CAIE P2 2016 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferentiating Transcendental Functions
TypeFind gradient at a point - direct evaluation
DifficultyEasy -1.2 This is a straightforward differentiation and substitution question requiring only direct application of standard rules (exponential and logarithmic derivatives with chain rule) followed by evaluation at a given point. It's below average difficulty as it involves routine recall with minimal problem-solving—simpler than a typical multi-part question but requires more than just basic index laws.
Spec1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07l Derivative of ln(x): and related functions

1 Find the gradient of the curve $$y = 3 e ^ { 4 x } - 6 \ln ( 2 x + 3 )$$ at the point for which \(x = 0\).

AnswerMarks Guidance
Obtain first derivative of form \(k_1e^{4x} + \frac{k_2}{2x+3}\)M1
Obtain correct \(12e^{4x} - \frac{12}{2x+3}\)A1
Obtain 8A1 [3]
Obtain first derivative of form $k_1e^{4x} + \frac{k_2}{2x+3}$ | M1 |
Obtain correct $12e^{4x} - \frac{12}{2x+3}$ | A1 |
Obtain 8 | A1 | [3]
1 Find the gradient of the curve

$$y = 3 e ^ { 4 x } - 6 \ln ( 2 x + 3 )$$

at the point for which $x = 0$.

\hfill \mbox{\textit{CAIE P2 2016 Q1 [3]}}