Moderate -0.3 This is a straightforward integration problem requiring students to integrate f'(x) to find f(x), apply the constant of integration using one point, then use the second point to find k. It involves standard techniques (integrating polynomials) with no conceptual challenges, making it slightly easier than average but still requiring multiple steps for the 5 marks.
A curve with equation \(y = f(x)\) passes through the points \((0, 2)\) and \((3, -1)\). It is given that \(f'(x) = kx^2 - 2x\), where \(k\) is a constant. Find the value of \(k\). [5]
Question 2:
2 | y= 1 kx3 −x2 (+c )
3 | M1A1 | Attempt integration for M mark
Sub (0, 2) | DM1 | Dep on c present. Expect c = 2
Sub (3, ‒1) → −1=9k−9+theirc | DM1
k = 2/3 | A1
5
Question | Answer | Marks | Guidance
A curve with equation $y = f(x)$ passes through the points $(0, 2)$ and $(3, -1)$. It is given that $f'(x) = kx^2 - 2x$, where $k$ is a constant. Find the value of $k$. [5]
\hfill \mbox{\textit{CAIE P1 2019 Q2 [5]}}