Note
Pascal's Triangle
WARNING This does not have any practical example. It is just a demonstration. See Binomial Expansion for technique. $$ \begin{array}{0} x + 2y ^2 = 1x^3 2y ^0 + 3x^2 2y + 3x 2y ^2...
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Negative and Fractional Indices
$$ \begin{array}{1} a^\frac{1}{m} = \sqrt m { a } \\ a^\frac{n}{m} = \sqrt m { a^n } \\ a^ m = \frac{1}{a^m} \\ a^0 = 1 \end{array} $$
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Note
Calculating the Midpoint of a Straight Line
Formula This formula calculates the midpoint of both the $x$ and $y$ axes individually. $$ \begin{array}{1} \left \frac{x {1} + x {2}}{2}, \frac{y {1} + y {2}}{2} \right \end{array...
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Completing The Square
NOTE Revise. $$ a x + h ^2 + k $$ To get the co ordinates of the maximum/minimum turning point. $ x + h = 0$ or $ h$ provides the $x$ co ordinate. $k$ provides the $y$ co ordinate....
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Calculating the Gradient
$$ m = \frac{\Delta y}{\Delta x} $$
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Finding the Length
To find the length of a line, you can use Pythagoras' Theorem. $$ A^2 = B^2 + C^2 $$ as: $$ d = \sqrt{ x^2 x^1 ^2 + y^2 y^2 ^2 } $$
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Parallel Lines
Parallel lines are two lines which have the same gradient but never touch. Example $$ \begin{array}{1} y {1} = 5x + 2 \\ y {2} = 5x + 4 \end{array} $$ These linear lines are parall...
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Perpendicular Lines
Perpendicular lines are two lines which meet at 90°. If a line has the gradient of $m$, a line perpendicular will have the gradient of $ \frac{1}{m}$. If two lines are perpendicula...
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