Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 78 · 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.What is the sum of all the whole numbers from 1 to 95? (a) 4561 (b) 4560 (c) 9120 (d) 4465
2. 2.In a class of 20 children, 7 like maths, 15 like science and 3 like both. How many like at least one of the two? (a) 19 (b) 16 (c) 20 (d) 22
3. 3.The mean of 6 numbers is 26. When the number 40 is added to them, what is the new mean? (a) 33 (b) 29 (c) 26 (d) 28
4. 4.What is the 37th term of the AP 17, 24, 31, 38, …? (a) 252 (b) 269 (c) 259 (d) 276
5. 5.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 125° (c) 110° (d) 56°
6. 6.A bag has 4 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 2 (c) 6 (d) 13
7. 7.A bag has 8 red, 8 green and 6 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 8/11 (b) 17/22 (c) 1/3 (d) 3/11
8. 8.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 8 (c) 5 (d) 6
10. 10.What is the median of 18, 36, 15, 31 and 27? (a) 27 (b) 31 (c) 18 (d) 15
11. 11.What is the sum of all the whole numbers from 1 to 52? (a) 2756 (b) 1378 (c) 1352 (d) 1326
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
13. 13.What is the mode of 14, 12, 12, 11, 14, 14 and 4? (a) 11 (b) 4 (c) 12 (d) 14
14. 14.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 145° (d) 35°
15. 15.Two angles of a triangle are 20° and 100°. What is the exterior angle at the third corner? (a) 60° (b) 160° (c) 80° (d) 120°
16. 16.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 9 cu cm (c) 36 cu cm (d) 27 cu cm
17. 17.What is the 37th term of the AP 3, 5, 7, 9, …? (a) 72 (b) 75 (c) 74 (d) 77
18. 18.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 25 (c) 240 (d) 120
19. 19.A drawer has lots of blue, red, green, black 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) 2 (b) 5 (c) 10 (d) 6
20. 20.If a + b = 18 and ab = 80, what is a² + b²? (a) 164 (b) 484 (c) 244 (d) 324
21. 21.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
22. 22.In a class of 44 children, 23 like cricket, 27 like football and 10 like both. How many like only cricket? (a) 23 (b) 10 (c) 17 (d) 13
23. 23.A bag has 6 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 13 (c) 7 (d) 2
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
25. 25.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 125° (b) 55° (c) 140° (d) 95°
26. 26.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 21 (c) 7 (d) 24
27. 27.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
28. 28.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
29. 29.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
30. 30.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
31. 31.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
32. 32.In which quadrant does the point (−2, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
33. 33.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 150° (b) 85° (c) 125° (d) 95°
34. 34.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 22 (d) 55
35. 35.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 160° (b) 155° (c) 45° (d) 135°
36. 36.What is the sum of the first 10 terms of the AP 2, 8, 14, …? (a) 290 (b) 56 (c) 580 (d) 320
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
38. 38.A bag has 10 blue balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 11 (c) 13 (d) 12
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
40. 40.Two angles of a triangle are 30° and 20°. What is the third angle? (a) 150° (b) 160° (c) 130° (d) 50°

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