Mathematics · Oct / Nov 2021 · Paper 42 · Question 8

12 x or 12 ÷ x final answer [1]

12 – their 12 x = 1.5oe x − 4 12x – 12(x – 4) = 1.5x(x – 4) or − − 12 x 12( x 4) [= 1.5] x x ( − 4) 12x – 12x + 48 = 1.5x2 – 6x [1.5x2 – 6x – 48 = 0 ] x2 – 4x – 32=0 [8]

M1 Accept 3 or more term equivalents M1 Correctly clearing fractions, or correctly collecting into a ‘single fraction’ FT their expression dep on two fractions both with algebraic denominators M1 Correctly multiplying their two sets of brackets FT their expression dep on two fractions both with algebraic denominators or first M1 given A1 One further step either 3 term equation or division throughout by 1.5 leading to solution With no errors or omissions seen, dep on M3

(x + 4)(x – 8) –4 and 8 [4]

M2 M1 for (x + a)(x + b) where ab = –32 or a + b = –4 or for x(x + 4) – 8(x + 4) or x(x – 8) + 4(x – 8) B1

3 [2]

FT 12 their 8 − 4 12 12

M1 for or + 1.5 oe − their 8 4 their 8 12 or for answer their 8

69.6 [3]

M2 for 430 to 440 or 440 5 − oe 6 + 0.25 6 to 6.5

or M1 for 440 + 5 oe or 440 – 5 oe or 6 + 0.25 oe or 6 – 0.25 oe seen