Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 542 · 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 sum of the roots of x² − 9x + 18 = 0? (a) 8 (b) 10 (c) 9 (d) 18
2. 2.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
3. 3.In a class of 37 children, 10 like maths, 23 like science and 4 like both. How many like neither? (a) 12 (b) 4 (c) 8 (d) 9
4. 4.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 35° (d) 110°
5. 5.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
6. 6.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
7. 7.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 2 (d) 4
8. 8.The mean of 9 numbers is 23. When the number 33 is added to them, what is the new mean? (a) 28 (b) 24 (c) 23 (d) 25
9. 9.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x + 4)(x + 9) (c) (x − 4)(x − 9) (d) (x + 1)(x + 12)
10. 10.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
11. 11.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 36 (c) 18 (d) 72
12. 12.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 280° (b) 140° (c) 100° (d) 80°
13. 13.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
14. 14.A drawer has lots of yellow, red, black and blue 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) 2 (c) 5 (d) 4
15. 15.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2³ × 7 (d) 2 × 7³
16. 16.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 40° (d) 30°
17. 17.What is the median of 4, 16, 33, 17 and 31? (a) 16 (b) 31 (c) 33 (d) 17
18. 18.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10001 (b) 9801 (c) 10201 (d) 10211
19. 19.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 1 (d) 2
20. 20.What is the 26th term of the AP 10, 14, 18, 22, …? (a) 114 (b) 104 (c) 110 (d) 100
21. 21.A bag has 7 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 8 (c) 10 (d) 4
22. 22.A drawer has lots of black, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 3 (d) 4
23. 23.How many prime numbers are there between 50 and 70? (a) 4 (b) 5 (c) 6 (d) 3
24. 24.A drawer has lots of blue, black, green, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 10 (c) 2 (d) 6
25. 25.In a class of 33 children, 17 like dance, 24 like music and 10 like both. How many like only dance? (a) 17 (b) 14 (c) 9 (d) 7
26. 26.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
27. 27.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 42 cu cm (b) 6 cu cm (c) 8 cu cm (d) 18 cu cm
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
29. 29.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 85° (b) 165° (c) 110° (d) 15°
30. 30.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
31. 31.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 8 (d) 7
32. 32.In a class of 28 children, 9 like maths, 21 like science and 5 like both. How many like neither? (a) 4 (b) 8 (c) 3 (d) 5
33. 33.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 1/4 (d) 3/8
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 18 (d) 7
35. 35.What is the sum of all the whole numbers from 1 to 34? (a) 578 (b) 595 (c) 561 (d) 1190
36. 36.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
37. 37.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
38. 38.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 276 (c) 307 (d) 306
39. 39.What is the sum of the first 10 terms of the AP 4, 7, 10, …? (a) 350 (b) 190 (c) 175 (d) 31
40. 40.In a class of 21 children, 14 like tea, 8 like coffee and 3 like both. How many like only tea? (a) 13 (b) 14 (c) 11 (d) 5

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