| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | log(y) vs x: convert and interpret |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question on logarithms and exponentials requiring standard techniques: substitution into a linear equation, applying log laws (log y^4 = 4log y), and converting between logarithmic and exponential form. All parts are routine manipulations with no problem-solving insight required, making it slightly easier than average but not trivial due to the multiple steps and potential for algebraic errors. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06d Natural logarithm: ln(x) function and properties1.06f Laws of logarithms: addition, subtraction, power rules |
9 You are given that $\log _ { 10 } y = 3 x + 2$.\\
(i) Find the value of $x$ when $y = 500$, giving your answer correct to 2 decimal places.\\
(ii) Find the value of $y$ when $x = - 1$.\\
(iii) Express $\log _ { 10 } \left( y ^ { 4 } \right)$ in terms of $x$.\\
(iv) Find an expression for $y$ in terms of $x$.
Section B (36 marks)
\hfill \mbox{\textit{OCR MEI C2 2008 Q9 [4]}}