(c) Hence, sketch the graph of \(y = 8x^2 - 18\) on the axes below. Mark clearly the coordinates of any point where this graph crosses an axis. [2]
Mark scheme (a)
Scheme
Marks
Comments
\(2(2x + 3)(2x - 3)\)
B3
Award B3−1 for a correct answer followed by further incorrect work.
Award B2 for the sight of any one of the following:
\((4x + 6)(2x - 3)\)
\((4x - 6)(2x + 3)\)
\(8(x + 3/2)(x - 3/2)\)
\((2x + 3)(2x - 3)\)
\(2(2x + 3)(2x + 3)\)
\(2(2x - 3)(2x - 3)\)
Award B1 for the sight of any one of the following:
\(2(4x^2 - 9)\)
\(8(x^2 - 9/4)\)
\((4x + 6)(2x + 3)\)
\((4x - 6)(2x - 3)\)
\((x + 3/2)(x - 3/2)\)
If no marks: Allow SC2 for \((2\sqrt{2}x + 3\sqrt{2})(2\sqrt{2}x - 3\sqrt{2})\) o.e. OR other valid, equivalent ‘factorisation’, e.g. \((8x - 12)(x + 1.5)\) o.e. Allow SC1 for \((\sqrt{8}x + \sqrt{18})(\sqrt{8}x - \sqrt{18})\) o.e.
Mark scheme (b)
Scheme
Marks
Comments
3/2 AND -3/2
B1
Or equivalent for either root. FT if possible, provided exactly 2 possible distinct solutions.
Corrected by Westie's Workshop
The board's mark scheme printed “Or equivalent for either roots.”. Changed to “Or equivalent for either root.” because “either” goes with a single root.
Original: see the board's mark scheme PDF (link above).
Mark scheme (c)
Scheme
Marks
Comments
A positive quadratic curve passing through (0,-18) as a minimum with -18 indicated on the y-axis AND passing through (–3/2,0) and (3/2,0) which are indicated on the x-axis.
B2
FT for x-axis intersections, provided exactly 2 possible distinct solutions.
Award B1 for any one of the following: A positive quadratic curve passing through (0, –18) as a minimum with –18 indicated on the y-axis OR A quadratic curve (either positive or negative) passing through (–3/2,0) and (3/2,0) which are indicated on the x-axis.
If the conditions for B2 are met, then only allow B1 for concave and/or convex curvature above the x-axis.
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