Foundation June 2018 Paper 1 Q31

AQACurrent spec4 marks2D Area & Perimeter

31 A large rectangle is made by joining three identical small rectangles as shown.

A large rectangle made of two small rectangles stacked on the left and one small rectangle standing upright on the right

Not drawn accurately

The perimeter of one small rectangle is 15 cm

Work out the perimeter of the large rectangle. [4 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1 – width of small rectangle is \(x\) (any letter)
\(x\) and \(2x\) or \(x + 2x + x + 2x\) or \(6x\)	M1	oe
\(x + 2x + x + 2x = 15\) or \(6x = 15\)	M1dep	oe
\((x =)\) 2.5	A1	from correct working or with 5 as the other dimension or with 7.5 as the length of the large rectangle
25	A1ft	ft \(10 \times\) their 2.5 with M1M1 awarded
Alternative method 2 – length of small rectangle is \(x\) (any letter)
\(x\) and \(\dfrac{x}{2}\) or \(x + \dfrac{x}{2} + x + \dfrac{x}{2}\) or \(3x\)	M1	oe
\(x + \dfrac{x}{2} + x + \dfrac{x}{2} = 15\) or \(3x = 15\)	M1dep	oe
\((x =)\) 5	A1	from correct working or with 2.5 as the other dimension or with 7.5 as the length of the large rectangle
25	A1ft	ft \(5 \times\) their 5 with M1M1 awarded
Alternative method 3 – \(a\) = width of small rectangle and \(b\) = length of small rectangle (any letters)
\(b = 2a\) or \(10a\) or \(5b\)	M1	correct expression for perimeter of the large rectangle in one variable
\(6a = 15\) or \(3b = 15\)	M1dep	correct equation in one variable
\((a =)\) 2.5 or \((b =)\) 5	A1	from correct working or with both values correct or with one value correct and 7.5 as the length of the large rectangle
25	A1ft	ft \(10 \times\) their \(a\) or \(5 \times\) their \(b\) with M1M1 awarded
Alternative method 4 – trial and improvement using ratio of sides
length \(= 2 \times\) width seen or implied	M1
Two correctly evaluated trials for perimeter of small rectangle with length \(= 2 \times\) width	M1dep	eg \(8 + 4 + 8 + 4 = 24\) and \(10 + 5 + 10 + 5 = 30\)
2.5 and 5	A1	implied by \(2.5 + 5 + 2.5 + 5 = 15\)
25	A1

Additional guidance

Note that there is no ft in method 4
In all methods, marks can be awarded for annotation of the diagram, with lengths clearly identified, or working inside or alongside the diagram
eg 2.5 and 5 marked correctly as the dimensions of the small rectangle	M1M1A1
2.5 marked as the width of the small rectangle and 7.5 marked as the length of the large rectangle	M1M1A1
If full marks not awarded, mark both the diagram and working then award the better mark
In alt 4, one or more trials may be crossed out to indicate that they do not give the correct perimeter. Do not treat this as the usual crossed out work not to be marked if replaced.