2D Area & Perimeter: WJEC GCSE Higher November 2022 Unit 2 Q3

Higher November 2022 Unit 2 Q3

3. A rectangle has a width of \(4x - 10\).

(a) Given that \(x\) is a whole number, explain why the value of \(x\) cannot be less than 3. [1]

(b) The perimeter of the rectangle is \(14x - 4\).

Diagram not drawn to scale

Find the length of the rectangle in terms of \(x\). [4]

Mark scheme (a)

Scheme	Marks	Comments
Valid written explanation referring to negative values representing sides e.g. “ (4 × 2 – 10 = -2) you can’t have a negative value for a side” “\(x\) must be greater than 2·5 to have a positive value for the side”	E1	Allow “you can’t have a negative length”. Do not allow calculations only “it can’t be negative” “the value can’t be negative”.

Mark scheme (b)

Scheme	Marks	Comments
\(14x - 4 - 2 \times (4x - 10)\) OR \(14x - 4 - 8x + 20\) or equivalent	M2	May be seen on diagram. Award M1 for intention for a method e.g. \(4x - 10 + 4x - 10 + \mathbf{?} = 14x - 4\) e.g. \(14x - 4 = \mathbf{?} + 2 \times (4x - 10)\) e.g. incorrect use of brackets but a clear attempt at the correct calculation is seen: \(14x - 4 - 8x - 20\).
(sum of both lengths=) \(6x + 16\)	A1	FT from M1: \(14x - 4\) – ‘their \(2 \times [4x - 10]\)’ or equivalent, provided ‘their \(8x - 20\)’ can be expressed in the form \(ax + b\), with a & b ≠ 0. Note: \(14x - 4 - 8x - 20 = 6x - 24\) is awarded M1A1.
(length=) \(3x + 8\)	B1	May be seen on diagram. Mark final answer. FT ‘their \(6x + 16\)’ ÷ 2, provided in the form \(ax + b\), with \(a\) & \(b\) ≠ 0. Unsupported \(3x + 8\) is awarded M2 A1 B1. If no marks awarded, award SC1 for a final answer of: \(3x + c\) (\(c\) ≠ 8) \(kx + 8\) (\(k\) ≠ 3 and positive).

Scheme	Marks	Comments
Sight of an appropriate \(7x - 2\)	B1	May be seen on diagram.
\(7x - 2 - 4x + 10\)	M2	Award M1 for intention for a method e.g. \(4x - 10 + \mathbf{?} = 7x - 2\) \([14x - 4] \div 2 - [4x - 10]\) or equivalent e.g. incorrect use of brackets but a clear attempt at the correct calculation is seen
(length=) \(3x + 8\)	A1	May be seen on diagram. Mark final answer. Allow FT from M1. Unsupported \(3x + 8\) is awarded B1 M2 A1. If no marks awarded, award SC1 for a final answer of: \(3x + c\) (\(c\) ≠ 8) \(kx + 8\) (\(k\) ≠ 3 and positive).