Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 736 · 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.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 12 (c) 40 (d) 64
2. 2.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) 81 (b) 9 (c) 27 (d) 30
3. 3.What is the missing term in the AP 19, 28, ?, 46, 55? (a) 37 (b) 36 (c) 46 (d) 38
4. 4.A drawer has lots of red 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) 2 (b) 4 (c) 5 (d) 3
5. 5.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
7. 7.How many prime numbers are there between 30 and 40? (a) 1 (b) 2 (c) 3 (d) 4
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
9. 9.What is the mode of 1, 16, 1, 6, 17, 16 and 16? (a) 6 (b) 16 (c) 17 (d) 1
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 3 (d) 14
11. 11.What are the roots of x² − 15x + 54 = 0? (a) 2 and 27 (b) 1 and 54 (c) 6 and 9 (d) 1 and 14
12. 12.6 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) 60 (b) 30 (c) 36 (d) 11
13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
14. 14.What is the midpoint of the line joining (2, 11) and (4, 3)? (a) (1, 4) (b) (3, 7) (c) (6, 14) (d) (7, 3)
15. 15.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 135° (d) 45°
16. 16.In a class of 38 children, 23 like mangoes, 17 like bananas and 7 like both. How many like at least one of the two? (a) 38 (b) 40 (c) 33 (d) 26
17. 17.What is the distance between the points (7, 0) and (12, 12)? (a) 169 (b) 13 (c) 17 (d) 14
18. 18.Using (a − b)² = a² − 2ab + b², what is 67²? (a) 4499 (b) 5329 (c) 4489 (d) 4891
19. 19.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
20. 20.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 4 (d) 2
21. 21.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
22. 22.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 54 (d) 18
23. 23.What is the 32nd term of the AP 3, 6, 9, 12, …? (a) 97 (b) 93 (c) 99 (d) 96
24. 24.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 5 (d) 7
25. 25.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 1/8 (d) 7/8
26. 26.What is the median of 29, 18, 36, 26, 11, 15 and 7? (a) 18 (b) 26 (c) 19 (d) 15
27. 27.The mean of 3 numbers is 34. When the number 30 is added to them, what is the new mean? (a) 35 (b) 32 (c) 33 (d) 34
28. 28.What is the median of 2, 32, 26, 5, 34, 18 and 9? (a) 5 (b) 26 (c) 9 (d) 18
29. 29.In which quadrant does the point (−5, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 28 (c) 21 (d) 14
31. 31.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
32. 32.What is the median of 28, 17, 36, 14, 1, 19 and 12? (a) 19 (b) 17 (c) 18 (d) 14
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
34. 34.The mean of 6 numbers is 21. When the number 42 is added to them, what is the new mean? (a) 25 (b) 21 (c) 23 (d) 24
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
36. 36.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
38. 38.How many factors does 72 have? (a) 11 (b) 10 (c) 13 (d) 12
39. 39.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 640 (b) 320 (c) 350 (d) 59
40. 40.In a class of 36 children, 20 like mangoes, 15 like bananas and 8 like both. How many like at least one of the two? (a) 19 (b) 36 (c) 27 (d) 35

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