Foundation June 2023 Paper 1 Q16

OCRFoundationCurrent spec4 marksForming Equations Simplifying Basic Expressions

16 The diagram shows a quadrilateral and an equilateral triangle.
The perimeter of the quadrilateral is equal to the perimeter of the equilateral triangle.

Quadrilateral with sides 5x + 4, x + 2, 9x - 5 and 6x + 8, and an equilateral triangle with three equal sides marked

Not to scale

Find an expression for the length of one side of the equilateral triangle.
Give your answer in terms of \(x\) in its simplest form. [4]

Mark scheme

Answer	Marks	Part marks and guidance
\(7x + 3\) final answer	4	M2 for \(21x + 9\) isw or M1 for \(5x + 4 + x + 2 + 9x - 5 + 6x + 8\) M1 for their \((21x + 9) \div 3\)	Must be an algebraic expression in the form \(ax + b\) \(b \ne 0\)