Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 425 · 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 + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
2. 2.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
3. 3.In a class of 44 children, 20 like dance, 23 like music and 9 like neither. How many like both? (a) 35 (b) 8 (c) 7 (d) 9
4. 4.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
5. 5.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 85° (c) 95° (d) 145°
6. 6.In a class of 43 children, 22 like maths, 28 like science and 3 like neither. How many like both? (a) 3 (b) 40 (c) 7 (d) 10
7. 7.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 16 (c) 5 (d) 15
9. 9.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 65 (b) 55 (c) 19 (d) 110
10. 10.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
11. 11.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 105 (d) 120
12. 12.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
13. 13.How many factors does 14 have? (a) 2 (b) 5 (c) 4 (d) 3
14. 14.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 135 (d) 136
15. 15.What is the midpoint of the line joining (5, 12) and (7, 8)? (a) (6, 10) (b) (12, 20) (c) (1, 2) (d) (10, 6)
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
18. 18.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 81 (d) 72
19. 19.In a class of 52 children, 30 like dance, 24 like music and 10 like neither. How many like both? (a) 10 (b) 42 (c) 12 (d) 2
20. 20.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
21. 21.What is the mode of 1, 16, 20, 1, 20, 10 and 20? (a) 20 (b) 10 (c) 16 (d) 1
22. 22.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
23. 23.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 34 (d) 33
24. 24.A bag has 5 red, 5 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/6 (b) 5/6 (c) 1/3 (d) 1/5
25. 25.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 15° (c) 16° (d) 195°
26. 26.If a + b = 20 and ab = 99, what is a² + b²? (a) 202 (b) 301 (c) 400 (d) 598
27. 27.Which term of the AP 4, 6, 8, 10, … is 36? (a) 19th (b) 18th (c) 17th (d) 16th
28. 28.Which term of the AP 1, 3, 5, 7, … is 57? (a) 30th (b) 29th (c) 28th (d) 31st
29. 29.In a class of 54 children, 24 like dance, 28 like music and 8 like both. How many like only dance? (a) 20 (b) 16 (c) 26 (d) 24
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 240 (d) 25
31. 31.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
32. 32.3 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) 12 (b) 9 (c) 18 (d) 6
33. 33.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 1 (d) 2
34. 34.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
35. 35.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 19 (b) 20 (c) 22 (d) 18
36. 36.A bag has 3 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 4 (c) 14 (d) 2
37. 37.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
38. 38.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 10 (c) 20 (d) 25
39. 39.What is the sum of all the whole numbers from 1 to 74? (a) 2738 (b) 5550 (c) 2775 (d) 2701
40. 40.In a class of 33 children, 16 like tea, 24 like coffee and 10 like both. How many like neither? (a) 3 (b) 10 (c) 4 (d) 13

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