Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 209 · 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 30 children, 15 like cricket, 20 like football and 11 like both. How many like at least one of the two? (a) 24 (b) 30 (c) 13 (d) 35
2. 2.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 48 sq cm (b) 92 sq cm (c) 184 sq cm (d) 46 sq cm
3. 3.A drawer has lots of blue, white and red 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) 4 (c) 2 (d) 6
4. 4.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
5. 5.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 27 sq cm (d) 36 sq cm
6. 6.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 45° (b) 100° (c) 135° (d) 125°
7. 7.What is the distance between the points (0, 14) and (16, 2)? (a) 20 (b) 28 (c) 400 (d) 21
8. 8.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
9. 9.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
10. 10.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
11. 11.Which term of the AP 11, 15, 19, 23, … is 147? (a) 36th (b) 37th (c) 34th (d) 35th
12. 12.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 46 (b) 45 (c) 42 (d) 49
13. 13.A drawer has lots of yellow, red, blue, green 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) 2 (b) 10 (c) 6 (d) 5
14. 14.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6241 (b) 6571 (c) 6561 (d) 6401
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 6 (c) 4 (d) 7
16. 16.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 4901 (c) 4761 (d) 5041
17. 17.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 125° (b) 90° (c) 270° (d) 145°
18. 18.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 4 times (d) 6 times
19. 19.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 324 (c) 342 (d) 35
21. 21.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6094 (b) 6724 (c) 6396 (d) 6084
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
23. 23.A bag has 4 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 4 (d) 5
24. 24.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 438 (d) 429
25. 25.A bag has 3 black balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 4 (c) 5 (d) 2
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
27. 27.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) 49 (c) 36 (d) 37
28. 28.What are the roots of x² − 13x + 40 = 0? (a) 2 and 20 (b) 1 and 12 (c) 5 and 8 (d) 1 and 40
29. 29.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 20 (d) 100
30. 30.Which term of the AP 20, 22, 24, 26, … is 84? (a) 34th (b) 42nd (c) 33rd (d) 32nd
31. 31.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
32. 32.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 15 (d) 18
33. 33.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 6 times (c) 3 times (d) 9 times
34. 34.A drawer has lots of 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) 4 (b) 5 (c) 8 (d) 2
35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
36. 36.What is the mode of 8, 17, 12, 17, 17, 1 and 8? (a) 1 (b) 17 (c) 12 (d) 8
37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
38. 38.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x + 5)(x + 6) (c) (x + 1)(x + 30) (d) (x − 5)(x − 6)
39. 39.If a + b = 15 and ab = 54, what is a² + b²? (a) 225 (b) 117 (c) 333 (d) 171
40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm

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