| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Express log in terms of given variables |
| Difficulty | Moderate -0.8 This is a straightforward C2 logarithm question requiring basic manipulation of log laws (recognizing 16 = 2^4 and 8 = 2^3) with no problem-solving insight needed. Part (a) is direct application of power law, part (b) adds one extra step using log addition. Easier than average A-level questions. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.06f Laws of logarithms: addition, subtraction, power rules |
\begin{enumerate}
\item Given that $p = \log _ { q } 16$, express in terms of $p$,\\
(a) $\log _ { q } 2$,\\
(b) $\log _ { q } ( 8 q )$.\\[0pt]
[P2 January 2002 Question 2]
\item $\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + c$, where $c$ is a constant.
\end{enumerate}
Given that $\mathrm { f } ( 4 ) = 0$,\\
(a) find the value of $c$,\\
(b) factorise $\mathrm { f } ( x )$ as the product of a linear factor and a quadratic factor.\\
(c) Hence show that, apart from $x = 4$, there are no real values of $x$ for which $\mathrm { f } ( x ) = 0$.\\
\hfill \mbox{\textit{Edexcel C2 Q1 [6]}}