| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Linear simultaneous equations |
| Difficulty | Easy -1.3 This is a straightforward linear simultaneous equations question requiring students to form two simple expressions and solve by equating them. The context is accessible, the algebra is basic (single-step rearrangement), and it's a standard textbook-style problem with no conceptual challenges beyond translating words to algebra. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02z Models in context: use functions in modelling |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((C =)\ 4000 + 4m\) | B1 | Correct equation/expression for \(A\); or \(40 + 0.04m\) |
| \((C =)\ 6(m - 100)\) | B1 | Correct equation/expression for \(B\); or \(0.06(m-100)\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(4000 + 4m = 6(m - 100)\) | M1 | Attempt to solve simultaneously, from two linear equations in \(m\); at least one equation must have constant term |
| \(2m = 4600\) | Could be implied by final answer of 38hrs 20 mins | |
| \(m = 2300\) | A1 | Obtain 2300 (minutes); isw once 2300 seen |
# Question 2:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(C =)\ 4000 + 4m$ | B1 | Correct equation/expression for $A$; or $40 + 0.04m$ |
| $(C =)\ 6(m - 100)$ | B1 | Correct equation/expression for $B$; or $0.06(m-100)$ |
**B1B0** if units inconsistent in two equations; **SC B1** for both $44 + 0.04m$ and $0.06m$ (or $4400 + 4m$ and $6m$) – from using $m = 0$ at 100 minutes
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4000 + 4m = 6(m - 100)$ | M1 | Attempt to solve simultaneously, from two linear equations in $m$; at least one equation must have constant term |
| $2m = 4600$ | | Could be implied by final answer of 38hrs 20 mins |
| $m = 2300$ | A1 | Obtain 2300 (minutes); isw once 2300 seen |
---2 Alex is comparing the cost of mobile phone contracts. Contract $\boldsymbol { A }$ has a set-up cost of $\pounds 40$ and then costs 4 p per minute. Contract $\boldsymbol { B }$ has no set-up cost, does not charge for the first 100 minutes and then costs 6 p per minute.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for the cost of each of the contracts in terms of $m$, where $m$ is the number of minutes for which the phone is used and $m > 100$.
\item Hence find the value of $m$ for which both contracts would cost the same.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2021 Q2 [4]}}