Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 957 · 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.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
2. 2.What is the sum of the roots of x² − 9x + 14 = 0? (a) 14 (b) 10 (c) 9 (d) 8
3. 3.The mean of 9 numbers is 32. When the number 22 is added to them, what is the new mean? (a) 31 (b) 27 (c) 30 (d) 32
4. 4.What is the mean of 2, 17, 7, 20, 9 and 11? (a) 12 (b) 10 (c) 11 (d) 13
5. 5.If a + b = 12 and ab = 32, what is a² + b²? (a) 112 (b) 208 (c) 80 (d) 144
6. 6.In a class of 22 children, 16 like dance, 11 like music and 8 like both. How many like at least one of the two? (a) 22 (b) 27 (c) 19 (d) 11
7. 7.What is the 29th term of the AP 10, 17, 24, 31, …? (a) 213 (b) 203 (c) 196 (d) 206
8. 8.In a class of 38 children, 17 like tea, 23 like coffee and 10 like both. How many like only tea? (a) 17 (b) 7 (c) 13 (d) 15
9. 9.Two angles of a triangle are 35° and 50°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 130° (d) 145°
10. 10.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
11. 11.How many factors does 92 have? (a) 4 (b) 7 (c) 6 (d) 5
12. 12.In a class of 34 children, 13 like maths, 24 like science and 7 like both. How many like at least one of the two? (a) 34 (b) 23 (c) 30 (d) 37
13. 13.How many factors does 113 have? (a) 1 (b) 2 (c) 3 (d) 4
14. 14.What is the 17th term of the AP 9, 11, 13, 15, …? (a) 34 (b) 32 (c) 41 (d) 43
15. 15.The mean of 9 numbers is 39. When the number 79 is added to them, what is the new mean? (a) 39 (b) 44 (c) 59 (d) 43
16. 16.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁵ × 5 (d) 2⁴ × 5
17. 17.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 48 (d) 12
18. 18.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
19. 19.What is the missing term in the AP 17, ?, 27, 32, 37? (a) 23 (b) 22 (c) 21 (d) 27
20. 20.A bag has 2 green, 6 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 4/5 (c) 1/5 (d) 9/10
21. 21.A bag has 10 black 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) 2 (b) 11 (c) 13 (d) 4
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
23. 23.The mean of 9 numbers is 13. When the number 23 is added to them, what is the new mean? (a) 13 (b) 18 (c) 14 (d) 15
24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
25. 25.What is the median of 38, 2, 11, 34, 12, 28 and 24? (a) 28 (b) 24 (c) 34 (d) 12
26. 26.A drawer has lots of red, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 6 (c) 3 (d) 2
27. 27.How many prime numbers are there between 40 and 50? (a) 3 (b) 4 (c) 2 (d) 5
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
29. 29.In a class of 13 children, 7 like dance, 7 like music and 4 like both. How many like at least one of the two? (a) 6 (b) 10 (c) 14 (d) 13
30. 30.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 16 (c) 12 (d) 6
31. 31.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 780 (d) 1560
32. 32.What is the 40th term of the AP 11, 18, 25, 32, …? (a) 280 (b) 273 (c) 284 (d) 291
33. 33.In a class of 50 children, 24 like maths, 29 like science and 8 like neither. How many like both? (a) 8 (b) 3 (c) 11 (d) 42
34. 34.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 56 (c) 64 (d) 28
35. 35.The mean of 5 numbers is 38. When the number 20 is added to them, what is the new mean? (a) 29 (b) 36 (c) 38 (d) 35
36. 36.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 1/4 (d) 3/8
37. 37.In a class of 33 children, 18 like mangoes, 13 like bananas and 4 like both. How many like at least one of the two? (a) 33 (b) 27 (c) 31 (d) 23
38. 38.What is the distance between the points (4, 30) and (11, 6)? (a) 31 (b) 625 (c) 26 (d) 25
39. 39.Two angles of a triangle are 35° and 50°. What is the third angle? (a) 130° (b) 145° (c) 95° (d) 85°
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm

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