Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 797 · 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 book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 346 (c) 411 (d) 412
2. 2.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
3. 3.What is the sum of the first 8 terms of the AP 6, 10, 14, …? (a) 320 (b) 34 (c) 176 (d) 160
4. 4.A bag has 8 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 9 (c) 10 (d) 2
5. 5.A bag has 7 white, 4 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 10/17 (b) 7/10 (c) 7/17 (d) 1/3
6. 6.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 150° (c) 60° (d) 90°
7. 7.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) 13 (b) 24 (c) 12 (d) 25
8. 8.What is the mode of 18, 7, 2, 8, 18, 18 and 8? (a) 2 (b) 7 (c) 8 (d) 18
9. 9.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3²
10. 10.If a + b = 13 and ab = 22, what is a² + b²? (a) 147 (b) 125 (c) 169 (d) 213
11. 11.In a class of 45 children, 27 like cricket, 26 like football and 9 like both. How many like at least one of the two? (a) 45 (b) 53 (c) 35 (d) 44
12. 12.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 160° (d) 130°
13. 13.What is the mode of 4, 4, 11, 7, 13, 4 and 7? (a) 13 (b) 4 (c) 7 (d) 11
14. 14.How many factors does 81 have? (a) 6 (b) 5 (c) 4 (d) 3
15. 15.The mean of 5 numbers is 18. When the number 30 is added to them, what is the new mean? (a) 24 (b) 18 (c) 21 (d) 20
16. 16.A cube has edges of 9 cm. What is its volume? (a) 729 cu cm (b) 324 cu cm (c) 486 cu cm (d) 27 cu cm
17. 17.What is the 26th term of the AP 3, 7, 11, 15, …? (a) 103 (b) 104 (c) 107 (d) 100
18. 18.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
19. 19.In a class of 36 children, 21 like mangoes, 26 like bananas and 12 like both. How many like at least one of the two? (a) 47 (b) 23 (c) 35 (d) 36
20. 20.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
21. 21.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 60° (b) 140° (c) 120° (d) 100°
22. 22.In a class of 29 children, 15 like maths, 15 like science and 9 like both. How many like only maths? (a) 15 (b) 9 (c) 14 (d) 6
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
25. 25.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 170 (b) 320 (c) 160 (d) 25
26. 26.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
27. 27.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2³ × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2² × 3² × 5
28. 28.What is the midpoint of the line joining (2, 22) and (4, 10)? (a) (16, 3) (b) (1, 6) (c) (6, 32) (d) (3, 16)
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 5/36 (d) 1/6
30. 30.A bag has 5 white, 5 green and 5 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/5 (b) 1/3 (c) 2/3 (d) 1/2
31. 31.What is the smallest prime factor of 341? (a) 31 (b) 11 (c) 2 (d) 1
32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 12 (d) 48
33. 33.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
34. 34.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 3 (d) 2
35. 35.What is the sum of the roots of x² − 14x + 48 = 0? (a) 48 (b) 15 (c) 13 (d) 14
36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
37. 37.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 37 (c) 380 (d) 361
38. 38.A cuboid is 12 cm long, 10 cm wide and 3 cm high. What is its total surface area? (a) 186 sq cm (b) 360 sq cm (c) 372 sq cm (d) 744 sq cm
39. 39.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
40. 40.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3

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