Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 817 · 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.Which term of the AP 17, 26, 35, 44, … is 233? (a) 27th (b) 25th (c) 26th (d) 24th
2. 2.A cuboid is 5 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 104 sq cm (b) 52 sq cm (c) 60 sq cm (d) 208 sq cm
3. 3.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
4. 4.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 27 (b) 7 (c) 54 (d) 30
5. 5.A bag has 9 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 11 (c) 10 (d) 2
6. 6.Which is the correct factorisation of x² + 11x + 24? (a) (x − 3)(x − 8) (b) (x + 1)(x + 24) (c) (x + 1)(x + 10) (d) (x + 3)(x + 8)
7. 7.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 24 (c) 30 (d) 10
8. 8.If a + b = 17 and ab = 66, what is a² + b²? (a) 421 (b) 289 (c) 223 (d) 157
9. 9.What are the roots of x² − 11x + 28 = 0? (a) 4 and 7 (b) 1 and 10 (c) 2 and 14 (d) 1 and 28
10. 10.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 222 (c) 226 (d) 231
11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 5 (d) 3
12. 12.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
13. 13.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 7/8 (c) 1/7 (d) 1/4
14. 14.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 90° (c) 140° (d) 270°
15. 15.In a class of 52 children, 32 like cricket, 23 like football and 12 like both. How many like only cricket? (a) 32 (b) 20 (c) 29 (d) 11
16. 16.A canteen sells 3 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 15 (c) 12 (d) 24
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 5 (c) 6 (d) 4
18. 18.What is the midpoint of the line joining (7, 6) and (19, 10)? (a) (6, 2) (b) (13, 8) (c) (8, 13) (d) (26, 16)
19. 19.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 19 (d) 18
21. 21.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 1 (d) 3
22. 22.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 169 (d) 91
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
24. 24.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 300° (c) 60° (d) 120°
25. 25.In a class of 39 children, 23 like dance, 19 like music and 5 like neither. How many like both? (a) 8 (b) 3 (c) 5 (d) 34
26. 26.The mean of 8 numbers is 22. When the number 58 is added to them, what is the new mean? (a) 27 (b) 22 (c) 26 (d) 40
27. 27.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 9035 (b) 8125 (c) 7225 (d) 9025
28. 28.What is the median of 17, 34, 39, 40, 23, 6 and 10? (a) 23 (b) 34 (c) 17 (d) 40
29. 29.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 3/11 (d) 1/9
31. 31.What is the distance between the points (4, 8) and (19, 16)? (a) 17 (b) 23 (c) 18 (d) 289
32. 32.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3146 (b) 3136 (c) 4096 (d) 3584
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
34. 34.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x − 7)(x − 8) (c) (x + 1)(x + 56) (d) (x + 7)(x + 8)
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
38. 38.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 182 (b) 91 (c) 169 (d) 25
39. 39.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
40. 40.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2³ × 7

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