Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 853 · 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 fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
3. 3.In a class of 38 children, 24 like dance, 10 like music and 8 like neither. How many like both? (a) 30 (b) 8 (c) 4 (d) 5
4. 4.If a + b = 18 and ab = 80, what is (a − b)²? (a) 324 (b) 4 (c) 2 (d) 164
5. 5.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 546 (c) 555 (d) 442
6. 6.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 35° (d) 25°
7. 7.What is the 33rd term of the AP 4, 12, 20, 28, …? (a) 268 (b) 264 (c) 256 (d) 260
8. 8.How many factors does 24 have? (a) 9 (b) 6 (c) 7 (d) 8
9. 9.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
10. 10.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 36 (c) 8 (d) 40
11. 11.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) 21 (b) 28 (c) 29 (d) 22
12. 12.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 150° (d) 60°
13. 13.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
14. 14.A bag has 8 yellow balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 7 (c) 14 (d) 2
15. 15.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 185 (b) 370 (c) 32 (d) 200
16. 16.The mean of 5 numbers is 18. When the number 30 is added to them, what is the new mean? (a) 21 (b) 18 (c) 20 (d) 24
17. 17.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 115° (b) 25° (c) 65° (d) 295°
18. 18.What is the midpoint of the line joining (4, 9) and (12, 17)? (a) (16, 26) (b) (13, 8) (c) (8, 13) (d) (4, 4)
19. 19.A bag has 5 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 14 (c) 10 (d) 6
20. 20.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
21. 21.What is the midpoint of the line joining (1, 14) and (11, 6)? (a) (10, 6) (b) (12, 20) (c) (5, 4) (d) (6, 10)
22. 22.A bag has 5 green balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 15 (c) 2 (d) 6
23. 23.What is the 32nd term of the AP 6, 15, 24, 33, …? (a) 288 (b) 279 (c) 285 (d) 294
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
25. 25.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
26. 26.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
27. 27.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 108 (c) 12 (d) 39
28. 28.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 14 (c) 9 (d) 28
29. 29.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2 × 3 (d) 2³ × 3
30. 30.How many factors does 86 have? (a) 3 (b) 5 (c) 2 (d) 4
31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
32. 32.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 72 (d) 24
33. 33.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 18 cu cm (b) 13 cu cm (c) 36 cu cm (d) 80 cu cm
34. 34.A drawer has lots of yellow, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 6
35. 35.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 81 (d) 18
36. 36.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
37. 37.How many factors does 53 have? (a) 2 (b) 1 (c) 4 (d) 3
38. 38.Which term of the AP 5, 9, 13, 17, … is 105? (a) 27th (b) 25th (c) 26th (d) 28th
39. 39.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
40. 40.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 30° (b) 145° (c) 150° (d) 65°

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