Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 100 · 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 smallest prime factor of 299? (a) 13 (b) 2 (c) 23 (d) 1
2. 2.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2525 (b) 3035 (c) 2025 (d) 3025
3. 3.7 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) 56 (b) 98 (c) 49 (d) 14
4. 4.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
5. 5.What is the smallest prime factor of 217? (a) 31 (b) 2 (c) 1 (d) 7
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19
7. 7.What are the roots of x² − 5x + 6 = 0? (a) 1 and 4 (b) 1 and 6 (c) 2 and 3 (d) 2 and 4
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
9. 9.In a class of 35 children, 24 like maths, 8 like science and 5 like both. How many like at least one of the two? (a) 32 (b) 22 (c) 35 (d) 27
10. 10.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 36 (c) 30 (d) 60
11. 11.What is the midpoint of the line joining (10, 10) and (22, 4)? (a) (7, 16) (b) (16, 7) (c) (6, 3) (d) (32, 14)
12. 12.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 110 (d) 22
13. 13.In a class of 28 children, 22 like tea, 7 like coffee and 3 like both. How many like only tea? (a) 22 (b) 21 (c) 4 (d) 19
14. 14.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 216 (c) 29 (d) 228
15. 15.Which is the correct factorisation of x² + 11x + 28? (a) (x − 4)(x − 7) (b) (x + 1)(x + 10) (c) (x + 1)(x + 28) (d) (x + 4)(x + 7)
16. 16.What is the midpoint of the line joining (0, 7) and (4, 11)? (a) (2, 9) (b) (9, 2) (c) (4, 18) (d) (2, 2)
17. 17.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
18. 18.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
19. 19.In a class of 39 children, 18 like dance, 26 like music and 3 like neither. How many like both? (a) 3 (b) 8 (c) 5 (d) 36
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
21. 21.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 420 (c) 39 (d) 400
22. 22.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
23. 23.What is the 28th term of the AP 1, 9, 17, 25, …? (a) 225 (b) 216 (c) 217 (d) 224
24. 24.A bag has 5 white, 2 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/9 (b) 1/3 (c) 2/7 (d) 2/9
25. 25.Two angles of a triangle are 25° and 30°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 155° (d) 150°
26. 26.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
27. 27.What is the 30th term of the AP 19, 26, 33, 40, …? (a) 222 (b) 229 (c) 210 (d) 203
28. 28.A drawer has lots of yellow, white, black 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) 5 (b) 4 (c) 2 (d) 8
29. 29.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 11) (b) (x + 3)(x + 9) (c) (x + 1)(x + 27) (d) (x − 3)(x − 9)
30. 30.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) 8 times (c) 4 times (d) 5 times
31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 9 (c) 30 (d) 25
32. 32.In a class of 45 children, 21 like cricket, 25 like football and 5 like neither. How many like both? (a) 1 (b) 6 (c) 40 (d) 5
33. 33.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) 18 (b) 162 (c) 57 (d) 54
34. 34.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 13 (c) 12 (d) 25
35. 35.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 110 (b) 190 (c) 31 (d) 95
36. 36.What is the smallest prime factor of 35? (a) 1 (b) 7 (c) 2 (d) 5
37. 37.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 15 (c) 14 (d) 22
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
39. 39.What is the smallest prime factor of 161? (a) 7 (b) 2 (c) 1 (d) 23
40. 40.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 305° (b) 35° (c) 125° (d) 55°

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