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 Reflection 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 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 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 , 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 Reciprocal Trigonometric Functions and their Inverses Angle Sum and Difference Identities 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 Combination of Trigonometric Functions Using radians r = amplitute α = phase. where where Differentiation If , then If , then If , then If , then If , then Integration For volumes of revolution: Numerical Methods Simpson's Rule where and n is even