4MA0 Foundation June 2013 Paper 1 Q12

EdexcelFoundationOld spec7 marksSolving Simple Equations Substitution

Shape made from a right-angled triangle with sides 3x, 4x and 5x joined to a rectangle 4x by y

Diagram NOT accurately drawn

The shape in the diagram is made from a rectangle and a right-angled triangle.
The diagram shows, in terms of \(x\) and \(y\), the lengths, in centimetres, of the sides of the rectangle and of the triangle.

The perimeter, \(P\) cm, of the shape is given by the formula

\[P = 12x + 2y\]

(a) Work out the value of \(P\) when \(x = 3\) and \(y = 7\) (2)

(b) Work out the value of \(x\) when \(P = 43\) and \(y = 6.5\) (3)

(c) Find, in terms of \(x\) and \(y\), a formula for the area, \(A\) cm², of the shape.
Give your answer as simply as possible. (2)

Scheme	Marks
\(12 \times 3 + 2 \times 7 = 36 + 14\)	M1
50	A1
	(2)

Mark scheme (b)

Scheme	Marks
\(43 = 12x + 2 \times 6.5\) or \(43 = 12x + 13\) or \(P - 2y = 12x\) (oe with \(\pm 12x\) or \(\pm x\) as the subject)	M1
\(12x = 43 - 13\) or \(12x = 30\) or \(-12x = 13 - 43\) or \(-12x = -30\)	M1
2.5 oe	A1
	(3)

Notes

M1: for correct rearrangement of original equation or substitution
M2 for \(43 - 2 \times 6.5\;(= 12x)\) or \(30\;(= 12x)\)

M1: for correct rearrangement and substitution

A1: Correct answer scores full marks

Mark scheme (c)

Scheme	Marks
\(4xy + \frac{1}{2} \times 3x \times 4x\) or \(\dfrac{3x + y + y}{2} \times 4x\)	M1
\(4xy + 6x^2\) etc	A1
	(2)

Notes

M1: for any one correct area eg. \(4xy\) oe or \(\frac{1}{2} \times 3x \times 4x\) oe or \(4x(3x + y)\)

A1: for \(4xy + 6x^2\) or \(4yx + 6x^2\) or \(2x(3x + 2y)\) or \(2(3x^2 + 2xy)\)
(No fractions or uncollected terms but could be multiplication signs and/or brackets present)