A-level Mathematics/OCR/C2/Appendix A: Formulae

< A-level Mathematics‎ | OCR‎ | C2

By the end of this module you will be expected to have learnt the following formulae:

Contents

Dividing and Factoring PolynomialsEdit

Remainder TheoremEdit

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 TheoremEdit

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 FunctionEdit

The Laws of ExponentsEdit

  1.  
  2.  
  3.  
  4.  
  5.  
  6.  
  7.   where c is a constant
  8.  
  9.  

Logarithmic FunctionEdit

The inverse of   is   which is equivalent to  

Change of Base Rule:   can be written as  

Laws of Logarithmic FunctionsEdit

When X and Y are positive.

  •  
  •  
  •  

Circles and AnglesEdit

Conversion of Degree Minutes and Seconds to a DecimalEdit

  where X is the degree, y is the minutes, and z is the seconds.

Arc LengthEdit

  Note: θ need to be in radians

Area of a SectorEdit

 Note: θ need to be in radians.

TrigonometryEdit

The Trigonometric Ratios Of An AngleEdit

Function Written Defined Inverse Function Written Equivalent to
Cosine          
Sine          
Tangent          

Important Trigonometric ValuesEdit

You need to have these values memorized.

         
  0 0 1 0
         
         
         
    1 0 -

The Law of CosinesEdit

 

 

 

The Law of SinesEdit

 

Area of a TriangleEdit

 

 

 

Trigonometric IdentitiesEdit

 

 

IntegrationEdit

Integration RulesEdit

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 IntegralsEdit

  1.  , F is the anti derivative of f such that F' = f
  2.  
  3.  
  4. Area between a curve and the x-axis is  
  5. Area between a curve and the y-axis is  
  6. Area between curves is  

Trapezium RuleEdit

 

Where:  

Midpoint RuleEdit

 

Where:   n is the number of strips.

and  

This is part of the C2 (Core Mathematics 2) module of the A-level Mathematics text.


Dividing and Factoring Polynomials / Sequences and Series / Logarithms and Exponentials / Circles and Angles / Integration

Appendix A: Formulae