| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Exponential growth/decay model setup |
| Difficulty | Easy -1.2 This is a straightforward proportionality question requiring only the setup of a relationship (x = ky²√z), finding constant k by substitution, then evaluating at new values. It involves basic algebraic manipulation with no problem-solving insight needed—simpler than average A-level questions which typically require multiple techniques or conceptual understanding. |
| Spec | 1.02r Proportional relationships: and their graphs |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x = ky^2\sqrt{z}\) | M1 | Attempt to find value for \(k\); from \(x = ky^2\sqrt{z}\) or \(x = kz^2\sqrt{y}\) only; using sum not product is M0 |
| \(30 = k \times 4 \times 3\), \(k = 2.5\) | ||
| \(x = 2.5y^2\sqrt{z}\) | A1 | Correct equation; ignore modulus sign if used around \(\sqrt{z}\); allow BOD if initial equation stated explicitly, \(k\) found correctly but final equation not seen or seen as now incorrect |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x = 2.5 \times 9 \times 5\) | M1 | Attempt to find \(x\) from equation in terms of \(y\), \(z\) and numerical \(k\); could be from direct proportion |
| \(x = 112.5\) | A1 | Obtain 112.5; or any exact equiv |
# Question 3:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = ky^2\sqrt{z}$ | M1 | Attempt to find value for $k$; from $x = ky^2\sqrt{z}$ or $x = kz^2\sqrt{y}$ only; using sum not product is M0 |
| $30 = k \times 4 \times 3$, $k = 2.5$ | | |
| $x = 2.5y^2\sqrt{z}$ | A1 | Correct equation; ignore modulus sign if used around $\sqrt{z}$; allow BOD if initial equation stated explicitly, $k$ found correctly but final equation not seen or seen as now incorrect |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 2.5 \times 9 \times 5$ | M1 | Attempt to find $x$ from equation in terms of $y$, $z$ and numerical $k$; could be from direct proportion |
| $x = 112.5$ | A1 | Obtain 112.5; or any exact equiv |
---3 It is given that $x$ is proportional to the product of the square of $y$ and the positive square root of $z$. When $y = 2$ and $z = 9 , x = 30$.
\begin{enumerate}[label=(\alph*)]
\item Write an equation for $x$ in terms of $y$ and $z$.
\item Find the value of $x$ when $y = 3$ and $z = 25$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2021 Q3 [4]}}