P1 or or or using a ratio approach eg (:) = : 1 = 1 : 2.5 k A1 cao 20 M1 for substitution of a rearrangement of 3x 13 e.g. (3x + 13)2 + = 25 y = x2 − x= M1 (dep M1) for expansion of bracket substitution (at least 3 terms correct out of the 4 terms) e.g. y= 9x2 +39x + 39x +169 M1 for forming quadratic ready for solving e.g. 10x2 + 78x + 144 (= 0) = x −3, M1 for factorising e.g. (5x + 24)(x + 3) (= 0) oe = 4 y = , = and = = 4 x y x y −3, A1 SC: B1 (if M0) for all 4 values mis-associated or one correct pair of values or values given as coordinates. 1MA1/1H Question Working Answer Mark Notes 21 C1 states (angle) = (angle) ABC BCD C1 states 2nd link = AB CD C1 states 3rd link with reason: = (common) BC BC C1 concludes proof by stating (triangle) (triangle) with reason SAS and = ABC DCB AC BD ≡ 22 Proof B1 (indep) for stating cos 30 = M1 for = 102 + 102 2 × 10 × 10 × cos or = + 2 × × × cos 30 (=x2(2−√3) ) PQ2 PBQ AC2 x2 x2 x x – – oe M1 for cos (implies previous M1) PBQ = for cos PBQ = cos PBQ= M1 = A1 conclusion of proof with all working seen
P1 or or or using a ratio approach eg (:) = k : 1 = 1 : 2.5 A1 cao 20 x= M1 for substitution of a rearrangement of y − 3x = 13 e.g. (3x + 13)2 + x2 = 25 y= M1 (dep M1) for expansion of bracket substitution (at least 3 terms correct out of the 4 terms) e.g. 9x2 +39x + 39x +169 x = −3, M1 for forming quadratic ready for solving e.g. 10x2 + 78x + 144 (= 0) y = 4 M1 for factorising e.g. (5x + 24)(x + 3) (= 0) oe A1 x = , y = and x = −3, y = 4 SC: B1 (if M0) for all 4 values mis-associated or one correct pair of values or values given as coordinates. 1MA1/1H Question Working Answer Mark Notes 21 C1 states (angle) ABC = (angle) BCD C1 states 2nd link AB = CD C1 states 3rd link with reason: BC = BC (common) C1 concludes proof by stating (triangle) ABC ≡ (triangle) DCB with reason SAS and AC = BD 22 Proof B1 (indep) for stating cos 30 = M1 for PQ2 = 102 + 102 – 2 × 10 × 10 × cos PBQ or AC2 = x2 + x2 – 2 × x × x × cos 30 (=x2(2−√3) ) oe M1 for cos PBQ = (implies previous M1) cos PBQ= = M1 for cos PBQ = A1 conclusion of proof with all working seen
1ma1_1h_-_may_2017_mark_scheme.docx