Mathematics A, Further H235: Sequences and Series Topical Past Paper Questions

In a long-running biochemical experiment, an initial amount of 1200 mg of an enzyme is placed into a mixture. The model for the amount of enzyme present in the mixture suggests that, at the end of each hour, one-eighth of the amount of enzyme that was present at the start of that…

When $ 10^{6} $ of a certain type of bacteria are detected in a blood sample of an infected animal, a course of treatment is started. The long-term aim of the treatment is to reduce the number of bacteria in such a sample to under 10000. At this level the animal's immune system c…

A sequence $\{u_n\}$ is defined by the recurrence system $u_1 = 1$ and $u_{n+1} = a - \frac{a^2}{2u_n}$ for $n \geq 1$, where $a$ is a positive constant. Determine with justification the behaviour of the sequence for all possible values of $a$. [7]