Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 645 · 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 75²? (a) 4225 (b) 5635 (c) 4925 (d) 5625
2. 2.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 12 (c) 6 (d) 5
3. 3.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
4. 4.What is the smallest prime factor of 217? (a) 1 (b) 2 (c) 31 (d) 7
5. 5.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
6. 6.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 30 (c) 9 (d) 81
7. 7.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x − 5)(x − 6) (c) (x + 1)(x + 10) (d) (x + 5)(x + 6)
8. 8.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 60° (c) 30° (d) 120°
9. 9.What is the median of 22, 32, 18, 30 and 33? (a) 18 (b) 30 (c) 32 (d) 27
10. 10.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 115° (c) 25° (d) 65°
11. 11.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 125° (c) 55° (d) 35°
12. 12.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 70° (b) 90° (c) 160° (d) 110°
13. 13.What is the 25th term of the AP 19, 22, 25, 28, …? (a) 94 (b) 91 (c) 72 (d) 75
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 1/9 (d) 4/11
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 8 (c) 7 (d) 14
16. 16.Two angles of a triangle are 60° and 105°. What is the third angle? (a) 165° (b) 120° (c) 15° (d) 75°
17. 17.How many factors does 59 have? (a) 3 (b) 1 (c) 4 (d) 2
18. 18.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 105° (c) 75° (d) 115°
19. 19.What is the smallest prime factor of 85? (a) 1 (b) 5 (c) 2 (d) 17
20. 20.A bag has 3 white balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 4 (c) 11 (d) 5
21. 21.What is the midpoint of the line joining (6, 17) and (8, 7)? (a) (12, 7) (b) (14, 24) (c) (7, 12) (d) (1, 5)
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
23. 23.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 11 (c) 35 (d) 60
24. 24.How many prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 6 (d) 7
25. 25.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2 × 3² × 7³
26. 26.The mean of 5 numbers is 15. When the number 3 is added to them, what is the new mean? (a) 15 (b) 9 (c) 13 (d) 14
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
28. 28.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
29. 29.The mean of 9 numbers is 33. When the number 53 is added to them, what is the new mean? (a) 43 (b) 35 (c) 33 (d) 36
30. 30.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
31. 31.A bag has 3 green, 2 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/9 (b) 1/3 (c) 4/5 (d) 4/9
32. 32.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 300 (d) 600
33. 33.What is the sum of all the whole numbers from 1 to 41? (a) 1722 (b) 820 (c) 862 (d) 861
34. 34.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 144 cu cm (c) 18 cu cm (d) 216 cu cm
35. 35.A bag has 5 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 6 (c) 7 (d) 2
36. 36.A bag has 6 green balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 7 (c) 2 (d) 15
37. 37.What is the median of 34, 9, 26, 33, 28, 22 and 32? (a) 28 (b) 26 (c) 32 (d) 33
38. 38.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2² × 7 (d) 2 × 7
39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 64 (c) 36 (d) 28
40. 40.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3

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