Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 144 · 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 missing term in the AP 13, 19, 25, ?, 37? (a) 31 (b) 37 (c) 32 (d) 30
2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 144 (d) 78
3. 3.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 240° (c) 120° (d) 60°
4. 4.The mean of 6 numbers is 19. When the number 12 is added to them, what is the new mean? (a) 17 (b) 20 (c) 18 (d) 19
5. 5.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 8 cu cm (d) 24 cu cm
6. 6.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 72 (d) 24
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
8. 8.How many factors does 44 have? (a) 7 (b) 5 (c) 6 (d) 4
9. 9.If a + b = 11 and ab = 30, what is a² + b²? (a) 181 (b) 61 (c) 91 (d) 121
10. 10.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 1 (d) 4
11. 11.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 21 (d) 28
12. 12.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 69 (d) 23
13. 13.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/8 (c) 3/8 (d) 1/4
14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 153 (b) 33 (c) 306 (d) 289
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
16. 16.In a class of 17 children, 11 like cricket, 9 like football and 3 like neither. How many like both? (a) 7 (b) 14 (c) 6 (d) 3
17. 17.What is the midpoint of the line joining (10, 2) and (22, 10)? (a) (32, 12) (b) (6, 16) (c) (6, 4) (d) (16, 6)
18. 18.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 100° (c) 80° (d) 81°
19. 19.If a + b = 11 and ab = 10, what is (a − b)²? (a) 9 (b) 101 (c) 81 (d) 121
20. 20.Which term of the AP 14, 23, 32, 41, … is 338? (a) 38th (b) 39th (c) 37th (d) 36th
21. 21.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 70° (b) 55° (c) 35° (d) 125°
22. 22.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 15 (d) 36
23. 23.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
24. 24.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
25. 25.What is the sum of all the whole numbers from 1 to 73? (a) 2628 (b) 2702 (c) 2701 (d) 5402
26. 26.In a class of 37 children, 14 like dance, 18 like music and 7 like neither. How many like both? (a) 30 (b) 3 (c) 2 (d) 7
27. 27.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 66 (c) 69 (d) 198
28. 28.What is the midpoint of the line joining (4, 9) and (6, 5)? (a) (10, 14) (b) (7, 5) (c) (1, 2) (d) (5, 7)
29. 29.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
30. 30.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 16 (d) 28
31. 31.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)
32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
33. 33.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
34. 34.If a + b = 19 and ab = 84, what is a² + b²? (a) 193 (b) 529 (c) 277 (d) 361
35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 140° (d) 70°
36. 36.What is the mode of 3, 17, 15, 20, 3, 17 and 3? (a) 20 (b) 15 (c) 17 (d) 3
37. 37.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) 27 times (c) 9 times (d) 3 times
38. 38.What is the mean of 9, 4, 20, 5 and 12? (a) 12 (b) 11 (c) 10 (d) 9
39. 39.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
40. 40.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 12 (d) 16

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