Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 353 · 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 midpoint of the line joining (1, 12) and (7, 6)? (a) (3, 3) (b) (9, 4) (c) (8, 18) (d) (4, 9)
2. 2.A bag has 7 yellow balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 17 (d) 11
3. 3.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 507 (c) 517 (d) 416
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
5. 5.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 136 (d) 126
6. 6.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
7. 7.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
8. 8.In a class of 45 children, 18 like mangoes, 21 like bananas and 8 like neither. How many like both? (a) 8 (b) 2 (c) 3 (d) 37
9. 9.How many factors does 77 have? (a) 2 (b) 5 (c) 3 (d) 4
10. 10.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 10 (c) 11 (d) 19
11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 351 (c) 676 (d) 702
12. 12.A drawer has lots of black, green, white, blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 10 (c) 6 (d) 5
13. 13.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
14. 14.The mean of 7 numbers is 28. When the number 4 is added to them, what is the new mean? (a) 25 (b) 28 (c) 26 (d) 16
15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
16. 16.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
17. 17.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
18. 18.In a class of 47 children, 28 like maths, 17 like science and 8 like both. How many like only maths? (a) 28 (b) 20 (c) 9 (d) 30
19. 19.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 217 sq cm (d) 216 sq cm
20. 20.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
21. 21.In a class of 33 children, 17 like cricket, 19 like football and 9 like both. How many like only cricket? (a) 10 (b) 8 (c) 14 (d) 17
22. 22.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
23. 23.Two angles of a triangle are 35° and 25°. What is the third angle? (a) 60° (b) 120° (c) 145° (d) 155°
24. 24.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
25. 25.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 44 (b) 216 (c) 432 (d) 221
26. 26.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
27. 27.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.What is the missing term in the AP 15, 21, 27, ?, 39? (a) 33 (b) 32 (c) 34 (d) 39
29. 29.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
30. 30.What is the midpoint of the line joining (6, 0) and (14, 2)? (a) (4, 1) (b) (10, 1) (c) (20, 2) (d) (1, 10)
31. 31.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 1 (d) 4
32. 32.If a + b = 9 and ab = 14, what is (a − b)²? (a) 5 (b) 81 (c) 25 (d) 53
33. 33.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 294 cu cm (c) 343 cu cm (d) 196 cu cm
34. 34.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7066 (b) 7056 (c) 6416 (d) 5776
35. 35.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 25 (b) 50 (c) 10 (d) 30
36. 36.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 115° (c) 65° (d) 145°
37. 37.If a + b = 8 and ab = 12, what is a² + b²? (a) 52 (b) 88 (c) 40 (d) 64
38. 38.In a class of 33 children, 14 like tea, 17 like coffee and 7 like both. How many like only tea? (a) 16 (b) 10 (c) 14 (d) 7
39. 39.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
40. 40.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 16 cu cm (b) 30 cu cm (c) 150 cu cm (d) 170 cu cm

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