Mathematics · Oct / Nov 2022 · Paper 41 · Question 9

( ) ( )[ ] x 3 x + 4 + 2 x − 1 = 20 Leading to 3 x 2 + 6 x − 22 = 0 with no errors or omissions [3]

M1 Correct expression with brackets unexpanded A1 Must see equated to 20 and brackets expanded first to award A1

−± 6 6 2 − 4(3)( 22) − oe 2.3 22 or for = −± 1 1 + oe 3 –3.887 and 1.887 cao [6]

B2 −+ − 6 or k or 2 − −

B1 for 6 4(3)( 22) or 2.3 ( ) 2 x + 1 = k oe

B2 B1 for one correct answer or for answers –3.89 or – 3.88 or -3.886 or –3.8868 to –3.8867 and 1.88 or 1.89 or 1.886 or 1.8867 to 1.8868 or correct answers seen in working or –1.887 and 3.887 answers

5.77 or 5.773 to 5.774 [1]

FTdep 2(positive x +1) evaluated to 3 sig. fig. or more, dep on x > 1

[ ] y 2 + 3 y − 40 = 0 oe + − ( y 8)( y 5) [= 0] oe 5 [14]

B4 Oe 3 term quadratic

M3 for 15 y − 20( y − 2) = y y ( − 2) oe

Or M2 for 15 20 2 − = 1 oe y − y

Or M1 for H(y – 2) = 15 or hy = 20 soi B2 Strict FT a three term quadratic B1FT for ( )( ) + + y a y b where ab = – 40 or a + b = 3 or y(y – 5) + 8 (y – 5) or y( ) ( ) y + 8 − 5 y + 8 B1