A-level Mathematics/OCR/C3/Formulae
By the end of this module you will be expected to have learnt the following formulae:
Transformations of Graphs edit
Reflection edit
- is a reflection of through the x axis.
- is a reflection of through the y axis.
- is a reflection of when y < 0, through the x-axis.
- is a reflection of when x < 0, through the y-axis.
- is a reflection of through the line y = x.
Note: exists only if is bijective, that is, one-to-one and onto.
Stretching edit
- is stretched toward the x-axis if and stretched away from the x-axis if . In both cases the change is by a units.
- 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
- is a translation of f(x) by h units to the right.
- is a translation of f(x) by h units to the left.
- is a translation of f(x) by k units upwards.
- is a translation of f(x) by k units downwards.
Natural Functions edit
- , where y(t) is the final value, is the initial value, k is the growth constant, t is the elapsed time.
- , 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.