Area with Inequality Constraints

Find or identify the area of a region defined by one or more inequalities involving curves and lines.

2 questions · Easy -1.3

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OCR H240/01 2022 June Q3
7 marks Moderate -0.8
3
  1. In this question you must show detailed reasoning.
    Find the coordinates of the points of intersection of the curves with equations \(y = x ^ { 2 } - 2 x + 1\) and \(y = - x ^ { 2 } + 6 x - 5\).
  2. The diagram shows the curves \(y = x ^ { 2 } - 2 x + 1\) and \(y = - x ^ { 2 } + 6 x - 5\). This diagram is repeated in the Printed Answer Booklet. \includegraphics[max width=\textwidth, alt={}, center]{38b515c2-4764-4b51-a1f5-9b48d46610f0-5_377_542_603_322} On the diagram in the Printed Answer Booklet, draw the line \(y = 2 x - 2\).
  3. Show on your diagram in the Printed Answer Booklet the region of the \(x - y\) plane within which all three of the following inequalities are satisfied. \(y \geqslant x ^ { 2 } - 2 x + 1 \quad y \leqslant - x ^ { 2 } + 6 x - 5 \quad y \leqslant 2 x - 2\) You should indicate the region for which all the inequalities hold by labelling the region \(R\).[1]
AQA Paper 3 2022 June Q2
1 marks Easy -1.8
The shaded region, shown in the diagram below, is defined by $$x^2 - 7x + 7 \leq y \leq 7 - 2x$$ \includegraphics{figure_2} Identify which of the following gives the area of the shaded region. Tick (\(\checkmark\)) one box. [1 mark] \(\int (7 - 2x) \, dx - \int (x^2 - 7x + 7) \, dx\) \(\int_0^5 (x^2 - 5x) \, dx\) \(\int_0^5 (5x - x^2) \, dx\) \(\int_0^5 (x^2 - 9x + 14) \, dx\)