Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 159 · 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.A cuboid is 6 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 144 cu cm (b) 180 cu cm (c) 17 cu cm (d) 18 cu cm
2. 2.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 190° (b) 10° (c) 170° (d) 11°
3. 3.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 22 (d) 55
4. 4.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 335° (d) 65°
5. 5.What is the distance between the points (5, 5) and (13, 20)? (a) 23 (b) 17 (c) 289 (d) 18
6. 6.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 120° (d) 145°
7. 7.The mean of 3 numbers is 23. When the number 19 is added to them, what is the new mean? (a) 21 (b) 23 (c) 24 (d) 22
8. 8.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
9. 9.In a class of 23 children, 14 like maths, 16 like science and 10 like both. How many like at least one of the two? (a) 10 (b) 20 (c) 23 (d) 30
10. 10.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 56° (c) 235° (d) 55°
11. 11.In a class of 49 children, 28 like maths, 31 like science and 11 like both. How many like only maths? (a) 18 (b) 20 (c) 28 (d) 17
12. 12.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 96 (c) 14 (d) 56
13. 13.What is the distance between the points (3, 13) and (9, 5)? (a) 14 (b) 100 (c) 11 (d) 10
14. 14.Two angles of a triangle are 20° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 95° (d) 115°
15. 15.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
16. 16.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 30) (c) (x + 1)(x + 10) (d) (x + 5)(x + 6)
17. 17.A bag has 7 white balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 8 (b) 2 (c) 15 (d) 9
18. 18.Two angles of a triangle are 80° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 140° (c) 120° (d) 40°
19. 19.In a class of 36 children, 17 like tea, 12 like coffee and 3 like both. How many like only tea? (a) 17 (b) 24 (c) 14 (d) 9
20. 20.How many factors does 95 have? (a) 4 (b) 5 (c) 2 (d) 3
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
22. 22.The mean of 7 numbers is 26. When the number 50 is added to them, what is the new mean? (a) 29 (b) 26 (c) 30 (d) 38
23. 23.In a class of 17 children, 11 like mangoes, 12 like bananas and 7 like both. How many like at least one of the two? (a) 16 (b) 23 (c) 9 (d) 17
24. 24.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 16 (c) 51 (d) 144
25. 25.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 616 cm (d) 176 cm
26. 26.What is the mean of 3, 5, 14 and 18? (a) 8 (b) 9 (c) 10 (d) 11
27. 27.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6724 (b) 6404 (c) 6734 (d) 6084
28. 28.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 135° (b) 90° (c) 46° (d) 45°
29. 29.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 48 (c) 16 (d) 24
30. 30.A bag has 10 green balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 20 (b) 12 (c) 11 (d) 2
31. 31.A bag has 11 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 12 (c) 10 (d) 2
32. 32.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) 2 (b) 4 (c) 5 (d) 8
33. 33.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) 14 (b) 15 (c) 7 (d) 8
34. 34.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
35. 35.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁵ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁴ × 3 × 5
36. 36.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 45° (b) 15° (c) 150° (d) 165°
37. 37.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 22 (d) 21
38. 38.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 676 (b) 1156 (c) 686 (d) 884
39. 39.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3 × 5 × 7
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 9 (c) 20 (d) 18

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