Mathematics · May / June 2022 · Paper 41 · Question 9

[ ] − − = x 2 x 30 0 ( )( ) − + x 6 x 5 oe = x 6 cao 12 or 2 × their x evaluated = or k 2 x stated [8]

B3 M1 for + − − = (2 x 1)( x 1) x 2 29 oe (2 x + 1)( x − 1) = 2 x 2 − 2 x + x − 1

B1 for oe soi M1 or correct factors for their 3 term quadratic equation or for correct substitution into quadratic formula or correctly completing the square for their 3 term quadratic equation B1 B1 FT

( ) 3 y + 1 − y 3 = 5 oe ( ) + 3 = 3 + 2 + + y 1 y 3 y 3 y 1 soi Completion to 3y2 + 3y – 4 = 0 [5]

M1 B2 B1 for ( ) + 2 = 2 + + + y 1 y y y 1 oe soi A1 With no errors or omissions

−± − − 3 3 2 4(3)( 4) × 2 3 0.44 [6]

B2 or B1 for − − 3 2 4(3)( 4) or for 3 −+ ... or 3 −− ... × × 2 3 2 3

B2 B1 for 0.758 or 0.7583...