Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 15 · 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 far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
2. 2.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 39 (d) 42
3. 3.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
4. 4.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
5. 5.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 582 (c) 466 (d) 592
6. 6.A bag has 4 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 11 (c) 6 (d) 5
7. 7.A bag has 4 blue, 8 yellow and 3 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 4/5 (b) 4/15 (c) 1/3 (d) 11/15
8. 8.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3² (c) 2² × 3 (d) 2 × 3³
9. 9.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 12 (d) 39
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
12. 12.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
13. 13.What is the mean of 20, 3, 10 and 7? (a) 10 (b) 11 (c) 9 (d) 8
14. 14.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
15. 15.A bag has 9 green, 4 red and 7 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 17/20 (b) 4/5 (c) 1/5 (d) 1/3
16. 16.What is the smallest prime factor of 143? (a) 11 (b) 1 (c) 2 (d) 13
17. 17.A bag has 9 black balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 6 (d) 14
18. 18.What is the median of 6, 18, 15, 10, 16, 9 and 33? (a) 10 (b) 16 (c) 15 (d) 14
19. 19.A bag has 7 white balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 2 (c) 8 (d) 9
20. 20.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1166 (b) 676 (c) 916 (d) 1156
21. 21.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5
22. 22.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
23. 23.In a class of 29 children, 8 like maths, 20 like science and 3 like both. How many like neither? (a) 7 (b) 1 (c) 4 (d) 3
24. 24.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 70 (d) 42
25. 25.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 130° (b) 115° (c) 65° (d) 66°
26. 26.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 11 (d) 33
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
28. 28.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
29. 29.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
30. 30.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 11 (b) 10 (c) 8 (d) 9
31. 31.What is the distance between the points (6, 5) and (18, 10)? (a) 17 (b) 169 (c) 14 (d) 13
32. 32.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 115° (c) 135° (d) 70°
33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 132 cm (d) 1386 cm
34. 34.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 100° (b) 125° (c) 80° (d) 135°
35. 35.A drawer has lots of red, blue, green 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) 8 (c) 5 (d) 4
36. 36.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
38. 38.In a class of 30 children, 6 like mangoes, 19 like bananas and 2 like both. How many like only mangoes? (a) 6 (b) 17 (c) 4 (d) 11
39. 39.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8101 (b) 7921 (c) 8291 (d) 8281
40. 40.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 75° (b) 105° (c) 135° (d) 120°

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