Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 711 · 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 factors does 21 have? (a) 4 (b) 2 (c) 5 (d) 3
2. 2.What is the distance between the points (2, 9) and (26, 16)? (a) 26 (b) 625 (c) 25 (d) 31
3. 3.What is the sum of the roots of x² − 12x + 32 = 0? (a) 12 (b) 11 (c) 32 (d) 13
4. 4.Which term of the AP 2, 4, 6, 8, … is 50? (a) 25th (b) 26th (c) 27th (d) 24th
5. 5.Two angles of a triangle are 40° and 30°. What is the third angle? (a) 110° (b) 150° (c) 140° (d) 70°
6. 6.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) 7 (b) 8 (c) 14 (d) 15
7. 7.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
8. 8.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 160° (c) 21° (d) 20°
9. 9.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 539 (b) 409 (c) 529 (d) 289
10. 10.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 1/8 (d) 7/8
11. 11.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 55° (d) 325°
12. 12.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 120 (d) 29
13. 13.In a class of 32 children, 20 like cricket, 15 like football and 9 like both. How many like only cricket? (a) 6 (b) 20 (c) 17 (d) 11
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
15. 15.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 176 (d) 175
16. 16.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 340 (c) 61 (d) 370
17. 17.What is the mode of 5, 20, 5, 20, 5, 4 and 3? (a) 4 (b) 5 (c) 3 (d) 20
18. 18.A drawer has lots of white 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) 2 (b) 4 (c) 3 (d) 5
19. 19.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 16
21. 21.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
22. 22.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 95° (d) 120°
23. 23.What is the product of the roots of x² − 8x + 15 = 0? (a) 14 (b) 15 (c) 8 (d) 16
24. 24.In a class of 40 children, 21 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 34 (b) 40 (c) 38 (d) 37
25. 25.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 6391 (b) 5939 (c) 6889 (d) 5929
26. 26.A bag has 12 green balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 18 (b) 13 (c) 2 (d) 14
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
28. 28.In a class of 47 children, 25 like maths, 23 like science and 11 like both. How many like at least one of the two? (a) 48 (b) 47 (c) 26 (d) 37
29. 29.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 5) (b) (x + 2)(x + 4) (c) (x + 1)(x + 8) (d) (x − 2)(x − 4)
30. 30.In a class of 35 children, 14 like dance, 28 like music and 9 like both. How many like neither? (a) 3 (b) 11 (c) 2 (d) 9
31. 31.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 486 (b) 248 (c) 47 (d) 243
32. 32.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
33. 33.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 25 (d) 24
34. 34.In a class of 35 children, 22 like dance, 11 like music and 8 like both. How many like only dance? (a) 3 (b) 22 (c) 24 (d) 14
35. 35.Two angles of a triangle are 45° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 40° (c) 135° (d) 140°
36. 36.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 870 (c) 841 (d) 57
37. 37.What is the distance between the points (7, 7) and (16, 19)? (a) 225 (b) 16 (c) 21 (d) 15
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 2/11 (d) 1/18
39. 39.If a + b = 15 and ab = 54, what is (a − b)²? (a) 9 (b) 3 (c) 225 (d) 117
40. 40.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x + 1)(x + 13) (c) (x − 5)(x − 9) (d) (x + 5)(x + 9)

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