Maths Olympiad Sample Paper 2 (Practice)
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.
NameDateTime takenScore ___ / 40
- 1.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
- 2.What is the mean of 12, 17, 4, 19 and 23? (a) 15 (b) 16 (c) 17 (d) 14
- 3.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 120° (c) 70° (d) 110°
- 4.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
- 5.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 23 (c) 156 (d) 78
- 6.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 8 (c) 18 (d) 30
- 7.In a class of 15 children, 11 like maths, 7 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 1 (d) 2
- 8.What is the mean of 20, 19, 11 and 18? (a) 18 (b) 19 (c) 17 (d) 16
- 9.What is the distance between the points (0, 3) and (12, 8)? (a) 13 (b) 169 (c) 14 (d) 17
- 10.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 115° (c) 65° (d) 155°
- 11.In a class of 30 children, 10 like dance, 24 like music and 7 like both. How many like at least one of the two? (a) 27 (b) 20 (c) 34 (d) 30
- 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
- 13.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
- 14.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
- 15.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 501 (c) 406 (d) 502
- 16.How many factors does 114 have? (a) 9 (b) 8 (c) 6 (d) 7
- 17.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°
- 18.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 90 (b) 45 (c) 55 (d) 17
- 19.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
- 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
- 21.The mean of 9 numbers is 16. When the number 6 is added to them, what is the new mean? (a) 11 (b) 14 (c) 16 (d) 15
- 22.What is the median of 8, 12, 13, 21, 29, 5 and 26? (a) 21 (b) 12 (c) 13 (d) 14
- 23.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 2 and 36 (c) 1 and 72 (d) 1 and 16
- 24.What is the 19th term of the AP 7, 14, 21, 28, …? (a) 140 (b) 126 (c) 133 (d) 134
- 25.In a class of 46 children, 25 like maths, 18 like science and 7 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 17
- 26.What is the distance between the points (4, 9) and (7, 13)? (a) 25 (b) 5 (c) 6 (d) 7
- 27.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
- 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 25 (c) 24 (d) 12
- 29.In a class of 33 children, 16 like cricket, 15 like football and 4 like both. How many like at least one of the two? (a) 23 (b) 31 (c) 33 (d) 27
- 30.A bag has 3 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 4 (d) 8
- 31.A drawer has lots of blue, red, yellow, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
- 32.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 31 (d) 29
- 33.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 160° (d) 55°
- 34.If a + b = 13 and ab = 36, what is a² + b²? (a) 97 (b) 133 (c) 169 (d) 241
- 35.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 32 (c) 24 (d) 10
- 36.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 95° (c) 85° (d) 150°
- 37.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 342 (c) 56 (d) 684
- 38.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 130° (d) 50°
- 39.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
- 40.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 100° (c) 80° (d) 135°
Answer key
- 10
- 15
- 70°
- 6
- 78
- 15
- 1
- 17
- 13
- 115°
- 27
- 45
- 4 times
- 7/8
- 501
- 8
- 40°
- 45
- 132
- 110°
- 15
- 13
- 8 and 9
- 133
- 10
- 5
- 80°
- 13
- 27
- 6
- 6
- 30
- 55°
- 97
- 16
- 95°
- 342
- 130°
- 17
- 100°
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