A-level Mathematics/OCR/C1/Appendix A: Formulae

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

The Laws of Indices

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  1.  
  2.  
  3.  
  4.  
  5.  
  6.  
  7.  
  8.  
  9.  

The Laws of Surds

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  1.  
  2.  
  3.  

Polynomials

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Parabolas

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If f(x) is in the form  

  1. -b is the axis of symmetry
  2. c is the maximum or minimum y value

Axis of Symmetry =  

Completing the Square

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  becomes  

The Quadratic Formula

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  • The solutions of the quadratic   are:  
  • The discriminant of the quadratic   is  

Errors

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  1.  
  2.  
  3.  

Coordinate Geometry

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Gradient of a line

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Point-Gradient Form

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The equation of a line passing through the point   and having a slope m is  .

Perpendicular lines

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Lines are perpendicular if  

Distance between two points

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Mid-point of a line

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General Circle Formulae

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Equation of a Circle

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 , where (h,k) is the center and r is the radius.

Differentiation

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Differentiation Rules

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  1. Derivative of a constant function:

 

  1. The Power Rule:

 

  1. The Constant Multiple Rule:

 

  1. The Sum Rule:

 

  1. The Difference Rule:

 

Rules of Stationary Points

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  • 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).