Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 676 · 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.How many factors does 98 have? (a) 7 (b) 5 (c) 4 (d) 6
2. 2.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 12) (b) (x − 4)(x − 9) (c) (x + 1)(x + 36) (d) (x + 4)(x + 9)
3. 3.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 3/8 (d) 1/8
4. 4.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 100°
5. 5.What is the smallest prime factor of 115? (a) 5 (b) 1 (c) 2 (d) 23
6. 6.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 110° (c) 40° (d) 70°
7. 7.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) 39 (c) 36 (d) 12
8. 8.A cuboid is 4 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 40 sq cm (b) 38 sq cm (c) 76 sq cm (d) 152 sq cm
9. 9.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁵ × 3 (d) 2⁴ × 3
10. 10.The mean of 9 numbers is 22. When the number 52 is added to them, what is the new mean? (a) 25 (b) 37 (c) 22 (d) 26
11. 11.What is the mean of 12, 9, 4 and 7? (a) 7 (b) 9 (c) 10 (d) 8
12. 12.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
13. 13.In a class of 28 children, 18 like dance, 8 like music and 4 like neither. How many like both? (a) 24 (b) 4 (c) 3 (d) 2
14. 14.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 289 (b) 409 (c) 539 (d) 529
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 18 (d) 16
16. 16.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) 11 (c) 99 (d) 33
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
18. 18.A bag has 6 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 7 (c) 2 (d) 15
19. 19.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 3/4 (d) 1/2
20. 20.What is the mode of 19, 13, 12, 12, 19, 1 and 19? (a) 13 (b) 19 (c) 12 (d) 1
21. 21.What is the 19th term of the AP 4, 10, 16, 22, …? (a) 108 (b) 118 (c) 114 (d) 112
22. 22.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
23. 23.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 70 (c) 35 (d) 40
24. 24.What is the mode of 1, 9, 18, 18, 1, 11 and 18? (a) 18 (b) 9 (c) 11 (d) 1
25. 25.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 1 (d) 3
26. 26.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 20° (c) 140° (d) 320°
27. 27.In a class of 30 children, 25 like maths, 10 like science and 6 like both. How many like neither? (a) 1 (b) 2 (c) 7 (d) 6
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
29. 29.If a + b = 16 and ab = 63, what is a² + b²? (a) 193 (b) 256 (c) 382 (d) 130
30. 30.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
31. 31.What is the sum of the first 8 terms of the AP 5, 9, 13, …? (a) 152 (b) 168 (c) 33 (d) 304
32. 32.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
33. 33.If a + b = 16 and ab = 60, what is (a − b)²? (a) 136 (b) 16 (c) 256 (d) 4
34. 34.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
35. 35.A bag has 5 yellow balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 6 (c) 11 (d) 2
36. 36.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
37. 37.What is the mean of 6, 4, 14, 10 and 6? (a) 10 (b) 8 (c) 7 (d) 9
38. 38.What is the distance between the points (7, 8) and (19, 3)? (a) 169 (b) 17 (c) 13 (d) 14
39. 39.What is the sum of the roots of x² − 12x + 32 = 0? (a) 32 (b) 12 (c) 13 (d) 11
40. 40.How many factors does 103 have? (a) 1 (b) 4 (c) 3 (d) 2

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