Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 513 · 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.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 12 (d) 3
2. 2.In a class of 46 children, 23 like maths, 28 like science and 10 like both. How many like at least one of the two? (a) 46 (b) 51 (c) 31 (d) 41
3. 3.If a + b = 17 and ab = 70, what is (a − b)²? (a) 149 (b) 289 (c) 3 (d) 9
4. 4.In a class of 43 children, 29 like maths, 22 like science and 11 like both. How many like only maths? (a) 18 (b) 21 (c) 11 (d) 29
5. 5.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 50° (d) 65°
6. 6.In a class of 29 children, 17 like dance, 7 like music and 9 like neither. How many like both? (a) 9 (b) 20 (c) 4 (d) 5
7. 7.A drawer has lots of white, blue, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 5 (d) 8
8. 8.The mean of 5 numbers is 11. When the number 29 is added to them, what is the new mean? (a) 15 (b) 11 (c) 14 (d) 20
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
10. 10.A bag has 10 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 11 (c) 2 (d) 21
11. 11.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 20°
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
13. 13.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 3/8 (d) 1/4
14. 14.Which is the correct factorisation of x² + 12x + 35? (a) (x − 5)(x − 7) (b) (x + 1)(x + 11) (c) (x + 5)(x + 7) (d) (x + 1)(x + 35)
15. 15.What is the 19th term of the AP 12, 17, 22, 27, …? (a) 107 (b) 102 (c) 95 (d) 90
16. 16.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
18. 18.A bag has 11 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 12 (c) 2 (d) 23
19. 19.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 841 (c) 971 (d) 901
20. 20.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
21. 21.What is the prime factorisation of 180? (a) 2² × 3² × 5 (b) 2 × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
22. 22.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 255° (c) 76° (d) 75°
23. 23.What is the distance between the points (3, 0) and (11, 15)? (a) 18 (b) 17 (c) 23 (d) 289
24. 24.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
25. 25.In a class of 37 children, 23 like dance, 8 like music and 4 like both. How many like only dance? (a) 23 (b) 19 (c) 4 (d) 29
26. 26.The mean of 6 numbers is 34. When the number 20 is added to them, what is the new mean? (a) 27 (b) 33 (c) 32 (d) 34
27. 27.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
28. 28.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1128 (c) 2256 (d) 1129
29. 29.What is the median of 14, 22, 30, 15 and 8? (a) 14 (b) 22 (c) 15 (d) 30
30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 15 (d) 16
31. 31.What is the distance between the points (7, 17) and (16, 5)? (a) 16 (b) 21 (c) 225 (d) 15
32. 32.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 32 (c) 56 (d) 28
33. 33.A bag has 3 yellow balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 12 (c) 5 (d) 2
34. 34.Two angles of a triangle are 20° and 75°. What is the exterior angle at the third corner? (a) 95° (b) 160° (c) 105° (d) 85°
35. 35.What is the 13th term of the AP 11, 18, 25, 32, …? (a) 102 (b) 95 (c) 91 (d) 84
36. 36.In a class of 19 children, 9 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 19 (b) 16 (c) 12 (d) 20
37. 37.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
38. 38.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
39. 39.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
40. 40.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4

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