Exponential Growth & Decay What are exponential growth and exponential decay? y = Aekt?is exponential?growth y = Ae-kt?is exponential?decay k > 0?so plus or minus sign in equation immediatel...
Exponential Equations What are exponential equations? An equation where the unknown is a power In simple cases the solutions can be “spotted” How do I solve exponential equations? Laws of Indices a...
Laws of Logarithms What are the laws of logarithms? Two of these were seen in the notes Logarithmic Functions Beware … …?log (x + y) ≠ log x + log y Results apply to?ln?too How do I use the laws of...
Derivatives of Exponential Functions What is the derivative of e? y = ex?has the particular property ie for?every?real number?x, the gradient of?y = ex?is also equal to?ex?(see Derivatives of Expon...
"e" Exponential Function What is e, the exponential function? The exponential function is?y = ex e?is an?irrational?number e ≈ 2.718 As with other exponential graphs?y = ex passes through (0, 1) ha...
Logarithmic Functions Logarithmic functions a = bx?and?log?b?a = x?are equivalent statements a > 0 b?is called the base Every time you write a logarithm statement say to yourself what it means l...
Exponential Functions Exponential functions Exponential functions of the form?y = ax?with?a > 0?are considered at A level Exponential graphs All graphs of the form?y = ax?will pass through (0, 1...
Modelling with Trigonometric Functions Modelling with trigonometric functions Various real-life situations can be modelled using trigonometric functions You need to be able to interpret the equatio...
Trigonometric Proof Proving trigonometric identities You can use trigonometric identities you already know to prove new identities Make sure you know the?simple trigonometric identities?and?further...
Strategy for Further Trigonometric Equations How to approach solving harder trig equations You can solve harder trig equations, such as those involving?reciprocal?and?inverse?functions in a variety...
R addition formulae Rcos Rsin etc How can I simplify expressions like?a?sin?x?±?b?cos?x? or?a?cos?x?±?b?sin?x? If?a?and?b?are positive constants, then a?sin?x?+?bcos?x?can be rewritten as?R?sin?(x?...
Double Angle Formulae What are the double angle formulae? The?double angle formulae?are derived from the 'A+B' versions of the?compound angle formulae: ?? Exam Tip The double angle formulae are?not...
