Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 261 · 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 40 children, 13 like mangoes, 22 like bananas and 4 like both. How many like at least one of the two? (a) 40 (b) 31 (c) 35 (d) 27
2. 2.A drawer has lots of yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 5 (d) 2
3. 3.A bag has 4 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 2 (c) 11 (d) 6
4. 4.A drawer has lots of yellow, black, red, white 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) 2 (b) 10 (c) 6 (d) 5
5. 5.In a class of 47 children, 24 like dance, 29 like music and 11 like both. How many like at least one of the two? (a) 53 (b) 42 (c) 47 (d) 31
6. 6.How many factors does 70 have? (a) 9 (b) 8 (c) 7 (d) 6
7. 7.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 98 (c) 49 (d) 14
8. 8.What is the midpoint of the line joining (9, 16) and (21, 4)? (a) (30, 20) (b) (15, 10) (c) (10, 15) (d) (6, 6)
9. 9.A bag has 6 black balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 16 (d) 11
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
11. 11.What is the midpoint of the line joining (10, 9) and (14, 15)? (a) (12, 12) (b) (13, 12) (c) (2, 3) (d) (24, 24)
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
13. 13.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 36 (d) 81
14. 14.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
15. 15.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
16. 16.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 150° (c) 270° (d) 90°
17. 17.How many factors does 60 have? (a) 12 (b) 10 (c) 13 (d) 11
18. 18.A bag has 7 white balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 8 (c) 18 (d) 2
19. 19.What is the 10th term of the AP 16, 23, 30, 37, …? (a) 70 (b) 86 (c) 79 (d) 63
20. 20.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 7 (c) 5 (d) 6
22. 22.If a + b = 15 and ab = 50, what is (a − b)²? (a) 225 (b) 5 (c) 125 (d) 25
23. 23.A drawer has lots of yellow, white, red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 8 (d) 2
24. 24.What is the midpoint of the line joining (0, 8) and (8, 18)? (a) (8, 26) (b) (4, 5) (c) (4, 13) (d) (13, 4)
25. 25.The mean of 7 numbers is 26. When the number 10 is added to them, what is the new mean? (a) 24 (b) 26 (c) 18 (d) 25
26. 26.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 160° (d) 80°
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
28. 28.In a class of 45 children, 20 like maths, 26 like science and 10 like neither. How many like both? (a) 11 (b) 35 (c) 10 (d) 1
29. 29.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
30. 30.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
31. 31.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.A bag has 11 red balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 19 (c) 2 (d) 12
33. 33.If a + b = 18 and ab = 80, what is a² + b²? (a) 164 (b) 324 (c) 484 (d) 244
34. 34.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
35. 35.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
36. 36.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 784 (c) 896 (d) 1024
37. 37.How many factors does 26 have? (a) 5 (b) 3 (c) 2 (d) 4
38. 38.How many factors does 35 have? (a) 5 (b) 2 (c) 4 (d) 3
39. 39.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 30° (b) 100° (c) 150° (d) 110°
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 7 (b) 9 (c) 6 (d) 8

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