Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 359 · 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 prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
3. 3.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 130° (c) 310° (d) 50°
4. 4.If a + b = 11 and ab = 28, what is a² + b²? (a) 65 (b) 93 (c) 121 (d) 177
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
6. 6.The mean of 3 numbers is 29. When the number 41 is added to them, what is the new mean? (a) 33 (b) 29 (c) 32 (d) 35
7. 7.The mean of 4 numbers is 24. When the number 29 is added to them, what is the new mean? (a) 27 (b) 26 (c) 24 (d) 25
8. 8.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 864 cu cm (d) 576 cu cm
9. 9.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 85° (b) 140° (c) 135° (d) 95°
10. 10.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
11. 11.What is the 28th term of the AP 7, 14, 21, 28, …? (a) 196 (b) 197 (c) 189 (d) 203
12. 12.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 9 (d) 12
13. 13.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
14. 14.What is the 40th term of the AP 13, 22, 31, 40, …? (a) 364 (b) 351 (c) 360 (d) 373
15. 15.In a class of 36 children, 22 like dance, 11 like music and 3 like both. How many like only dance? (a) 22 (b) 8 (c) 19 (d) 25
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
17. 17.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
18. 18.What is the mean of 18, 6, 13 and 7? (a) 10 (b) 12 (c) 13 (d) 11
19. 19.What is the midpoint of the line joining (8, 4) and (18, 2)? (a) (5, 1) (b) (26, 6) (c) (13, 3) (d) (3, 13)
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
21. 21.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x + 1)(x + 9) (c) (x + 1)(x + 24) (d) (x − 4)(x − 6)
22. 22.What is the 11th term of the AP 18, 20, 22, 24, …? (a) 22 (b) 38 (c) 20 (d) 40
23. 23.What is the median of 37, 12, 40, 20, 4, 19 and 14? (a) 20 (b) 14 (c) 19 (d) 18
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
25. 25.What is the sum of the first 8 terms of the AP 1, 7, 13, …? (a) 200 (b) 352 (c) 43 (d) 176
26. 26.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 40°
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/6 (d) 1/11
28. 28.What is the smallest prime factor of 341? (a) 1 (b) 2 (c) 11 (d) 31
29. 29.What is the 25th term of the AP 14, 19, 24, 29, …? (a) 139 (b) 120 (c) 125 (d) 134
30. 30.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 48 (d) 16
31. 31.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21
32. 32.How many factors does 65 have? (a) 2 (b) 5 (c) 4 (d) 3
33. 33.What is the mean of 15, 12, 6, 20, 16 and 3? (a) 13 (b) 12 (c) 14 (d) 11
34. 34.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
35. 35.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 82 (c) 74 (d) 73
36. 36.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 606 (c) 607 (d) 597
37. 37.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) 22 (b) 14 (c) 21 (d) 15
38. 38.A cuboid is 9 cm long, 8 cm wide and 8 cm high. What is its volume? (a) 416 cu cm (b) 25 cu cm (c) 576 cu cm (d) 72 cu cm
39. 39.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 110° (d) 235°
40. 40.What is the midpoint of the line joining (3, 0) and (7, 4)? (a) (2, 2) (b) (2, 5) (c) (5, 2) (d) (10, 4)

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