Mathematics Pure Math 2,3 9709: ALGEBRA Topical Past Paper Questions

It is given that $ \frac{2+ai}{a-3i} = \lambda(1-5i) $, where $ a $ and $ \lambda $ are real constants. (a) Show that $ a^2 - 5a + 6 = 0 $. (b) Hence, find the possible values of $a$ and the corresponding values of $\lambda$.

The variables $x$ and $y$ satisfy the equation $Ay = b^x$, where $A$ and $b$ are constants. **(a)** Show that the graph of $\ln y$ against $x$ is a straight line. [2] **(b)** When $x = 3.4$, $\ln y = 0.86$ and when $x = 5.7$, $\ln y = 2.56$. Find the value of $A$ and the value of…

Let $ f(x)=\frac{7a^{2}}{(a-2x)(3a+x)} $, where $ a $ is a positive constant. (a) Express $ f(x) $ in partial fractions. [3] (b) Hence obtain the expansion of $f(x)$ in ascending powers of $x$, up to and including the term in $x^{2}$. [4] (c) State the set of values of x for whic…