Mathematics AA: EXPONENTIALS - LOGARITHMS Topical Past Paper Questions

[Maximum mark:29] The following question uses Maclaurin series to investigate approximations of mathematical constants and the accuracies of such approximations. (a) Given $ |x| [2] (b) Hence, use integration to show that the Maclaurin series of $ \arctan x $ may be expressed as…

[Maximum mark: 5] Consider the function $h(x)=\log_{10}(4x^{2}-rx+r-1)$, where $x\in\mathbb{R}$. Find the possible values of $r$.

[Maximum mark: 5] Consider the function $f(x)=\mathrm{e}^{x}-3x-4$. (a) On the following axes, sketch the graph of $f$ for $-4 \leq x \leq 3$. [3] The function g is defined by $ g(x) = e^{2x} - 6x - 7 $. (b) The graph of g is obtained from the graph of f by a horizontal stretch w…