Mathematics A H230: Exponentials and Logarithms Topical Past Paper Questions

At the point P on the curve $ y = e^{3x} - 21x - 8 $ the gradient of the tangent is 3. (a) Determine the x-coordinate of P. Give your answer in the form $ \ln a $, where a is an integer to be determined. [4] (b) Hence determine the equation of the tangent at $P$. Give your answer…

The diagram shows the graphs of $y=2^{3x}$ and $y=2^{3x+2}$. The graph of $y=2^{3x}$ can be transformed to the graph of $y=2^{3x+2}$ by means of a stretch. (a) Give details of the stretch. [2] The point $A$ lies on $y = 2^{3x}$ and the point $B$ lies on $y = 2^{3x+2}$. The line s…

The relationship between the variables P and Q is modelled by the formula $ Q = aP^{n} $ where $a$ and $n$ are constants. Some values of $P$ and $\mathcal{Q}$ are obtained from an experiment. (a) State appropriate quantities to plot so that the resulting points lie approximately…