Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 63 · 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 KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
2. 2.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 165° (b) 16° (c) 30° (d) 15°
3. 3.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 35 (c) 40 (d) 70
4. 4.In a class of 48 children, 28 like dance, 27 like music and 12 like both. How many like only dance? (a) 15 (b) 28 (c) 21 (d) 16
5. 5.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 48 (c) 16 (d) 144
6. 6.In a class of 28 children, 15 like maths, 11 like science and 9 like neither. How many like both? (a) 19 (b) 8 (c) 9 (d) 7
7. 7.The mean of 3 numbers is 28. When the number 24 is added to them, what is the new mean? (a) 28 (b) 26 (c) 29 (d) 27
8. 8.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
9. 9.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 150° (d) 125°
10. 10.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 16) (b) (x + 2)(x + 8) (c) (x + 1)(x + 9) (d) (x − 2)(x − 8)
11. 11.In a class of 40 children, 26 like mangoes, 19 like bananas and 12 like both. How many like neither? (a) 8 (b) 12 (c) 19 (d) 7
12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
13. 13.In a class of 43 children, 32 like maths, 20 like science and 12 like both. How many like only maths? (a) 23 (b) 8 (c) 32 (d) 20
14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 289 (b) 153 (c) 306 (d) 33
15. 15.In a class of 34 children, 20 like mangoes, 12 like bananas and 3 like both. How many like only mangoes? (a) 22 (b) 20 (c) 9 (d) 17
16. 16.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
17. 17.What is the midpoint of the line joining (6, 0) and (10, 12)? (a) (6, 8) (b) (8, 6) (c) (16, 12) (d) (2, 6)
18. 18.What is the distance between the points (8, 2) and (11, 6)? (a) 5 (b) 6 (c) 7 (d) 25
19. 19.A drawer has lots of green, white 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) 3 (b) 4 (c) 6 (d) 2
20. 20.A bag has 5 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 6 (c) 2 (d) 7
21. 21.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 24 (c) 8 (d) 18
22. 22.What is the midpoint of the line joining (8, 3) and (18, 11)? (a) (26, 14) (b) (5, 4) (c) (7, 13) (d) (13, 7)
23. 23.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 88 (b) 160 (c) 17 (d) 80
24. 24.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 576 sq cm (d) 864 sq cm
25. 25.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 4235 (b) 4875 (c) 5625 (d) 4225
26. 26.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 196 cu cm (d) 343 cu cm
27. 27.A bag has 9 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 15 (b) 10 (c) 11 (d) 2
28. 28.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 30 (d) 15
29. 29.Two angles of a triangle are 40° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 45° (d) 135°
30. 30.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 4 (c) 2 (d) 3
31. 31.The numbers 17 to 25 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) 189 (c) 63 (d) 66
32. 32.The mean of 5 numbers is 38. When the number 56 is added to them, what is the new mean? (a) 47 (b) 42 (c) 41 (d) 38
33. 33.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 81 sq cm (d) 729 sq cm
34. 34.If a + b = 16 and ab = 48, what is (a − b)²? (a) 256 (b) 160 (c) 64 (d) 8
35. 35.Two angles of a triangle are 70° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 220° (c) 140° (d) 40°
36. 36.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 55° (b) 35° (c) 125° (d) 70°
37. 37.How many factors does 70 have? (a) 6 (b) 9 (c) 7 (d) 8
38. 38.What is the sum of the first 6 terms of the AP 6, 8, 10, …? (a) 72 (b) 132 (c) 16 (d) 66
39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
40. 40.A bag has 3 yellow, 3 red and 9 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/5 (b) 4/5 (c) 1/3 (d) 1/4

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