A-level Mathematics/OCR/C3/Formulae

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

Transformations of Graphs[edit]

Reflection[edit]

  1. is a reflection of through the x axis.
  2. is a reflection of through the y axis.
  3. is a reflection of when y < 0, through the x-axis.
  4. is a reflection of when x < 0, through the y-axis.
  5. is a reflection of through the line y = x.
    Note: exists only if is bijective, that is, one-to-one and onto.

Stretching[edit]

  1. is stretched toward the x-axis if and stretched away from the x-axis if . In both cases the change is by a units.
  2. is stretched away from the y-axis if and stretched toward the y-axis if . In both cases the change is by b units.

Translations[edit]

  1. is a translation of f(x) by h units to the right.
  2. is a translation of f(x) by h units to the left.
  3. is a translation of f(x) by k units upwards.
  4. is a translation of f(x) by k units downwards.

Natural Functions[edit]

  1. , where y(t) is the final value, is the initial value, k is the growth constant, t is the elapsed time.
  2. , k for calculations involving half-lives.

Trigonometry[edit]

Reciprocal Trigonometric Functions and their Inverses[edit]

Angle Sum and Difference Identities[edit]

Note: The sign means that if you add the angles (A+B) then you subtract in the identity and vice versa. It is present in the cosine identity and the denominator of the tangent identity.

Double Angle Identities[edit]

Combination of Trigonometric Functions[edit]

Using radians r = amplitute α = phase.

where

where

Differentiation[edit]

  • If , then
  • If , then
  • If , then
  • If , then
  • If , then

Integration[edit]

For volumes of revolution:

Numerical Methods[edit]

Simpson's Rule

where and n is even

This is part of the C3 (Core Mathematics 3) module of the A-level Mathematics text.