Foundation June 2017 Paper 2 Q10

10 A square is divided into three rectangles, A, B and C.

Not to scale

Rectangle A has length \(n\) cm and a width of 2 cm.
Rectangle C has length 4 cm.

(a)

(i) Write down an algebraic expression for the width of rectangle C. [1]

(ii) Write down an algebraic expression for the area of rectangle A. [1]

(b) The three rectangles all have the same area.

Work out the value of \(n\). [3]

Mark scheme (a)

Answer	Marks	Part marks and guidance
(i) \(4 - n\) final answer	1		Accept eg \(4 - x\) Ignore \(C =\) or \(w =\) etc Ignore any units given in all parts
(ii) \(2n\) final answer	1		Accept \(n2\), \(2 \times n\), \(n \times 2\) Condone \(4(4 - n)\) Ignore \(A =\) etc

Mark scheme (b)

Answer	Marks	Part marks and guidance
\(\dfrac{16}{6}\) or \(\dfrac{8}{3}\) or \(2\dfrac{4}{6}\) or \(2\dfrac{2}{3}\) or 2.6[6…] or 2.7	3	M1 for \(4(4 - n)\) oe or \(4 \times 4 \div 3\) or better And M1 for their \(4(4 - n) = 2n\) or better or \(2n = \dfrac{16}{3}\) oe or \(4(4 - n) = \dfrac{16}{3}\) oe	Isw Accept eg \(5\dfrac{1}{3}\) or 5.33[…] for \(\dfrac{16}{3}\) M1M1 implied by eg \(5.33 \div 2\)