| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 1 (Further AS Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Solve f(x) > g(x) using sketch |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question involving sketching a rational function and solving an inequality graphically. Finding asymptotes of a simple rational function is routine, drawing a linear function is trivial, and reading off the solution from the sketch requires minimal problem-solving. While it's Further Maths content, the techniques are standard and mechanical, making it slightly easier than an average A-level question overall. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| States \(x = \frac{5}{3}\) or \(y = \frac{2}{3}\) | M1 (2.2a) | — |
| States \(x = \frac{5}{3}\) and \(y = \frac{2}{3}\) with no incorrect equations seen | A1 (2.2a) | — |
| Answer | Marks | Guidance |
|---|---|---|
| Draws a straight line with negative gradient passing through \((0,2)\); accept freehand if intention is clear | M1 (1.1a) | — |
| Draws a straight line passing through \((0,2)\) and \((5,0)\) | A1 (1.1b) | — |
| Answer | Marks | Guidance |
|---|---|---|
| Deduces one of the ranges \(x \leq 0\) or \(\frac{5}{3} < x \leq 5\); condone \(\frac{5}{3} \leq x \leq 5\) or \(\frac{5}{3} < x < 5\) for this mark only; ignore any incorrect ranges | M1 (2.2a) | — |
| Deduces the solution \(x \leq 0\) , \(\frac{5}{3} < x \leq 5\) | A1 (2.2a) | — |
## Question 10(a):
States $x = \frac{5}{3}$ **or** $y = \frac{2}{3}$ | M1 (2.2a) | —
States $x = \frac{5}{3}$ **and** $y = \frac{2}{3}$ with no incorrect equations seen | A1 (2.2a) | —
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## Question 10(b)(i):
Draws a straight line with negative gradient passing through $(0,2)$; accept freehand if intention is clear | M1 (1.1a) | —
Draws a straight line passing through $(0,2)$ and $(5,0)$ | A1 (1.1b) | —
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## Question 10(b)(ii):
Deduces one of the ranges $x \leq 0$ **or** $\frac{5}{3} < x \leq 5$; condone $\frac{5}{3} \leq x \leq 5$ or $\frac{5}{3} < x < 5$ for this mark only; ignore any incorrect ranges | M1 (2.2a) | —
Deduces the solution $x \leq 0$ , $\frac{5}{3} < x \leq 5$ | A1 (2.2a) | —
---10
\begin{enumerate}[label=(\alph*)]
\item Write down the equations of the asymptotes of $C$\\
10
\item The line $L$ has equation
$$y = - \frac { 2 } { 5 } x + 2$$
10 (b) (i) Draw the line $L$ on Figure 1
10 (b) (ii) Hence, or otherwise, solve the inequality
$$\frac { 2 x - 10 } { 3 x - 5 } \leq - \frac { 2 } { 5 } x + 2$$
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 1 2024 Q10 [6]}}