First Principles Differentiation What is the derivative or gradient function? For a curve y = f(x) there is an associated function called the derivative or gradient function The derivative of f(x) ...
由于疫情原因，不管是在国内的孩子们还是在国外的孩子们上学、考试都受到了影响。 英国教育局深知学生们在疫情期间受到的影响很大，所以在今年的考试评分也将会相对宽松一些。 那让我们来看看，今年GCSE考试的相...
Definition of Gradient What is the gradient of a curve? At a given point the gradient of a curve is defined as the gradient of the tangent to the curve at that point A tangent to a curve is a line ...
Using Log Graphs in Modelling What are log graphs? Log graphs are used when the scale of a graph increases or decreases exponentially It can very difficult to read specific values from graphs with ...
Using Exps & Logs in Modelling What is exponential modelling? Exponential modelling is where real-life situations are modelled using exponential growth and decay Exponential growth is typically...
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...
