Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 833 · 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 far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
2. 2.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
3. 3.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.What is the mean of 14, 7, 11 and 16? (a) 11 (b) 12 (c) 16 (d) 13
5. 5.What is the 38th term of the AP 15, 23, 31, 39, …? (a) 304 (b) 296 (c) 319 (d) 311
6. 6.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
7. 7.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 240 (c) 25 (d) 20
8. 8.In a class of 38 children, 29 like cricket, 18 like football and 11 like both. How many like at least one of the two? (a) 25 (b) 38 (c) 36 (d) 47
9. 9.In a class of 25 children, 6 like maths, 12 like science and 2 like both. How many like neither? (a) 11 (b) 7 (c) 9 (d) 2
10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
11. 11.In a class of 33 children, 20 like mangoes, 21 like bananas and 12 like both. How many like neither? (a) 12 (b) 16 (c) 5 (d) 4
12. 12.What is the median of 28, 22, 7, 6, 12, 27 and 9? (a) 22 (b) 9 (c) 6 (d) 12
13. 13.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) 4 times (c) 5 times (d) 2 times
14. 14.In a class of 39 children, 21 like mangoes, 26 like bananas and 1 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 38
15. 15.Two angles of a triangle are 25° and 95°. What is the third angle? (a) 85° (b) 60° (c) 120° (d) 155°
16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
17. 17.A bag has 6 red, 6 green and 2 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 3/7 (b) 3/4 (c) 4/7 (d) 1/3
18. 18.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
19. 19.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
20. 20.What is the mean of 11, 5, 16, 6 and 17? (a) 13 (b) 10 (c) 12 (d) 11
21. 21.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
22. 22.What are the roots of x² − 12x + 35 = 0? (a) 1 and 11 (b) 1 and 35 (c) 5 and 7 (d) 2 and 10
23. 23.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 105°
24. 24.What is the midpoint of the line joining (3, 4) and (9, 14)? (a) (3, 5) (b) (6, 9) (c) (9, 6) (d) (12, 18)
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
26. 26.In a class of 26 children, 17 like mangoes, 16 like bananas and 9 like both. How many like at least one of the two? (a) 24 (b) 26 (c) 33 (d) 15
27. 27.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
28. 28.What is the missing term in the AP 18, 25, ?, 39, 46? (a) 33 (b) 39 (c) 32 (d) 31
29. 29.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2 × 3⁴ (c) 2³ × 3 (d) 2⁴ × 3
30. 30.If a + b = 12 and ab = 20, what is a² + b²? (a) 184 (b) 144 (c) 124 (d) 104
31. 31.The mean of 4 numbers is 24. When the number 29 is added to them, what is the new mean? (a) 24 (b) 25 (c) 27 (d) 26
32. 32.What is the midpoint of the line joining (3, 4) and (11, 12)? (a) (4, 4) (b) (8, 7) (c) (14, 16) (d) (7, 8)
33. 33.What is the sum of the first 11 terms of the AP 9, 13, 17, …? (a) 638 (b) 341 (c) 49 (d) 319
34. 34.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 1034 (b) 784 (c) 904 (d) 1024
35. 35.What is the distance between the points (1, 13) and (13, 4)? (a) 225 (b) 21 (c) 16 (d) 15
36. 36.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 24 (d) 66
37. 37.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 231 (b) 462 (c) 41 (d) 441
38. 38.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) 12 (d) 36
39. 39.What is the distance between the points (9, 14) and (18, 2)? (a) 21 (b) 16 (c) 225 (d) 15
40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm

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