Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 343 · 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.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
2. 2.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
3. 3.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 21 (c) 24 (d) 10
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
5. 5.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 150° (c) 30° (d) 120°
6. 6.A cube has edges of 4 cm. What is its volume? (a) 12 cu cm (b) 65 cu cm (c) 64 cu cm (d) 96 cu cm
7. 7.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) 14 (b) 8 (c) 15 (d) 7
8. 8.What is the mode of 3, 6, 3, 3, 11, 13 and 13? (a) 13 (b) 11 (c) 6 (d) 3
9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 5/8 (d) 3/8
10. 10.In a class of 42 children, 14 like mangoes, 25 like bananas and 9 like neither. How many like both? (a) 7 (b) 9 (c) 6 (d) 33
11. 11.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
12. 12.Two angles of a triangle are 25° and 145°. What is the third angle? (a) 170° (b) 35° (c) 155° (d) 10°
13. 13.In a class of 31 children, 7 like dance, 20 like music and 3 like both. How many like neither? (a) 7 (b) 10 (c) 4 (d) 3
14. 14.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) 65° (c) 25° (d) 115°
15. 15.In a class of 36 children, 16 like dance, 21 like music and 11 like both. How many like neither? (a) 10 (b) 9 (c) 11 (d) 21
16. 16.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 37 (c) 36 (d) 49
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
18. 18.What is the mode of 1, 7, 10, 3, 7, 3 and 3? (a) 10 (b) 3 (c) 7 (d) 1
19. 19.A bag has 5 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 15 (c) 2 (d) 6
20. 20.What is the mean of 2, 19, 6 and 13? (a) 9 (b) 10 (c) 8 (d) 11
21. 21.The mean of 7 numbers is 17. When the number 9 is added to them, what is the new mean? (a) 15 (b) 17 (c) 13 (d) 16
22. 22.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
23. 23.How many prime numbers are there between 70 and 80? (a) 4 (b) 3 (c) 2 (d) 5
24. 24.In a class of 21 children, 11 like tea, 14 like coffee and 6 like both. How many like neither? (a) 6 (b) 8 (c) 3 (d) 2
25. 25.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 30 (d) 36
26. 26.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 576 (b) 586 (c) 256 (d) 416
27. 27.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 0 (d) 1
28. 28.A bag has 8 white, 3 green and 8 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/11 (b) 1/3 (c) 11/19 (d) 8/19
29. 29.What is the median of 20, 39, 1, 25, 26, 14 and 19? (a) 19 (b) 20 (c) 21 (d) 25
30. 30.How many factors does 80 have? (a) 8 (b) 11 (c) 9 (d) 10
31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
32. 32.The mean of 3 numbers is 17. When the number 25 is added to them, what is the new mean? (a) 21 (b) 19 (c) 20 (d) 17
33. 33.The mean of 8 numbers is 10. When the number 37 is added to them, what is the new mean? (a) 10 (b) 14 (c) 12 (d) 13
34. 34.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
35. 35.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 48 (d) 45
36. 36.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 36 (d) 81
37. 37.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 3 (c) 5 (d) 4
38. 38.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
39. 39.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 565 (c) 555 (d) 448
40. 40.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 256 (b) 384 (c) 266 (d) 576

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