Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 891 · 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 35° and 20°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 160° (d) 145°
2. 2.What is the median of 29, 4, 31, 19, 22, 12 and 2? (a) 12 (b) 22 (c) 17 (d) 19
3. 3.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
4. 4.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 21 (c) 14 (d) 9
5. 5.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 48 (c) 11 (d) 32
6. 6.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
7. 7.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 16 (b) 18 (c) 17 (d) 20
8. 8.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/5 (d) 3/8
10. 10.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
11. 11.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 12 cu cm (b) 82 cu cm (c) 6 cu cm (d) 42 cu cm
12. 12.A bag has 2 yellow, 6 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/11 (b) 1/3 (c) 2/9 (d) 2/11
13. 13.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
15. 15.What is the sum of the roots of x² − 12x + 35 = 0? (a) 13 (b) 12 (c) 35 (d) 11
16. 16.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 135° (d) 150°
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
19. 19.What is the prime factorisation of 180? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2 × 3² × 5
20. 20.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 72)
21. 21.What are the roots of x² − 12x + 35 = 0? (a) 1 and 11 (b) 2 and 10 (c) 5 and 7 (d) 1 and 35
22. 22.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 32 (c) 31 (d) 40
23. 23.What is the distance between the points (3, 25) and (10, 1)? (a) 31 (b) 26 (c) 625 (d) 25
24. 24.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 9 cu cm (d) 36 cu cm
25. 25.How many factors does 87 have? (a) 3 (b) 4 (c) 5 (d) 2
26. 26.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
27. 27.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 2 (d) 1
28. 28.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 2/3 (d) 1/4
29. 29.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 75° (d) 145°
30. 30.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 6 (c) 9 (d) 12
31. 31.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 150° (b) 45° (c) 15° (d) 165°
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
33. 33.Which is the correct factorisation of x² + 11x + 18? (a) (x + 1)(x + 10) (b) (x − 2)(x − 9) (c) (x + 2)(x + 9) (d) (x + 1)(x + 18)
34. 34.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 135° (b) 90° (c) 270° (d) 45°
35. 35.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 136 (d) 126
36. 36.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
37. 37.In a class of 31 children, 9 like maths, 17 like science and 9 like neither. How many like both? (a) 9 (b) 4 (c) 22 (d) 5
38. 38.A bag has 5 yellow, 9 blue and 3 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 15/17 (c) 14/17 (d) 3/17
39. 39.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 18 (d) 57
40. 40.What is the missing term in the AP 10, ?, 22, 28, 34? (a) 16 (b) 15 (c) 22 (d) 17

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