Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 962 · 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 (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
2. 2.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 6 (d) 8
3. 3.Which term of the AP 11, 16, 21, 26, … is 136? (a) 25th (b) 26th (c) 27th (d) 28th
4. 4.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 266 (b) 576 (c) 256 (d) 384
5. 5.If a + b = 19 and ab = 90, what is (a − b)²? (a) 181 (b) 271 (c) 1 (d) 361
6. 6.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
7. 7.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 21 (d) 7
8. 8.A drawer has lots of white and yellow 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) 5 (c) 2 (d) 3
9. 9.In a class of 36 children, 14 like cricket, 24 like football and 4 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 34 (d) 30
10. 10.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 36 (c) 99 (d) 33
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 5 (d) 3
13. 13.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 105° (c) 135° (d) 150°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
15. 15.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 55° (d) 160°
16. 16.How many factors does 109 have? (a) 2 (b) 3 (c) 4 (d) 1
17. 17.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 90° (b) 91° (c) 45° (d) 135°
18. 18.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 10201 (b) 9999 (c) 9811 (d) 9801
19. 19.In a class of 22 children, 17 like cricket, 12 like football and 8 like both. How many like neither? (a) 1 (b) 8 (c) 2 (d) 9
20. 20.What is the midpoint of the line joining (1, 14) and (11, 2)? (a) (6, 8) (b) (12, 16) (c) (5, 6) (d) (8, 6)
21. 21.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 676 (b) 884 (c) 1156 (d) 686
22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 10 (c) 6 (d) 9
23. 23.What is the median of 36, 34, 25, 10, 18, 26 and 8? (a) 10 (b) 26 (c) 18 (d) 25
24. 24.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 30° (d) 15°
25. 25.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 120 (d) 240
26. 26.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 2)(x + 3) (c) (x + 1)(x + 4) (d) (x + 1)(x + 6)
27. 27.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2³ × 7
28. 28.A drawer has lots of green, blue and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 6
29. 29.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 32 (c) 11 (d) 56
30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 21 (d) 14
32. 32.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 5)(x + 8) (c) (x + 1)(x + 40) (d) (x + 1)(x + 12)
33. 33.In a class of 29 children, 7 like cricket, 22 like football and 4 like neither. How many like both? (a) 4 (b) 25 (c) 5 (d) 3
34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.The mean of 3 numbers is 15. When the number 23 is added to them, what is the new mean? (a) 17 (b) 18 (c) 19 (d) 15
36. 36.In which quadrant does the point (−5, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 155° (b) 115° (c) 270° (d) 90°
38. 38.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 285° (c) 75° (d) 15°
39. 39.In a class of 39 children, 18 like mangoes, 22 like bananas and 11 like both. How many like at least one of the two? (a) 18 (b) 29 (c) 40 (d) 39
40. 40.What is the mode of 19, 19, 14, 9, 5, 5 and 5? (a) 9 (b) 5 (c) 19 (d) 14

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