Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 692 · 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.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x − 7)(x − 8) (d) (x + 1)(x + 14)
2. 2.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 105° (b) 130° (c) 55° (d) 125°
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
4. 4.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
5. 5.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
6. 6.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3249 (b) 3591 (c) 3259 (d) 3969
7. 7.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 125° (d) 55°
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
9. 9.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
10. 10.Which is the correct factorisation of x² + 10x + 21? (a) (x + 3)(x + 7) (b) (x + 1)(x + 9) (c) (x − 3)(x − 7) (d) (x + 1)(x + 21)
11. 11.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 70° (c) 35° (d) 55°
12. 12.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 9 (d) 8
13. 13.In a class of 32 children, 25 like dance, 15 like music and 4 like neither. How many like both? (a) 28 (b) 12 (c) 8 (d) 4
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
15. 15.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
16. 16.A bag has 4 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 2 (c) 5 (d) 6
17. 17.Using (a − b)² = a² − 2ab + b², what is 67²? (a) 4489 (b) 4891 (c) 5329 (d) 4499
18. 18.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
19. 19.A drawer has lots of black 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) 2 (b) 3 (c) 5 (d) 4
20. 20.What is the distance between the points (1, 27) and (8, 3)? (a) 25 (b) 625 (c) 31 (d) 26
21. 21.What is the midpoint of the line joining (3, 1) and (11, 3)? (a) (7, 2) (b) (4, 1) (c) (14, 4) (d) (2, 7)
22. 22.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 11 (b) 56 (c) 28 (d) 35
23. 23.What is the 26th term of the AP 18, 22, 26, 30, …? (a) 104 (b) 122 (c) 100 (d) 118
24. 24.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
25. 25.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 25 (d) 240
26. 26.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
27. 27.What is the midpoint of the line joining (2, 4) and (8, 8)? (a) (10, 12) (b) (3, 2) (c) (5, 6) (d) (6, 5)
28. 28.In a class of 36 children, 18 like cricket, 18 like football and 10 like both. How many like only cricket? (a) 18 (b) 9 (c) 8 (d) 10
29. 29.A bag has 5 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 6 (c) 9 (d) 2
30. 30.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 136 cu cm (b) 12 cu cm (c) 96 cu cm (d) 15 cu cm
31. 31.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 80° (b) 135° (c) 100° (d) 145°
32. 32.In a class of 30 children, 18 like maths, 13 like science and 4 like both. How many like at least one of the two? (a) 30 (b) 27 (c) 31 (d) 23
33. 33.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
34. 34.A bag has 9 blue, 3 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 1/4 (c) 4/5 (d) 1/5
35. 35.Two angles of a triangle are 65° and 70°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 45°
36. 36.A bag has 3 red balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 4 (c) 6 (d) 5
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 3850 cm (d) 440 cm
38. 38.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
39. 39.In a class of 19 children, 6 like mangoes, 9 like bananas and 2 like both. How many like only mangoes? (a) 6 (b) 4 (c) 10 (d) 7
40. 40.In a class of 29 children, 13 like tea, 20 like coffee and 6 like both. How many like only tea? (a) 13 (b) 14 (c) 7 (d) 9

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