Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 753 · 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.What is the product of the roots of x² − 14x + 48 = 0? (a) 48 (b) 49 (c) 47 (d) 14
2. 2.What is the distance between the points (5, 17) and (13, 2)? (a) 23 (b) 18 (c) 289 (d) 17
3. 3.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
4. 4.In a class of 30 children, 17 like dance, 18 like music and 10 like both. How many like at least one of the two? (a) 25 (b) 35 (c) 30 (d) 15
5. 5.The mean of 4 numbers is 31. When the number 21 is added to them, what is the new mean? (a) 30 (b) 31 (c) 26 (d) 29
6. 6.In a class of 29 children, 18 like maths, 15 like science and 11 like both. How many like only maths? (a) 18 (b) 4 (c) 14 (d) 7
7. 7.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3²
8. 8.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 130° (d) 80°
9. 9.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
10. 10.If a + b = 17 and ab = 72, what is a² + b²? (a) 433 (b) 217 (c) 145 (d) 289
11. 11.How many factors does 96 have? (a) 13 (b) 11 (c) 10 (d) 12
12. 12.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 16 (d) 48
13. 13.The mean of 3 numbers is 19. When the number 23 is added to them, what is the new mean? (a) 19 (b) 20 (c) 21 (d) 22
14. 14.The mean of 7 numbers is 12. When the number 28 is added to them, what is the new mean? (a) 15 (b) 20 (c) 12 (d) 14
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 14 (d) 16
16. 16.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 80° (c) 160° (d) 70°
17. 17.Which term of the AP 17, 26, 35, 44, … is 350? (a) 39th (b) 38th (c) 37th (d) 40th
18. 18.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 15 (c) 7 (d) 14
19. 19.Two angles of a triangle are 45° and 125°. What is the third angle? (a) 170° (b) 55° (c) 135° (d) 10°
20. 20.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
21. 21.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.In a class of 42 children, 28 like tea, 18 like coffee and 10 like both. How many like neither? (a) 10 (b) 7 (c) 16 (d) 6
23. 23.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 48 cu cm (b) 6 cu cm (c) 13 cu cm (d) 92 cu cm
24. 24.What is the 10th term of the AP 10, 19, 28, 37, …? (a) 91 (b) 81 (c) 90 (d) 100
25. 25.In a class of 42 children, 26 like cricket, 27 like football and 12 like both. How many like only cricket? (a) 12 (b) 14 (c) 26 (d) 15
26. 26.What is the mode of 4, 19, 5, 8, 4, 4 and 19? (a) 5 (b) 4 (c) 8 (d) 19
27. 27.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5³ (d) 2² × 3 × 5
28. 28.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 108 (c) 116 (d) 107
29. 29.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 40° (c) 220° (d) 140°
30. 30.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 7225 (b) 5625 (c) 5635 (d) 6375
31. 31.In a class of 55 children, 31 like tea, 27 like coffee and 11 like both. How many like only tea? (a) 16 (b) 20 (c) 28 (d) 31
32. 32.What is the smallest prime factor of 319? (a) 2 (b) 1 (c) 11 (d) 29
33. 33.In a class of 45 children, 24 like cricket, 23 like football and 12 like both. How many like neither? (a) 11 (b) 10 (c) 12 (d) 22
34. 34.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 66 (d) 63
35. 35.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 2970 (c) 1458 (d) 1485
36. 36.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
37. 37.A bag has 6 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 2 (c) 7 (d) 9
38. 38.In a class of 22 children, 7 like maths, 8 like science and 2 like both. How many like only maths? (a) 14 (b) 5 (c) 7 (d) 6
39. 39.In a class of 21 children, 15 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 19 (b) 21 (c) 25 (d) 13
40. 40.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7

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