By the end of this module you will be expected to have learnt the following formulae:
Dividing and Factoring Polynomials[edit]
Remainder Theorem[edit]
If you have a polynomial f(x) divided by x - c, the remainder is equal to f(c). Note if the equation is x + c then you need to negate c: f(-c).
The Factor Theorem[edit]
A polynomial f(x) has a factor x - c if and only if f(c) = 0. Note if the equation is x + c then you need to negate c: f(-c).
Formula For Exponential and Logarithmic Function[edit]
The Laws of Exponents[edit]






where c is a constant


Logarithmic Function[edit]
The inverse of
is
which is equivalent to 
Change of Base Rule:
can be written as 
Laws of Logarithmic Functions[edit]
When X and Y are positive.



Circles and Angles[edit]
Conversion of Degree Minutes and Seconds to a Decimal[edit]
where X is the degree, y is the minutes, and z is the seconds.
Arc Length[edit]
Note: θ need to be in radians
Area of a Sector[edit]
Note: θ need to be in radians.
Trigonometry[edit]
The Trigonometric Ratios Of An Angle[edit]
Function |
Written |
Defined |
Inverse Function |
Written |
Equivalent to |
Cosine |
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Sine |
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Tangent |
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Important Trigonometric Values[edit]
You need to have these values memorized.
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0 |
0 |
1 |
0 |
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1 |
0 |
- |
The Law of Cosines[edit]



The Law of Sines[edit]

Area of a Triangle[edit]



Trigonometric Identities[edit]


Integration[edit]
Integration Rules[edit]
The reason that we add a + C when we compute the integral is because the derivative of a constant is zero, therefore we have an unknown constant when we compute the integral. 



Rules of Definite Integrals[edit]
, F is the anti derivative of f such that F' = f


- Area between a curve and the x-axis is

- Area between a curve and the y-axis is

- Area between curves is

Trapezium Rule[edit]

Where: 
Midpoint Rule[edit]
![{\displaystyle \int _{a}^{b}f\left(x\right)\,dx\approx =h\left[f\left(x_{1}\right)+f\left(x_{2}\right)+\ldots +f\left(x_{n}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8892220f2181ca22226fdf533fd77b93b9ac525)
Where:
n is the number of strips.
and ![{\displaystyle x_{i}={\frac {1}{2}}\left[\left(a+\left\{i-1\right\}h\right)+\left(a+ih\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5259213f3fabd4478a2a51ec53b732043773d266)