Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 809 · 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 product of the roots of x² − 12x + 27 = 0? (a) 12 (b) 28 (c) 27 (d) 26
2. 2.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 13 (d) 2
3. 3.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 70° (c) 40° (d) 110°
4. 4.A bag has 5 white balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 17 (c) 6 (d) 7
5. 5.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3003 (c) 3004 (d) 6006
6. 6.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 7/8 (d) 3/8
7. 7.What is the midpoint of the line joining (7, 6) and (11, 0)? (a) (18, 6) (b) (3, 9) (c) (9, 3) (d) (2, 3)
8. 8.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 66° (c) 245° (d) 65°
9. 9.What is the median of 36, 27, 2, 30, 13, 12 and 40? (a) 13 (b) 28 (c) 27 (d) 30
10. 10.If a + b = 18 and ab = 80, what is (a − b)²? (a) 324 (b) 4 (c) 2 (d) 164
11. 11.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 15° (d) 16°
12. 12.A drawer has lots of green, 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) 5 (b) 8 (c) 2 (d) 4
13. 13.In a class of 33 children, 17 like tea, 13 like coffee and 2 like both. How many like at least one of the two? (a) 28 (b) 33 (c) 30 (d) 26
14. 14.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 94 (c) 102 (d) 84
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
16. 16.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
18. 18.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 45 (d) 15
19. 19.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
20. 20.The mean of 9 numbers is 39. When the number 29 is added to them, what is the new mean? (a) 37 (b) 39 (c) 38 (d) 34
21. 21.How many factors does 26 have? (a) 3 (b) 4 (c) 5 (d) 2
22. 22.What is the median of 27, 32, 19, 40 and 17? (a) 28 (b) 19 (c) 27 (d) 32
23. 23.A bag has 4 yellow, 4 green and 8 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 5/16 (b) 3/4 (c) 1/4 (d) 1/3
24. 24.If a + b = 12 and ab = 27, what is a² + b²? (a) 198 (b) 117 (c) 90 (d) 144
25. 25.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 55° (d) 155°
26. 26.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
27. 27.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 901 (b) 971 (c) 961 (d) 841
28. 28.What is the sum of all the whole numbers from 1 to 72? (a) 2556 (b) 2628 (c) 2592 (d) 5256
29. 29.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 144 (d) 126
30. 30.What is the missing term in the AP 7, 13, 19, ?, 31? (a) 24 (b) 31 (c) 26 (d) 25
31. 31.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
32. 32.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
33. 33.What is the distance between the points (1, 5) and (16, 13)? (a) 17 (b) 23 (c) 18 (d) 289
34. 34.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
35. 35.Which is the correct factorisation of x² + 12x + 27? (a) (x − 3)(x − 9) (b) (x + 1)(x + 11) (c) (x + 3)(x + 9) (d) (x + 1)(x + 27)
36. 36.A bag has 9 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 10 (c) 11 (d) 15
37. 37.A cuboid is 10 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 332 sq cm (b) 664 sq cm (c) 166 sq cm (d) 360 sq cm
38. 38.What is the 24th term of the AP 3, 11, 19, 27, …? (a) 184 (b) 192 (c) 195 (d) 187
39. 39.What is the smallest prime factor of 203? (a) 1 (b) 29 (c) 7 (d) 2
40. 40.What is the distance between the points (2, 1) and (9, 25)? (a) 26 (b) 31 (c) 25 (d) 625

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