Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 639 · 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 cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 144 sq cm (b) 176 sq cm (c) 352 sq cm (d) 88 sq cm
2. 2.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
3. 3.What is the 18th term of the AP 6, 13, 20, 27, …? (a) 132 (b) 126 (c) 119 (d) 125
4. 4.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 5 times (d) 2 times
6. 6.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
7. 7.In a class of 43 children, 21 like maths, 18 like science and 6 like neither. How many like both? (a) 37 (b) 3 (c) 6 (d) 2
8. 8.Which term of the AP 13, 17, 21, 25, … is 141? (a) 35th (b) 33rd (c) 34th (d) 32nd
9. 9.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 24 (d) 132
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
11. 11.What is the sum of the roots of x² − 11x + 18 = 0? (a) 10 (b) 12 (c) 18 (d) 11
12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 15 (d) 21
14. 14.What is the missing term in the AP 11, 20, 29, ?, 47? (a) 38 (b) 37 (c) 47 (d) 39
15. 15.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 756 (c) 378 (d) 729
16. 16.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
17. 17.A bag has 3 blue balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 2 (c) 4 (d) 7
18. 18.A drawer has lots of black, 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) 6 (b) 4 (c) 2 (d) 3
19. 19.A drawer has lots of green 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) 5 (b) 2 (c) 4 (d) 3
20. 20.What is the distance between the points (2, 3) and (17, 11)? (a) 23 (b) 17 (c) 18 (d) 289
21. 21.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 400 (d) 210
22. 22.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 16 sq cm (b) 20 sq cm (c) 40 sq cm (d) 80 sq cm
23. 23.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 6 (d) 7
24. 24.What is the 10th term of the AP 4, 7, 10, 13, …? (a) 34 (b) 30 (c) 31 (d) 27
25. 25.What is the 23rd term of the AP 20, 23, 26, 29, …? (a) 69 (b) 86 (c) 89 (d) 66
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 18 (b) 16 (c) 17 (d) 6
27. 27.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 155° (c) 125° (d) 25°
28. 28.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 24 (c) 18 (d) 9
29. 29.In a class of 39 children, 13 like dance, 24 like music and 8 like both. How many like only dance? (a) 13 (b) 15 (c) 5 (d) 16
30. 30.A drawer has lots of red, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 4 (d) 2
31. 31.What is the mean of 8, 6, 5 and 17? (a) 10 (b) 9 (c) 8 (d) 12
32. 32.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
33. 33.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 28 (c) 32 (d) 11
34. 34.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
35. 35.A cuboid is 10 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 22 cu cm (b) 270 cu cm (c) 294 cu cm (d) 30 cu cm
36. 36.A drawer has lots of white, yellow, blue and green 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) 8 (d) 5
37. 37.What is the distance between the points (6, 3) and (30, 10)? (a) 25 (b) 31 (c) 625 (d) 26
38. 38.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
39. 39.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 14) (c) (x + 1)(x + 56) (d) (x + 7)(x + 8)
40. 40.What is the 33rd term of the AP 17, 22, 27, 32, …? (a) 165 (b) 160 (c) 182 (d) 177

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