Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 871 · 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 smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
2. 2.The mean of 5 numbers is 33. When the number 27 is added to them, what is the new mean? (a) 30 (b) 33 (c) 31 (d) 32
3. 3.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 16 (b) 32 (c) 20 (d) 8
4. 4.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 55°
5. 5.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7
6. 6.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 54 (c) 6 (d) 18
7. 7.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
8. 8.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 3 (d) 7
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
10. 10.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2401 (b) 2601 (c) 2501 (d) 2611
11. 11.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 90 (c) 10 (d) 33
12. 12.What is the distance between the points (6, 2) and (21, 10)? (a) 18 (b) 17 (c) 289 (d) 23
13. 13.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1099 (b) 909 (c) 1089 (d) 729
14. 14.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
15. 15.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 891 (b) 1089 (c) 729 (d) 739
16. 16.What is the 20th term of the AP 18, 20, 22, 24, …? (a) 56 (b) 38 (c) 40 (d) 58
17. 17.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3721 (b) 3731 (c) 3601 (d) 3481
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
19. 19.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 102 (c) 112 (d) 120
20. 20.What is the mode of 14, 8, 14, 20, 20, 19 and 20? (a) 14 (b) 19 (c) 8 (d) 20
21. 21.What is the midpoint of the line joining (8, 9) and (10, 15)? (a) (12, 9) (b) (1, 3) (c) (18, 24) (d) (9, 12)
22. 22.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 140° (b) 85° (c) 135° (d) 45°
23. 23.What is the sum of the first 9 terms of the AP 9, 14, 19, …? (a) 261 (b) 49 (c) 522 (d) 266
24. 24.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 20° (c) 160° (d) 10°
25. 25.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 85° (c) 95° (d) 150°
26. 26.What is the sum of all the whole numbers from 1 to 82? (a) 3403 (b) 3321 (c) 3362 (d) 6806
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm
28. 28.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
29. 29.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 30° (b) 110° (c) 150° (d) 100°
30. 30.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 80° (d) 110°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 25° (b) 155° (c) 310° (d) 130°
32. 32.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
33. 33.If a + b = 11 and ab = 10, what is a² + b²? (a) 111 (b) 101 (c) 141 (d) 121
34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 2 (d) 1
35. 35.What is the prime factorisation of 18? (a) 2 × 3² (b) 2² × 3 (c) 2 × 3³ (d) 2² × 3²
36. 36.Which term of the AP 16, 21, 26, 31, … is 181? (a) 35th (b) 33rd (c) 34th (d) 36th
37. 37.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
38. 38.What is the mode of 16, 3, 16, 9, 6, 16 and 9? (a) 9 (b) 3 (c) 16 (d) 6
39. 39.A drawer has lots of black, yellow, white, red 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) 2 (c) 6 (d) 5
40. 40.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18

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