By the end of this module you will be expected to have learned the following formulae:
![{\displaystyle x^{a}x^{b}=x^{a+b}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59036f0c02a51bcc1c7b8c9f762e1959d7a5d56a)
![{\displaystyle {\frac {x^{a}}{x^{b}}}=x^{a-b}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d757fe963df0f9d18226da4c6625a967d85745bc)
![{\displaystyle x^{-n}={\frac {1}{x^{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9749a10746dbfca04d331530cbac91e12f6e4b8e)
![{\displaystyle \left(x^{a}\right)^{b}=x^{ab}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0cdc5cfa504e55af829db3a9e78057887b424ecd)
![{\displaystyle \left(xy\right)^{n}=x^{n}y^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/795a6ea7d11b091f10dfd4ea8e2b7daef68b0602)
![{\displaystyle \left({\frac {x}{y}}\right)^{n}={\frac {x^{n}}{y^{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e3b22dfc371abfbad65d1bb621a660cde6696067)
![{\displaystyle x^{\frac {a}{b}}={\sqrt[{b}]{x^{a}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c334c9763de15e6e7f7cd9c6f0edf4905026a548)
![{\displaystyle x^{0}=1\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b00cbb6cfd7d48ec1f13ae393f776d1e179c813)
![{\displaystyle x^{1}=x\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f06fb9d7bc91e8ef6bd308736a4191a21685e4a)
![{\displaystyle {\sqrt {xy}}={\sqrt {x}}\times {\sqrt {y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6da90f0c7330a0b192ee91146347be9ae0cd3bb4)
![{\displaystyle {\sqrt {\frac {x}{y}}}={\frac {\sqrt {x}}{\sqrt {y}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a720c84058a6ed798c4952be554f0f69902f369)
![{\displaystyle {\frac {a}{b+{\sqrt {c}}}}={\frac {a}{b+{\sqrt {c}}}}\times {\frac {b-{\sqrt {c}}}{b-{\sqrt {c}}}}={\frac {a(b-{\sqrt {c}})}{b^{2}-c}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6e6ca77baa8c8a3ef46f41dda29f308972abb2ff)
If f(x) is in the form
- -b is the axis of symmetry
- c is the maximum or minimum y value
Axis of Symmetry =
becomes
- The solutions of the quadratic
are: ![{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/00c22777378f9c594c71158fea8946f2495f2a28)
- The discriminant of the quadratic
is ![{\displaystyle b^{2}-4ac}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc2c88a48e0087a5786b460b2e856d118b5e23ab)
![{\displaystyle Absolute\ error=value\ obtained-true\ value}](https://wikimedia.org/api/rest_v1/media/math/render/svg/984aca5531425c40ad7c9936d66db86ff74c2707)
![{\displaystyle Relative\ error={\frac {absolute\ error}{true\ value}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2995b28032cd84b28515497feaca4f696e0950e)
![{\displaystyle Percentage\ error=relative\ error\times 100}](https://wikimedia.org/api/rest_v1/media/math/render/svg/245054b7b42fa941798d7d835dfc8b5173b1dac1)
The equation of a line passing through the point
and having a slope m is
.
Lines are perpendicular if
, where (h,k) is the center and r is the radius.
- Derivative of a constant function:
- The Power Rule:
- The Constant Multiple Rule:
- The Sum Rule:
- The Difference Rule:
- If
and
, then c is a local maximum point of f(x). The graph of f(x) will be concave down on the interval.
- If
and
, then c is a local minimum point of f(x). The graph of f(x) will be concave up on the interval.
- If
and
and
, then c is a local inflection point of f(x).