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.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
- 2.In a class of 27 children, 7 like maths, 19 like science and 3 like both. How many like neither? (a) 4 (b) 1 (c) 7 (d) 3
- 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
- 4.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) 29 (b) 21 (c) 22 (d) 28
- 5.In a class of 35 children, 28 like mangoes, 15 like bananas and 9 like both. How many like neither? (a) 10 (b) 2 (c) 9 (d) 1
- 6.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 55° (d) 125°
- 7.In a class of 36 children, 29 like cricket, 15 like football and 9 like both. How many like at least one of the two? (a) 36 (b) 26 (c) 44 (d) 35
- 8.In a class of 41 children, 14 like tea, 27 like coffee and 9 like both. How many like at least one of the two? (a) 23 (b) 41 (c) 33 (d) 32
- 9.What is the sum of the roots of x² − 13x + 36 = 0? (a) 12 (b) 13 (c) 36 (d) 14
- 10.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
- 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
- 12.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
- 13.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 125° (b) 55° (c) 130° (d) 105°
- 14.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
- 15.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
- 16.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 488 (d) 625
- 17.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
- 18.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
- 19.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 75° (b) 160° (c) 105° (d) 125°
- 20.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
- 21.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 120° (c) 60° (d) 145°
- 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
- 23.What is the mode of 2, 12, 5, 5, 3, 5 and 3? (a) 12 (b) 3 (c) 5 (d) 2
- 24.If a + b = 12 and ab = 11, what is a² + b²? (a) 166 (b) 133 (c) 144 (d) 122
- 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
- 26.In a class of 28 children, 8 like dance, 23 like music and 4 like both. How many like neither? (a) 5 (b) 4 (c) 1 (d) 2
- 27.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 252 sq cm (b) 254 sq cm (c) 127 sq cm (d) 508 sq cm
- 28.If a + b = 9 and ab = 18, what is a² + b²? (a) 45 (b) 117 (c) 63 (d) 81
- 29.If a + b = 19 and ab = 88, what is a² + b²? (a) 361 (b) 537 (c) 273 (d) 185
- 30.Which term of the AP 10, 16, 22, 28, … is 142? (a) 22nd (b) 23rd (c) 25th (d) 24th
- 31.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
- 32.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
- 33.In a class of 46 children, 29 like maths, 16 like science and 9 like both. How many like neither? (a) 9 (b) 1 (c) 19 (d) 10
- 34.If a + b = 12 and ab = 35, what is a² + b²? (a) 144 (b) 214 (c) 109 (d) 74
- 35.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 300 (b) 45 (c) 276 (d) 552
- 36.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 160°
- 37.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 18 (c) 9 (d) 6
- 38.7 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) 28 (b) 21 (c) 14 (d) 9
- 39.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 1008 (b) 504 (c) 75 (d) 540
- 40.What is the distance between the points (6, 2) and (18, 11)? (a) 16 (b) 21 (c) 15 (d) 225
Answer key
- 144
- 4
- 10
- 22
- 1
- 125°
- 35
- 32
- 13
- 15
- 44 cm
- 1/12
- 55°
- Second quadrant
- 37
- 624
- 5
- 45
- 75°
- 1/2
- 120°
- 88 cm
- 5
- 122
- 64 times
- 1
- 254 sq cm
- 45
- 185
- 23rd
- 7/8
- 24
- 10
- 74
- 276
- 100°
- 9
- 14
- 504
- 15
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