Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 109 · 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 64²? (a) 4106 (b) 4096 (c) 3136 (d) 3616
2. 2.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 125° (b) 100° (c) 135° (d) 55°
3. 3.What is the mean of 18, 4, 2, 19, 14 and 3? (a) 12 (b) 11 (c) 10 (d) 9
4. 4.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 447 (c) 456 (d) 376
5. 5.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
6. 6.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
7. 7.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
8. 8.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) 110° (d) 71°
9. 9.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
10. 10.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
11. 11.A bag has 12 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 13 (c) 19 (d) 2
12. 12.A drawer has lots of black, red, yellow, green and blue 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) 6 (c) 2 (d) 10
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
14. 14.5 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) 50 (c) 10 (d) 30
15. 15.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 196 (d) 182
16. 16.Which term of the AP 10, 15, 20, 25, … is 135? (a) 27th (b) 26th (c) 28th (d) 25th
17. 17.In a class of 37 children, 18 like cricket, 21 like football and 12 like both. How many like at least one of the two? (a) 15 (b) 37 (c) 39 (d) 27
18. 18.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 7 (d) 2
19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 49 (d) 28
20. 20.The mean of 6 numbers is 24. When the number 31 is added to them, what is the new mean? (a) 26 (b) 25 (c) 27 (d) 24
21. 21.What is the midpoint of the line joining (5, 1) and (17, 9)? (a) (22, 10) (b) (5, 11) (c) (11, 5) (d) (6, 4)
22. 22.If a + b = 21 and ab = 108, what is (a − b)²? (a) 441 (b) 225 (c) 3 (d) 9
23. 23.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 70° (c) 340° (d) 20°
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
25. 25.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
26. 26.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
27. 27.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
28. 28.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 18
30. 30.A bag has 8 red, 6 white and 6 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/5 (b) 2/5 (c) 1/3 (d) 13/20
31. 31.A bag has 8 yellow, 3 red and 5 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/16 (b) 1/3 (c) 1/2 (d) 9/16
32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
33. 33.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 6 times (c) 8 times (d) 4 times
34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
35. 35.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) 54 (d) 6
36. 36.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
37. 37.In a class of 34 children, 21 like maths, 9 like science and 4 like both. How many like only maths? (a) 25 (b) 5 (c) 21 (d) 17
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
39. 39.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 12 (d) 6
40. 40.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 144 (d) 132

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