2 out of 3
Kyle and his teacher disagree about his test score - who is right?
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The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
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An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.
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Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
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Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate a(n) and b(n) for n<8. What do you notice about these sequences? (ii) Find a relation between a(p) and b(q). (iii) Prove your conjectures.
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It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
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Can you find a rule which relates triangular numbers to square numbers?
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Jasmine buys three different types of plant. How many triffids did she buy?
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What fractions can you divide the diagonal of a square into by simple folding?
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L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
