Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 798 · 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 two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
2. 2.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 15 (c) 5 (d) 18
3. 3.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 43 (d) 484
4. 4.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 591 (c) 582 (d) 592
5. 5.What is the median of 25, 19, 24, 13, 9, 23 and 32? (a) 19 (b) 13 (c) 24 (d) 23
6. 6.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 48 (d) 12
7. 7.In a class of 15 children, 10 like maths, 9 like science and 6 like both. How many like only maths? (a) 4 (b) 6 (c) 3 (d) 10
8. 8.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 6 (c) 8 (d) 12
9. 9.Which term of the AP 1, 9, 17, 25, … is 249? (a) 33rd (b) 34th (c) 32nd (d) 31st
10. 10.What is the mode of 19, 15, 4, 20, 20, 20 and 15? (a) 20 (b) 19 (c) 15 (d) 4
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 154 sq cm (d) 44 sq cm
12. 12.Which is the correct factorisation of x² + 9x + 14? (a) (x + 2)(x + 7) (b) (x − 2)(x − 7) (c) (x + 1)(x + 14) (d) (x + 1)(x + 8)
13. 13.In a class of 51 children, 23 like maths, 27 like science and 7 like both. How many like at least one of the two? (a) 51 (b) 50 (c) 43 (d) 36
14. 14.What is the mean of 18, 7, 10, 4, 14 and 7? (a) 10 (b) 11 (c) 9 (d) 12
15. 15.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
16. 16.A drawer has lots of blue, yellow 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) 2 (c) 4 (d) 6
17. 17.4 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) 32 (b) 16 (c) 8 (d) 20
18. 18.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 230° (b) 115° (c) 130° (d) 50°
19. 19.In a class of 27 children, 14 like cricket, 15 like football and 11 like both. How many like only cricket? (a) 14 (b) 12 (c) 3 (d) 4
20. 20.A bag has 5 green, 5 white and 8 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 13/18 (b) 5/18 (c) 5/13 (d) 1/3
21. 21.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 24 (d) 12
22. 22.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 2/3 (d) 5/6
23. 23.In a class of 40 children, 20 like dance, 25 like music and 10 like both. How many like at least one of the two? (a) 40 (b) 25 (c) 45 (d) 35
24. 24.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) 9 times (c) 3 times (d) 27 times
25. 25.A bag has 9 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 21 (c) 10 (d) 2
26. 26.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 208 cu cm (b) 192 cu cm (c) 24 cu cm (d) 18 cu cm
27. 27.If a + b = 13 and ab = 12, what is (a − b)²? (a) 145 (b) 11 (c) 169 (d) 121
28. 28.The mean of 7 numbers is 21. When the number 37 is added to them, what is the new mean? (a) 29 (b) 21 (c) 23 (d) 24
29. 29.In a class of 35 children, 18 like mangoes, 22 like bananas and 11 like both. How many like neither? (a) 17 (b) 11 (c) 7 (d) 6
30. 30.In a class of 27 children, 15 like maths, 16 like science and 2 like neither. How many like both? (a) 25 (b) 2 (c) 4 (d) 6
31. 31.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 75° (d) 155°
32. 32.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x + 1)(x + 12) (c) (x + 4)(x + 9) (d) (x − 4)(x − 9)
33. 33.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
34. 34.A cuboid is 4 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 108 cu cm (b) 12 cu cm (c) 150 cu cm (d) 16 cu cm
35. 35.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
36. 36.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 2 (d) 4
37. 37.What is the midpoint of the line joining (2, 9) and (4, 13)? (a) (6, 22) (b) (11, 3) (c) (3, 11) (d) (1, 2)
38. 38.The mean of 6 numbers is 24. When the number 3 is added to them, what is the new mean? (a) 20 (b) 21 (c) 24 (d) 22
39. 39.In a class of 29 children, 20 like maths, 14 like science and 6 like neither. How many like both? (a) 6 (b) 23 (c) 11 (d) 5
40. 40.What is the 11th term of the AP 18, 20, 22, 24, …? (a) 22 (b) 38 (c) 20 (d) 40

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