Surface Areas of Frustums

A frustum is that past of a pyramid or cone that lines between two parallel planes cutting it. If one of the planes is the base and the other is horizontal then the result is the shape shown below right (for a cone). The smaller cone top right and the original cone left are similar […]

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Ratios and Similar Shapes

If a shape is enlarged, so that all the sides are multiplied by the same factor, it will remain the same basic shape, the only difference being that all the sides are larger by the same factor. Sometimes though, we may deconstruct a diagram into similar shapes so that an enlargement exists from one shape […]

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The Ambiguous Case

The ambiguous case arises when using the Sine Rule to find an angle in a triangle. It occurs because the Sin function is symmetric about 90°, so that When we solve forthere is an acute solution,and an obtuse solution, Example: Find the angle A in the triangle below. The Sine Rule states Then This is […]

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Tessellations

Tessellating a plane is to cover it with shapes leaving no gaps. The shapes may all be the same, or there may be several shapes. Each shape may be rotated, reflected or translated to fit somewhere else leaving no gaps. The shapes tessellating the planes below are all identical, but have been rotated, translated or […]

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Vectors I

A vector is the difference between two points. If two points areandthen we can write the difference(when written in a column between brackets) asThe arrow above means that we are going from the pointto the pointIf we swapandthen we are going fromtoand writeThis is shown below. We can also write points as pairs of coordinates and […]

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Parts of a Circle

Labels for the different parts of a circle are given below Radius – the radius of a circle is the distance from the centre labelled O to the circumference. The radius is labelled The circumference of a circle is the perimeter, and is labelled Diameter – diameter of a circle is the length of a […]

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