= 2x2 + + + A1 for (m + t(m n t) n)t But + + = m n t x So = 2x2 + A tx But the sides are of length 2x, so = 4x2 A M1 M1 for adding all separate components Then 2x2 + 4x2 tx= and 2x2 tx= 2x t= Squaring each side gives: 5t2 = 4x2 = t2 A1 Whole area = 4x2 A A1 for correct statement of A M1 Hence the middle square, is of t2, A. M1 for substituting (m + + n t) B1 M1 B1 for whole area 4x2 M1 for equating the two equations A1 M1 A1 for equation enabling to be identified t M1 for squaring A1 A1 for correct expression for t2 C1 C1 for clear explanation showing idea C1 C1 for complete clear solution 15
= 2x2 + t(m + n + t) But m + n + t = x So A = 2x2 + tx But the sides are of length 2x, so A = 4x2 Then 2x2 + tx= 4x2 and tx= 2x2 t= 2x Squaring each side gives: 5t2 = 4x2 t2 = Whole area A = 4x2 Hence the middle square, t2, is of A. M1 A1 M1 B1 M1 A1 M1 A1 C1 C1 A1 for (m + n)t M1 for adding all separate components A1 for correct statement of A M1 for substituting (m + n + t) B1 for whole area 4x2 M1 for equating the two equations A1 for equation enabling t to be identified M1 for squaring A1 for correct expression for t2 C1 for clear explanation showing idea C1 for complete clear solution 15
Higher_Skills_Geometry_MarkScheme_Edexcel.docx