9. The table shows some of the values of \(y = x^2 - 2x - 3\) for \(-2 \leqslant x \leqslant 4\).
\(x\)
\(-2\)
\(-1\)
0
1
2
3
4
\(y = x^2 - 2x - 3\)
5
0
\(-3\)
\(-3\)
0
5
(a) Complete the table above. [1]
(b) On the graph paper below, draw the graph of \(y = x^2 - 2x - 3\) for \(-2 \leqslant x \leqslant 4\). [2]
(c) Write down the roots of \(x^2 - 2x - 3 = 0\). [1]
(d) Use your graph to solve the simultaneous equations\[\begin{aligned} &y = x^2 - 2x - 3,\\ &y = 1. \end{aligned}\][3]
Mark scheme (a)
Scheme
Marks
Comments
\(-4\)
B1
Mark scheme (b)
Scheme
Marks
Comments
All 7 correct points plotted correctly and joined with a smooth curve
B2
Tolerance ± a small square; FT ‘their points’ and ‘their curve’ for 2 marks provided the curve is reasonably parabolic
B1 for a smooth curve at least through 4 pairs of coordinates or for all of ‘their 7 pairs of coordinates’ plotted correctly
Mark scheme (c)
Scheme
Marks
Comments
\(-1\), 3
B1
Must be exact as values given in the table. Do not award for (\(-1\), 0) and (3, 0)
Mark scheme (d)
Scheme
Marks
Comments
The line \(y = 1\) drawn
B1
Allow for appropriate marks on the curve at \(y = 1\) for at least one intersection
\(x = -1.2\) to \(-1.3\) \(x = 3.2\) to \(3.3\)
B1 B1
FT ‘their curve’ provided there are at least 2 intersections; if their curve has more than 2 intersections with \(y = 1\), they must give all their solutions for B2.
Allow these marks for calculated solutions e.g. \(x = -1.2360…\) and \(x = 3.2360…\)
Award B1 only if both solutions are given as coordinates e.g. (-1.2, 1) and (3.2, 1)
(7)
Corrected by Westie's Workshop
The board's mark scheme printed “(-1,2, 1)”. Changed to “(-1.2, 1)” because the point is \((-1.2,\ 1)\); a comma was printed instead of the decimal point.
Original: see the board's mark scheme PDF (link above).
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