Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 30 · 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.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2401 (b) 2411 (c) 2601 (d) 2499
2. 2.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 116 (d) 106
3. 3.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 294 sq cm (d) 343 sq cm
4. 4.In a class of 46 children, 19 like tea, 29 like coffee and 12 like both. How many like at least one of the two? (a) 48 (b) 24 (c) 46 (d) 36
5. 5.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 7 (d) 2
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/3 (c) 1/5 (d) 1/6
7. 7.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
10. 10.If a + b = 6 and ab = 8, what is (a − b)²? (a) 20 (b) 36 (c) 4 (d) 2
11. 11.What is the distance between the points (4, 27) and (11, 3)? (a) 26 (b) 25 (c) 625 (d) 31
12. 12.In a class of 37 children, 19 like dance, 21 like music and 8 like both. How many like only dance? (a) 16 (b) 11 (c) 19 (d) 13
13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
14. 14.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7⁴
15. 15.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 90° (b) 145° (c) 270° (d) 125°
16. 16.What is the mean of 19, 18, 3, 3, 10 and 13? (a) 12 (b) 10 (c) 13 (d) 11
17. 17.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
18. 18.What is the mean of 2, 17, 7, 4 and 20? (a) 10 (b) 11 (c) 9 (d) 12
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 132 cm (d) 264 cm
20. 20.What is the distance between the points (8, 7) and (20, 12)? (a) 13 (b) 14 (c) 17 (d) 169
21. 21.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
22. 22.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
23. 23.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 140° (b) 65° (c) 115° (d) 155°
24. 24.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 140° (b) 115° (c) 105° (d) 75°
25. 25.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 130° (b) 35° (c) 50° (d) 25°
26. 26.A bag has 11 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 2 (c) 21 (d) 13
27. 27.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 4 times (d) 16 times
28. 28.What is the mean of 7, 19, 12, 16 and 6? (a) 10 (b) 12 (c) 15 (d) 13
29. 29.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
30. 30.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 110° (b) 100° (c) 150° (d) 80°
31. 31.What is the 13th term of the AP 10, 15, 20, 25, …? (a) 70 (b) 60 (c) 65 (d) 75
32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
33. 33.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
34. 34.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 29 (b) 240 (c) 120 (d) 225
35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 16 (b) 7 (c) 17 (d) 18
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 19 (d) 17
37. 37.What is the median of 22, 29, 6, 38, 2, 16 and 37? (a) 16 (b) 29 (c) 38 (d) 22
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 7 (c) 5 (d) 6
39. 39.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
40. 40.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

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