Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 282 · 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.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
2. 2.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
3. 3.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2126 (b) 2484 (c) 2916 (d) 2116
4. 4.How many factors does 82 have? (a) 2 (b) 5 (c) 4 (d) 3
5. 5.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
6. 6.How many factors does 12 have? (a) 6 (b) 4 (c) 7 (d) 5
7. 7.Which term of the AP 13, 19, 25, 31, … is 217? (a) 34th (b) 37th (c) 35th (d) 36th
8. 8.What is the mode of 19, 19, 13, 13, 19, 16 and 3? (a) 19 (b) 16 (c) 3 (d) 13
9. 9.What is the median of 16, 30, 15, 1 and 23? (a) 23 (b) 17 (c) 16 (d) 15
10. 10.In a class of 33 children, 17 like mangoes, 12 like bananas and 4 like both. How many like at least one of the two? (a) 29 (b) 21 (c) 33 (d) 25
11. 11.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 140° (b) 85° (c) 125° (d) 95°
12. 12.What is the median of 27, 3, 19, 10 and 21? (a) 19 (b) 16 (c) 21 (d) 10
13. 13.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
14. 14.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
15. 15.What is the distance between the points (6, 15) and (30, 8)? (a) 625 (b) 31 (c) 26 (d) 25
16. 16.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3³ × 5 × 7
17. 17.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
18. 18.What is the distance between the points (4, 16) and (12, 1)? (a) 23 (b) 18 (c) 17 (d) 289
19. 19.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25
20. 20.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) 8 (b) 15 (c) 14 (d) 7
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
22. 22.4 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) 9 (b) 24 (c) 40 (d) 20
23. 23.What is the mode of 5, 18, 11, 18, 5, 3 and 18? (a) 3 (b) 18 (c) 5 (d) 11
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
25. 25.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 16 cu cm (d) 8 cu cm
26. 26.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
27. 27.Which term of the AP 4, 6, 8, 10, … is 68? (a) 32nd (b) 33rd (c) 34th (d) 35th
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/6 (d) 1/11
29. 29.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
30. 30.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 21 (c) 28 (d) 22
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
32. 32.A cuboid is 11 cm long, 8 cm wide and 10 cm high. What is its volume? (a) 88 cu cm (b) 556 cu cm (c) 29 cu cm (d) 880 cu cm
33. 33.A drawer has lots of yellow 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) 4 (c) 5 (d) 3
34. 34.A drawer has lots of black, blue, green, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 2 (d) 6
35. 35.In a class of 44 children, 21 like mangoes, 21 like bananas and 6 like both. How many like at least one of the two? (a) 36 (b) 42 (c) 44 (d) 30
36. 36.What is the 15th term of the AP 14, 20, 26, 32, …? (a) 90 (b) 104 (c) 98 (d) 84
37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 18 (d) 7
38. 38.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 1/8 (d) 3/4
39. 39.The mean of 4 numbers is 35. When the number 30 is added to them, what is the new mean? (a) 35 (b) 36 (c) 33 (d) 34
40. 40.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times

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