| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2010 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Applied rate of change |
| Difficulty | Easy -1.2 This is a straightforward application of the chain rule to differentiate a simple composite function (square root of a linear expression), followed by direct substitution. It requires only basic differentiation technique with no problem-solving or conceptual insight, making it easier than average for A-level. |
| Spec | 1.07b Gradient as rate of change: dy/dx notation1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((k(2t-1)^{-1/2}\) | M1 | \(k \neq 1\) |
| \(0.7(2t-1)^{-1/2}\) | A1 | oe |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Sub \(t=5\) into their derivative | M1 | |
| \(0.23(3)\) | A1 | Ignore units |
## Question 3:
**Part (i)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(k(2t-1)^{-1/2}$ | M1 | $k \neq 1$ |
| $0.7(2t-1)^{-1/2}$ | A1 | oe |
**Part (ii)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| Sub $t=5$ into their derivative | M1 | |
| $0.23(3)$ | A1 | Ignore units |
---3 The length, $x$ metres, of a Green Anaconda snake which is $t$ years old is given approximately by the formula
$$x = 0.7 \sqrt { } ( 2 t - 1 ) ,$$
where $1 \leqslant t \leqslant 10$. Using this formula, find\\
(i) $\frac { \mathrm { d } x } { \mathrm {~d} t }$,\\
(ii) the rate of growth of a Green Anaconda snake which is 5 years old.
\hfill \mbox{\textit{CAIE P1 2010 Q3 [4]}}