Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 505 · 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.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 48 (d) 15
2. 2.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 10°
3. 3.What is the mean of 20, 17, 2, 4 and 7? (a) 9 (b) 10 (c) 11 (d) 12
4. 4.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 508 (c) 498 (d) 507
5. 5.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
6. 6.What is the smallest prime factor of 209? (a) 11 (b) 1 (c) 2 (d) 19
7. 7.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 120° (d) 60°
8. 8.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
9. 9.A bag has 4 yellow, 3 red and 9 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 7/16 (c) 5/8 (d) 9/16
10. 10.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
11. 11.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 145° (b) 75° (c) 140° (d) 40°
12. 12.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
13. 13.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 961 (b) 841 (c) 901 (d) 971
14. 14.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
16. 16.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 45° (c) 55° (d) 46°
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
18. 18.What is the 16th term of the AP 4, 11, 18, 25, …? (a) 105 (b) 112 (c) 116 (d) 109
19. 19.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 75° (c) 150° (d) 30°
20. 20.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 120 (c) 25 (d) 20
21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
22. 22.A drawer has lots of black, yellow and white 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) 3 (c) 6 (d) 4
23. 23.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
25. 25.In a class of 35 children, 27 like mangoes, 14 like bananas and 7 like both. How many like only mangoes? (a) 20 (b) 7 (c) 21 (d) 27
26. 26.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
27. 27.What is the missing term in the AP 5, 8, 11, ?, 17? (a) 17 (b) 13 (c) 14 (d) 15
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
29. 29.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 2 (d) 5
30. 30.In a class of 40 children, 22 like dance, 19 like music and 2 like both. How many like at least one of the two? (a) 39 (b) 40 (c) 37 (d) 41
31. 31.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 140° (b) 25° (c) 65° (d) 155°
32. 32.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 650 (d) 325
33. 33.In a class of 27 children, 16 like mangoes, 17 like bananas and 11 like both. How many like at least one of the two? (a) 27 (b) 22 (c) 11 (d) 33
34. 34.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
35. 35.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 40° (c) 20° (d) 110°
36. 36.What is the median of 19, 14, 40, 24, 25, 4 and 8? (a) 14 (b) 24 (c) 19 (d) 20
37. 37.In which quadrant does the point (−8, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
38. 38.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
39. 39.Using (a + b)² = a² + 2ab + b², what is 73²? (a) 5339 (b) 4489 (c) 4909 (d) 5329
40. 40.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 120° (c) 59° (d) 61°

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