Mathematics · Oct / Nov 2023 · Paper 42 · Question 5

20 [2]

M1 for 11x = 10(x + 2) oe

95 147 + = 12 + y y 2 + + = + 95( y 2) 147 y 12 ( y y 2) oe leading to 6y2 – 109y – 95 = 0 [5]

M2 M1 for 95 147 or + y y 2 M1 Allow correct or for clearing their equation with algebraic fractions in y and y + 2 + + = 2 + Allow 95 y 190 147 y 12 y 24 y oe A1 With all brackets shown expanded and no errors or omissions

(6y + 5)(y – 19) [2]

B1 for (6y + a)(y + b) with ab = –95 or a + 6b = –109 or (3y + a) (2y + b) with ab = –95 or 2a + 3b = –109 or for partial factorisation y(6y + 5) – 19(6y + 5) or 6y(y – 19) + 5(y – 19)

19 [1]

Correct or FT their positive answer from factors dep on B1 earned