Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 666 · 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 mode of 3, 19, 3, 4, 4, 4 and 11? (a) 19 (b) 11 (c) 4 (d) 3
2. 2.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 140° (c) 110° (d) 70°
3. 3.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 465 (c) 930 (d) 59
4. 4.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) 60 (c) 36 (d) 30
5. 5.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
6. 6.The mean of 5 numbers is 35. When the number 41 is added to them, what is the new mean? (a) 35 (b) 37 (c) 38 (d) 36
7. 7.What is the smallest prime factor of 161? (a) 1 (b) 2 (c) 23 (d) 7
8. 8.A bag has 7 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 8 (d) 9
9. 9.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
10. 10.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
11. 11.What is the sum of the first 10 terms of the AP 4, 10, 16, …? (a) 58 (b) 620 (c) 310 (d) 340
12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
13. 13.The mean of 5 numbers is 36. When the number 30 is added to them, what is the new mean? (a) 33 (b) 36 (c) 34 (d) 35
14. 14.In a class of 50 children, 24 like tea, 31 like coffee and 12 like both. How many like only tea? (a) 13 (b) 19 (c) 24 (d) 12
15. 15.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 120° (b) 110° (c) 130° (d) 50°
16. 16.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) 22 (c) 15 (d) 14
17. 17.Which term of the AP 14, 22, 30, 38, … is 158? (a) 18th (b) 19th (c) 20th (d) 21st
18. 18.A bag has 3 blue balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 4 (c) 11 (d) 2
19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
20. 20.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 135° (b) 115° (c) 160° (d) 65°
21. 21.If a + b = 12 and ab = 32, what is a² + b²? (a) 112 (b) 144 (c) 80 (d) 208
22. 22.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
23. 23.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
24. 24.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) 21 (b) 28 (c) 22 (d) 29
25. 25.A bag has 7 green balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 4 (c) 2 (d) 8
26. 26.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
27. 27.In a class of 23 children, 14 like maths, 10 like science and 7 like both. How many like only maths? (a) 13 (b) 7 (c) 3 (d) 14
28. 28.What is the midpoint of the line joining (0, 14) and (6, 4)? (a) (3, 5) (b) (3, 9) (c) (6, 18) (d) (9, 3)
29. 29.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 78 (d) 60
30. 30.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
31. 31.The mean of 5 numbers is 15. When the number 21 is added to them, what is the new mean? (a) 17 (b) 18 (c) 15 (d) 16
32. 32.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 294 cu cm (c) 196 cu cm (d) 21 cu cm
33. 33.What is the median of 37, 39, 22, 9, 12, 6 and 23? (a) 12 (b) 23 (c) 9 (d) 22
34. 34.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 16 (c) 24 (d) 7
35. 35.What is the mean of 13, 20, 13, 11, 6 and 15? (a) 13 (b) 15 (c) 12 (d) 14
36. 36.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 276 (b) 552 (c) 45 (d) 529
37. 37.The mean of 8 numbers is 17. When the number 35 is added to them, what is the new mean? (a) 20 (b) 17 (c) 19 (d) 26
38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 6 (d) 17
39. 39.How many factors does 17 have? (a) 4 (b) 2 (c) 3 (d) 1
40. 40.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5

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