Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 410 · 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.If a + b = 17 and ab = 60, what is (a − b)²? (a) 7 (b) 169 (c) 289 (d) 49
2. 2.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
3. 3.How many factors does 53 have? (a) 1 (b) 3 (c) 4 (d) 2
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 88 sq cm
5. 5.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
6. 6.What is the median of 28, 6, 32, 5, 3, 27 and 18? (a) 5 (b) 17 (c) 18 (d) 27
7. 7.In a class of 30 children, 17 like tea, 12 like coffee and 5 like neither. How many like both? (a) 3 (b) 5 (c) 4 (d) 25
8. 8.What is the mean of 14, 2, 17, 20, 14 and 11? (a) 13 (b) 15 (c) 12 (d) 14
9. 9.A bag has 5 yellow balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 6 (d) 12
10. 10.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
11. 11.What is the sum of the first 6 terms of the AP 6, 11, 16, …? (a) 222 (b) 31 (c) 111 (d) 126
12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 25 (d) 240
13. 13.In a class of 26 children, 11 like cricket, 21 like football and 8 like both. How many like only cricket? (a) 5 (b) 13 (c) 3 (d) 11
14. 14.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
15. 15.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
17. 17.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 70°
18. 18.A cube has edges of 4 cm. What is its total surface area? (a) 16 sq cm (b) 64 sq cm (c) 97 sq cm (d) 96 sq cm
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
20. 20.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
21. 21.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
22. 22.What is the midpoint of the line joining (2, 7) and (14, 1)? (a) (16, 8) (b) (4, 8) (c) (6, 3) (d) (8, 4)
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 3 (c) 8 (d) 9
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 6/11 (d) 7/36
25. 25.In a class of 47 children, 24 like tea, 30 like coffee and 10 like both. How many like neither? (a) 3 (b) 13 (c) 10 (d) 4
26. 26.What is the mean of 3, 17, 15 and 17? (a) 12 (b) 14 (c) 15 (d) 13
27. 27.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
28. 28.What is the sum of the first 9 terms of the AP 2, 6, 10, …? (a) 324 (b) 180 (c) 162 (d) 34
29. 29.In a class of 33 children, 12 like cricket, 22 like football and 2 like both. How many like neither? (a) 3 (b) 1 (c) 2 (d) 0
30. 30.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
31. 31.A bag has 3 white balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 4 (c) 2 (d) 11
32. 32.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 3/8 (d) 1/4
33. 33.What is the 39th term of the AP 14, 22, 30, 38, …? (a) 312 (b) 304 (c) 318 (d) 326
34. 34.In a class of 26 children, 16 like mangoes, 14 like bananas and 2 like neither. How many like both? (a) 6 (b) 24 (c) 2 (d) 4
35. 35.What is the distance between the points (0, 7) and (9, 19)? (a) 15 (b) 16 (c) 21 (d) 225
36. 36.What is the 36th term of the AP 7, 12, 17, 22, …? (a) 175 (b) 182 (c) 180 (d) 187
37. 37.In a class of 25 children, 15 like dance, 14 like music and 6 like both. How many like neither? (a) 8 (b) 3 (c) 6 (d) 2
38. 38.In a class of 38 children, 13 like dance, 29 like music and 6 like neither. How many like both? (a) 4 (b) 32 (c) 10 (d) 6
39. 39.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°
40. 40.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5

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