Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 802 · 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 44 children, 23 like dance, 20 like music and 3 like both. How many like at least one of the two? (a) 40 (b) 37 (c) 44 (d) 43
2. 2.A drawer has lots of red, white, blue 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) 2 (c) 5 (d) 8
3. 3.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2³ × 7 (d) 2 × 7²
4. 4.What is the 21st term of the AP 16, 18, 20, 22, …? (a) 58 (b) 42 (c) 40 (d) 56
5. 5.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 170 cu cm (b) 30 cu cm (c) 16 cu cm (d) 150 cu cm
6. 6.In a class of 47 children, 23 like cricket, 21 like football and 10 like neither. How many like both? (a) 10 (b) 8 (c) 7 (d) 37
7. 7.What is the sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 15 (c) 16 (d) 14
8. 8.The mean of 5 numbers is 30. When the number 24 is added to them, what is the new mean? (a) 28 (b) 27 (c) 29 (d) 30
9. 9.In a class of 30 children, 16 like cricket, 16 like football and 1 like neither. How many like both? (a) 1 (b) 3 (c) 2 (d) 29
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
11. 11.What is the sum of the first 10 terms of the AP 2, 7, 12, …? (a) 47 (b) 270 (c) 245 (d) 490
12. 12.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 150° (c) 25° (d) 30°
13. 13.A bag has 11 black balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 12 (d) 23
14. 14.The mean of 3 numbers is 23. When the number 15 is added to them, what is the new mean? (a) 23 (b) 19 (c) 22 (d) 21
15. 15.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
16. 16.A bag has 6 blue balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 17 (b) 8 (c) 2 (d) 7
17. 17.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
18. 18.In a class of 30 children, 19 like mangoes, 11 like bananas and 3 like both. How many like only mangoes? (a) 19 (b) 8 (c) 16 (d) 3
19. 19.The mean of 4 numbers is 16. When the number 1 is added to them, what is the new mean? (a) 16 (b) 13 (c) 12 (d) 14
20. 20.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 399 (b) 361 (c) 441 (d) 371
21. 21.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 100 cu cm (b) 8 cu cm (c) 56 cu cm (d) 13 cu cm
22. 22.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
24. 24.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
25. 25.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 379 (c) 324 (d) 369
26. 26.Which term of the AP 17, 23, 29, 35, … is 101? (a) 17th (b) 15th (c) 14th (d) 16th
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
28. 28.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 120 (d) 25
29. 29.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the median of 10, 17, 2, 38, 20, 29 and 23? (a) 17 (b) 23 (c) 20 (d) 38
31. 31.What is the distance between the points (0, 12) and (24, 5)? (a) 26 (b) 31 (c) 25 (d) 625
32. 32.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
33. 33.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 15 (d) 30
34. 34.A bag has 11 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 15 (d) 5
35. 35.What is the 26th term of the AP 11, 19, 27, 35, …? (a) 200 (b) 219 (c) 208 (d) 211
36. 36.In a class of 35 children, 20 like dance, 18 like music and 9 like both. How many like only dance? (a) 11 (b) 17 (c) 9 (d) 20
37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 20 (c) 25 (d) 120
38. 38.In a class of 26 children, 20 like maths, 12 like science and 9 like both. How many like only maths? (a) 3 (b) 20 (c) 14 (d) 11
39. 39.A drawer has lots of yellow, red 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) 3 (b) 6 (c) 4 (d) 2
40. 40.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 120° (d) 100°

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