Drawing & Using Graphs: WJEC GCSE Intermediate November 2020 Unit 1 Q14

Intermediate November 2020 Unit 1 Q14

14. The table below shows some of the values of \(y = x^2 - 4x - 3\) for values of \(x\) from –2 to 5.

\(x\)	−2	–1	0	1	2	3	4	5
\(y = x^2 - 4x - 3\)		2	−3	−6		−6	−3	2

(a) Complete the table by finding the value of \(y\) for \(x = -2\) and the value of \(y\) for \(x = 2\). [2]

(b) On the graph paper below, draw the graph of \(y = x^2 - 4x - 3\) for values of \(x\) from –2 to 5. [2]

(c) Draw the line \(y = 1\) on the graph paper.
Write down the values of \(x\) where the line \(y = 1\) cuts the curve \(y = x^2 - 4x - 3\). [2]

Values of \(x\) are …………………… and ……………………

Mark scheme (a)

Scheme	Marks	Comments
9 −7	B2	B1 for each.

Mark scheme (b)

Scheme	Marks	Comments
At least 6 correct plots and no incorrect plot.	P1	FT ‘their (−2,9)’ and ‘their (2,−7)’ Allow ± ‘½ a small square’.
A smooth curve drawn through their plots.	C1	FT ‘their 8 plots’. OR a curve through the 6 given points and (−2,9) and (2,−7). Allow intention to pass through their plots. (± 1 small square horizontal or vertical.)

Mark scheme (c)

Scheme	Marks	Comments
Line y = 1 drawn	B1	Must be at least 2cm long.
−0·8 AND 4·8	B1	FT intersection of ‘their curve’ with ‘their \(y\) = 1’ only if exactly two points of intersection and y ≠ 0. If curve drawn, but no line drawn, allow a FT from intersection of ‘their curve’ with line \(y\) = 1 only if exactly two points of intersection for B0B1. Allow ± ‘1 small square’.