| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2016 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Rational exponential equation |
| Difficulty | Moderate -0.3 This is a straightforward algebraic manipulation question requiring substitution (let u = 2^y to get a quadratic) followed by routine logarithm application. While it requires multiple steps, the techniques are standard and the path is clear once the substitution is recognized, making it slightly easier than average. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use \(4^y = 2^{2y}\) | B1 | |
| Attempt solution of quadratic equation in \(2^y\) | M1 | |
| Obtain finally \(2^y = 7\) only | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Apply logarithms to solve equation of form \(2^y = k\) where \(k > 0\) | M1 | Must be using their positive answer for (i) |
| Obtain \(2.81\) | A1 |
## Question 2(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use $4^y = 2^{2y}$ | B1 | |
| Attempt solution of quadratic equation in $2^y$ | M1 | |
| Obtain finally $2^y = 7$ only | A1 | |
## Question 2(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Apply logarithms to solve equation of form $2^y = k$ where $k > 0$ | M1 | Must be using their positive answer for (i) |
| Obtain $2.81$ | A1 | |
---2 (i) Given that $\frac { 1 + 4 ^ { y } } { 3 + 2 ^ { y } } = 5$, find the value of $2 ^ { y }$.\\
(ii) Use logarithms to find the value of $y$ correct to 3 significant figures.
\hfill \mbox{\textit{CAIE P2 2016 Q2 [5]}}