Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 557 · 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.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 115° (d) 95°
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
3. 3.Which term of the AP 16, 18, 20, 22, … is 34? (a) 10th (b) 11th (c) 9th (d) 17th
4. 4.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 125° (b) 80° (c) 155° (d) 25°
5. 5.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 15 (d) 10
6. 6.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 150° (b) 50° (c) 80° (d) 130°
7. 7.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 416 (b) 256 (c) 576 (d) 586
8. 8.What is the mode of 2, 14, 2, 14, 13, 2 and 7? (a) 13 (b) 14 (c) 7 (d) 2
9. 9.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 105 (d) 196
10. 10.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 1 (d) 3
11. 11.Which is the correct factorisation of x² + 7x + 12? (a) (x − 3)(x − 4) (b) (x + 3)(x + 4) (c) (x + 1)(x + 6) (d) (x + 1)(x + 12)
12. 12.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 4925 (b) 5635 (c) 4225 (d) 5625
13. 13.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 22 (d) 69
14. 14.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
15. 15.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 7921 (b) 7931 (c) 8099 (d) 8281
16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240
17. 17.A drawer has lots of black, red, yellow, green 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) 10 (b) 6 (c) 2 (d) 5
18. 18.What is the product of the roots of x² − 13x + 40 = 0? (a) 41 (b) 13 (c) 40 (d) 39
19. 19.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 22 (c) 21 (d) 29
20. 20.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 35° (c) 60° (d) 145°
21. 21.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 55° (d) 70°
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
23. 23.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3
24. 24.Which term of the AP 4, 12, 20, 28, … is 108? (a) 15th (b) 14th (c) 16th (d) 13th
25. 25.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 15 (c) 14 (d) 7
26. 26.What is the sum of the roots of x² − 15x + 54 = 0? (a) 14 (b) 54 (c) 16 (d) 15
27. 27.In a class of 41 children, 14 like tea, 26 like coffee and 6 like both. How many like at least one of the two? (a) 40 (b) 41 (c) 34 (d) 28
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
29. 29.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
30. 30.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 150 (b) 290 (c) 145 (d) 19
31. 31.In a class of 29 children, 19 like tea, 6 like coffee and 3 like both. How many like at least one of the two? (a) 29 (b) 19 (c) 22 (d) 25
32. 32.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
33. 33.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 85° (b) 95° (c) 125° (d) 140°
34. 34.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
35. 35.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 220° (c) 40° (d) 110°
36. 36.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1379 (c) 1591 (d) 1369
37. 37.A bag has 8 red, 2 blue and 6 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 11/16 (b) 1/3 (c) 3/8 (d) 5/8
38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 39 (b) 420 (c) 210 (d) 400
39. 39.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 615 (c) 482 (d) 616
40. 40.How many factors does 37 have? (a) 2 (b) 1 (c) 3 (d) 4

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