) 8464 (c) 7744 (d) 8474
6. 6.Which term of the AP 1, 5, 9, 13, … is 89? (a) 22nd (b) 25th (c) 23rd (d) 24th
7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
8. 8.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 65° (d) 150°
9. 9.If a + b = 16 and ab = 60, what is (a − b)²? (a) 4 (b) 136 (c) 256 (d) 16
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
11. 11.In a class of 23 children, 16 like dance, 12 like music and 7 like both. How many like only dance? (a) 5 (b) 16 (c) 11 (d) 9
12. 12.What is the mean of 11, 6, 12 and 23? (a) 12 (b) 15 (c) 14 (d) 13
13. 13.What is the missing term in the AP 15, 18, 21, ?, 27? (a) 25 (b) 24 (c) 27 (d) 23
14. 14.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 44 cm (d) 616 cm
15. 15.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 25° (c) 155° (d) 65°
16. 16.If a + b = 9 and ab = 14, what is (a − b)²? (a) 25 (b) 81 (c) 53 (d) 5
17. 17.A cuboid is 8 cm long, 3 cm wide and 7 cm high. What is its volume? (a) 18 cu cm (b) 168 cu cm (c) 24 cu cm (d) 202 cu cm
18. 18.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/8 (c) 5/8 (d) 3/5
19. 19.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
20. 20.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 108 (c) 98 (d) 116
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
22. 22.What is the midpoint of the line joining (0, 2) and (6, 10)? (a) (3, 4) (b) (6, 12) (c) (3, 6) (d) (6, 3)
23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
24. 24.In a class of 42 children, 24 like cricket, 21 like football and 7 like both. How many like neither? (a) 4 (b) 7 (c) 11 (d) 5
25. 25.A bag has 7 green, 2 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/11 (b) 9/11 (c) 2/9 (d) 1/3
26. 26.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 1 (d) 3
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
28. 28.What is the sum of the first 6 terms of the AP 1, 5, 9, …? (a) 21 (b) 132 (c) 66 (d) 78
29. 29.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 36 (c) 56 (d) 64
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
31. 31.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 28 (c) 56 (d) 32
32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 2 (c) 4 (d) 3
33. 33.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 270° (c) 90° (d) 45°
34. 34.What is the midpoint of the line joining (7, 9) and (19, 21)? (a) (15, 13) (b) (6, 6) (c) (13, 15) (d) (26, 30)
35. 35.The mean of 4 numbers is 15. When the number 20 is added to them, what is the new mean? (a) 16 (b) 18 (c) 17 (d) 15
36. 36.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
37. 37.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 2 (d) 17
38. 38.What is the midpoint of the line joining (8, 21) and (18, 9)? (a) (26, 30) (b) (5, 6) (c) (15, 13) (d) (13, 15)
39. 39.In a class of 33 children, 11 like cricket, 24 like football and 6 like neither. How many like both? (a) 27 (b) 6 (c) 8 (d) 2
40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 7 (d) 21

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