Category: Algebra

Multiples of 3 and Consecutive Numbers

Numbers that are multiples of 3 are 3, 6, 9, 12, …. Problem Prove that numbers that are multiples of 3 can be expressed as sum of three consecutive numbers. Solution (2 out of 5 marks) 3 = 0 + 1 + 2 6 = 1 + 2 +3 9 = 2 + 3 +…

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Describing solutions of equations

You get a full mark not only because you have the correct answer but also because you have expressed your answer in a clear and concise way using the language of mathematics. Let me illustrate it in the problems below which involve solving equations. Problem 1 Find all the possible solution to the equation y-1…

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Solution to semicircle road trip problems #1 and #2

The circumference of a circle is π x diameter so the length of a semicircle is (1/2)π x d. The solution to problem #2 is shown below. Let the diameters of the smaller circles be p, q, r, s. Use the formula to find the lengths of each semicircle. The same thinking is applicable to semicircle…

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Semicircle Road Trip #2

If you figured out Semicircle road trip problem #1, you will find this second problem easy. The challenge is setting-up the solution/ explanation and not really in figuring out which road is longer. If you have an explanation, share them in the comment section. Problem There are two ways to get from Town A to…

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