| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | October |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Simultaneous equations |
| Type | Linear function from conditions |
| Difficulty | Easy -1.3 This is a straightforward application of forming and solving two simultaneous linear equations from given conditions. Students substitute t=2 and t=7 into H=at+b, then solve the resulting system using basic algebraic manipulation. Part (b) requires only recognizing that t=0 gives the initial height. This is simpler than average A-level content, requiring only routine algebraic skills with no problem-solving insight. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02z Models in context: use functions in modelling |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(1.85 = 2a + b\) | M1 | For either equation |
| \(1.85 = 2a+b\) and \(3.45 = 7a+b\) | A1 | For both equations correct |
| Solves simultaneously to get \(a = 0.32, b = 1.21\) (oe) | dM1 | Solves simultaneously to get a value for \(a\) and \(b\) |
| \(a = 0.32, b = 1.21\) | A1 | Or equivalent fractions. May be seen in the equation |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| States 1.21 m or 121 cm (oe) | B1ft | Correct answer or follow through on their positive \(b\). Accept oe including units |
# Question 2:
## Part (a)
| Working | Mark | Guidance |
|---------|------|----------|
| $1.85 = 2a + b$ | M1 | For either equation |
| $1.85 = 2a+b$ and $3.45 = 7a+b$ | A1 | For both equations correct |
| Solves simultaneously to get $a = 0.32, b = 1.21$ (oe) | dM1 | Solves simultaneously to get a value for $a$ and $b$ |
| $a = 0.32, b = 1.21$ | A1 | Or equivalent fractions. May be seen in the equation |
## Part (b)
| Working | Mark | Guidance |
|---------|------|----------|
| States 1.21 m or 121 cm (oe) | B1ft | Correct answer or follow through on their positive $b$. Accept oe including units |
---2. A tree was planted in the ground.
Exactly 2 years after it was planted, the height of the tree was 1.85 m .
Exactly 7 years after it was planted, the height of the tree was 3.45 m .
Given that the height, $H$ metres, of the tree, $t$ years after it was planted in the ground, can be modelled by the equation
$$H = a t + b$$
where $a$ and $b$ are constants,
\begin{enumerate}[label=(\alph*)]
\item find the value of $a$ and the value of $b$.
\item State, according to the model, the height of the tree when it was planted.\\
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2019 Q2 [5]}}