SPS SPS SM 2021 January — Question 5 8 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2021
SessionJanuary
Marks8
TopicSimultaneous equations
TypeLine intersecting quadratic curve
DifficultyModerate -0.8 This is a straightforward simultaneous equations question requiring substitution to find intersection points, then sketching both graphs with axis intercepts. The algebra is routine (solving a quadratic), and the sketching requires only standard techniques with no geometric insight. Easier than average A-level content.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02n Sketch curves: simple equations including polynomials1.03a Straight lines: equation forms y=mx+c, ax+by+c=0

5. A curve \(C\) and a straight line \(L\) have respective equations $$y = x ^ { 2 } - 4 x - 5 \text { and } y = 2 x - 14$$ a) Find the coordinates of any points of intersection between \(C\) and \(L\).
b) Sketch in the same diagram the graph of \(C\) and the graph of \(L\). The sketch must include of any points of intersection between the graph of \(C\) and the coordinate axes, and any points of intersection between the graph of \(L\) and the coordinate axes.

5.

A curve $C$ and a straight line $L$ have respective equations

$$y = x ^ { 2 } - 4 x - 5 \text { and } y = 2 x - 14$$

a) Find the coordinates of any points of intersection between $C$ and $L$.\\
b) Sketch in the same diagram the graph of $C$ and the graph of $L$.

The sketch must include of any points of intersection between the graph of $C$ and the coordinate axes, and any points of intersection between the graph of $L$ and the coordinate axes.\\

\hfill \mbox{\textit{SPS SPS SM 2021 Q5 [8]}}