Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 16 · 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 14 have? (a) 5 (b) 3 (c) 2 (d) 4
2. 2.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 70° (c) 145° (d) 110°
3. 3.Which term of the AP 17, 26, 35, 44, … is 89? (a) 8th (b) 10th (c) 9th (d) 11th
4. 4.What is the mean of 16, 15, 4 and 21? (a) 16 (b) 13 (c) 15 (d) 14
5. 5.What is the mean of 19, 2, 6 and 21? (a) 13 (b) 16 (c) 11 (d) 12
6. 6.In a class of 23 children, 16 like tea, 10 like coffee and 5 like both. How many like only tea? (a) 11 (b) 13 (c) 16 (d) 5
7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 19
8. 8.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
9. 9.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 36 (c) 15 (d) 64
10. 10.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 3 (d) 2
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
12. 12.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 100° (c) 51° (d) 50°
13. 13.If a + b = 14 and ab = 40, what is a² + b²? (a) 276 (b) 156 (c) 116 (d) 196
14. 14.What is the median of 23, 17, 3, 31 and 20? (a) 23 (b) 3 (c) 17 (d) 20
15. 15.What is the mode of 4, 4, 17, 17, 4, 5 and 15? (a) 15 (b) 5 (c) 4 (d) 17
16. 16.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 5929 (b) 5939 (c) 6391 (d) 6889
17. 17.How many factors does 58 have? (a) 2 (b) 5 (c) 3 (d) 4
18. 18.What is the 37th term of the AP 11, 13, 15, 17, …? (a) 74 (b) 85 (c) 83 (d) 72
19. 19.Two angles of a triangle are 45° and 80°. What is the third angle? (a) 125° (b) 100° (c) 55° (d) 135°
20. 20.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 115°
21. 21.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 120° (b) 60° (c) 140° (d) 100°
22. 22.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
23. 23.What is the median of 26, 23, 40, 11 and 6? (a) 11 (b) 26 (c) 23 (d) 40
24. 24.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
25. 25.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 6)(x + 7)
26. 26.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) 15 (b) 45 (c) 5 (d) 18
27. 27.What is the 17th term of the AP 11, 15, 19, 23, …? (a) 75 (b) 64 (c) 79 (d) 68
28. 28.What is the distance between the points (2, 7) and (6, 4)? (a) 7 (b) 6 (c) 5 (d) 25
29. 29.What is the mean of 11, 3, 4 and 6? (a) 6 (b) 8 (c) 7 (d) 5
30. 30.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 20° (d) 40°
31. 31.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 66° (c) 115° (d) 65°
32. 32.What is the sum of all the whole numbers from 1 to 80? (a) 6480 (b) 3160 (c) 3200 (d) 3240
33. 33.What is the mean of 17, 8, 12, 7 and 16? (a) 15 (b) 13 (c) 10 (d) 12
34. 34.In a class of 41 children, 20 like mangoes, 23 like bananas and 5 like both. How many like neither? (a) 4 (b) 3 (c) 5 (d) 8
35. 35.How many factors does 76 have? (a) 5 (b) 7 (c) 4 (d) 6
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
37. 37.What are the roots of x² − 9x + 20 = 0? (a) 4 and 5 (b) 1 and 8 (c) 1 and 20 (d) 2 and 10
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
39. 39.The mean of 6 numbers is 19. When the number 26 is added to them, what is the new mean? (a) 21 (b) 20 (c) 22 (d) 19
40. 40.If a + b = 11 and ab = 18, what is (a − b)²? (a) 7 (b) 121 (c) 49 (d) 85

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