Write inequalities from graph

Edexcel P1 2021 October Q3

6 marks Moderate -0.3

3. (i) Solve
(ii) $$\frac { 3 } { x } > 4$$ Figure 1 shows a sketch of the curve $C$ and the straight line $l$.
The infinite region $R$, shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by $C$ and $l$ only. Given that

$\quad l$ has a gradient of 3
$C$ has equation $y = 2 x ^ { 2 } - 50$
$\quad C$ and $l$ intersect on the negative $x$-axis
use inequalities to define the region $R$.

\begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-06_643_652_575_648} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} Figure 1 shows a sketch of the curve $C$ and the straight line $l$.
The infinite region $R$, shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by $C$ and $l$ only.
Given that

$l$ has a gradient of 3
$C$ has equation $y = 2 x ^ { 2 } - 50$
$C$ and $l$ intersect on the negative $x$-axis
use inequalities to define the region $R$.

Edexcel AS Paper 1 2023 June Q8

5 marks Moderate -0.8

8. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{ce4f8375-0d88-4e48-85de-35f7e90b014d-16_661_855_283_605} \captionsetup{labelformat=empty} \caption{Figure 3}

\end{figure} Figure 3 shows a sketch of a curve $C$ and a straight line $l$.
Given that

$C$ has equation $y = \mathrm { f } ( x )$ where $\mathrm { f } ( x )$ is a quadratic expression in $x$
$C$ cuts the $x$-axis at 0 and 6
$l$ cuts the $y$-axis at 60 and intersects $C$ at the point $( 10,80 )$ use inequalities to define the region $R$ shown shaded in Figure 3.

Edexcel AS Paper 1 Specimen Q12

8 marks Moderate -0.3

12.

[diagram]

Figure 3 shows a sketch of the curve $C$ with equation $y = 3 x - 2 \sqrt { x } , x \geqslant 0$ and the line $l$ with equation $y = 8 x - 16$ The line cuts the curve at point $A$ as shown in Figure 3.

Using algebra, find the $x$ coordinate of point $A$.
[diagram]
The region $R$ is shown unshaded in Figure 4. Identify the inequalities that define $R$.

Edexcel PMT Mocks Q7

5 marks Moderate -0.8

7. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{802e56f7-5cff-491a-b90b-0759a9b35778-09_928_1093_258_497} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} Figure 1 shows a sketch of a curve $C$ with equation $y = \mathrm { f } ( x )$ and a straight line $l$. The curve $C$ meets $l$ at the points $( 2,4 )$ and $( 6,0 )$ as shown. The shaded region $R$, shown shaded in Figure 1, is bounded by $\mathrm { C } , l$ and the $y$-axis. Given that $\mathrm { f } ( x )$ is a quadratic function in $x$, use inequalities to define region $R$.

Edexcel Paper 1 2020 October Q7

5 marks Moderate -0.8

7. \begin{figure}[h]

\includegraphics[alt={},max width=\textwidth]{dc0ac5df-24a7-41b5-8410-f0e9b332ba64-16_868_805_242_632} \captionsetup{labelformat=empty} \caption{Figure 1}

\end{figure} Figure 1 shows a sketch of a curve $C$ with equation $y = \mathrm { f } ( x )$ and a straight line $l$.
The curve $C$ meets $l$ at the points $( - 2,13 )$ and $( 0,25 )$ as shown.
The shaded region $R$ is bounded by $C$ and $l$ as shown in Figure 1.
Given that

$\mathrm { f } ( x )$ is a quadratic function in $x$
( $- 2,13$ ) is the minimum turning point of $y = \mathrm { f } ( x )$ use inequalities to define $R$.

OCR PURE Q2

3 marks Easy -1.2

2 \includegraphics[max width=\textwidth, alt={}, center]{31b0d5b6-1593-489b-bbcd-486e7c96ff18-03_835_545_749_244} The diagram shows the line $y = - 2 x + 4$ and the curve $y = x ^ { 2 } - 4$. The region $R$ is the unshaded region together with its boundaries. Write down the inequalities that define $R$.

OCR MEI Paper 1 2021 November Q3

5 marks Moderate -0.8

3

The diagram shows the line $y = x + 5$ and the curve $y = 8 - 2 x - x ^ { 2 }$. The shaded region is the finite region between the line and the curve. The curved part of the boundary is included in the region but the straight part is not included. Write down the inequalities that define the shaded region. \includegraphics[max width=\textwidth, alt={}, center]{4fac72cb-85cb-48d9-8817-899ef3f80a0f-04_846_716_1379_322} \section*{(b) In this question you must show detailed reasoning.} Solve the inequality $8 - 2 x - x ^ { 2 } > x + 5$ giving your answer in exact form.

AQA AS Paper 2 2022 June Q9

12 marks Standard +0.3

9 The diagram below shows the graphs of $y = x ^ { 2 } - 4 x - 12$ and $y = x + 2$ \includegraphics[max width=\textwidth, alt={}, center]{11168e8f-5ba5-4d27-83ab-0327cc23d08c-10_933_912_358_566} 9

Write down three inequalities which together describe the shaded region.
9
Find the coordinates of the points $A , B$ and $C$.
9
Find the exact area of the shaded region.
Fully justify your answer.
[0pt] [6 marks]

WJEC Unit 1 Specimen Q11

3 marks Moderate -0.8

\includegraphics{figure_11} The diagram shows a sketch of the curve $y = 6 + 4x - x^2$ and the line $y = x + 2$. The point $P$ has coordinates $(a, b)$. Write down the three inequalities involving $a$ and $b$ which are such that the point $P$ will be strictly contained within the shaded area above, if and only if, all three inequalities are satisfied. [3]

SPS SPS SM 2023 October Q3

5 marks Standard +0.8

\includegraphics{figure_3} Figure 3 shows a sketch of a curve $C$ and a straight line $l$. Given that • $C$ has equation $y = f(x)$ where $f(x)$ is a quadratic expression in $x$ • $C$ cuts the $x$-axis at $0$ and $6$ • $l$ cuts the $y$-axis at $60$ and intersects $C$ at the point $(10, 80)$ use inequalities to define the region $R$ shown shaded in Figure 3. [5]