Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 914 · 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 16th term of the AP 6, 8, 10, 12, …? (a) 36 (b) 32 (c) 38 (d) 30
2. 2.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 24 sq cm (b) 104 sq cm (c) 52 sq cm (d) 26 sq cm
3. 3.If a + b = 12 and ab = 20, what is a² + b²? (a) 144 (b) 104 (c) 184 (d) 124
4. 4.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 55°
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
6. 6.In a class of 39 children, 26 like cricket, 13 like football and 9 like both. How many like only cricket? (a) 17 (b) 26 (c) 9 (d) 4
7. 7.What is the smallest prime factor of 121? (a) 3 (b) 1 (c) 2 (d) 11
8. 8.A bag has 5 yellow, 7 blue and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/18 (c) 13/18 (d) 5/13
9. 9.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 42 (c) 12 (d) 72
10. 10.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
11. 11.A cuboid is 10 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 251 cu cm (b) 50 cu cm (c) 250 cu cm (d) 20 cu cm
12. 12.What is the sum of the first 11 terms of the AP 5, 8, 11, …? (a) 35 (b) 223 (c) 440 (d) 220
13. 13.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
14. 14.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 496 (d) 636
15. 15.What is the mode of 18, 2, 18, 16, 6, 16 and 16? (a) 2 (b) 18 (c) 16 (d) 6
16. 16.A bag has 9 green, 5 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/2 (b) 8/21 (c) 1/3 (d) 2/3
17. 17.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 2415 (d) 4970
18. 18.What is the mean of 4, 20, 9 and 7? (a) 8 (b) 9 (c) 10 (d) 11
19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
20. 20.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
21. 21.The numbers 7 to 15 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) 99 (c) 11 (d) 33
22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 8 (d) 6
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 1/12 (d) 3/11
24. 24.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
25. 25.In a class of 40 children, 21 like dance, 24 like music and 10 like both. How many like only dance? (a) 14 (b) 21 (c) 11 (d) 16
26. 26.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 12 (d) 48
27. 27.A bag has 8 red, 3 green and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/11 (b) 11/18 (c) 1/3 (d) 7/18
28. 28.A drawer has lots of blue, black, yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 5 (d) 2
29. 29.What is the product of the roots of x² − 11x + 28 = 0? (a) 27 (b) 11 (c) 29 (d) 28
30. 30.A bag has 2 red, 7 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/14 (b) 1/3 (c) 9/14 (d) 5/7
31. 31.What is the missing term in the AP 1, 8, 15, ?, 29? (a) 21 (b) 23 (c) 29 (d) 22
32. 32.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x + 1)(x + 35) (c) (x + 1)(x + 11) (d) (x − 5)(x − 7)
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
34. 34.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
36. 36.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
37. 37.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 125 cu cm (d) 100 cu cm
38. 38.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 14 (c) 16 (d) 15
39. 39.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
40. 40.If a + b = 17 and ab = 72, what is a² + b²? (a) 217 (b) 145 (c) 433 (d) 289

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