Mathematics · May / June 2023 · Paper 41 · Question 7

( )( ) − + 3 3 y 1 3 y 1 final answer [3]

B2 for ( )( ) or ( )( ) − + − + 9 y 3 3 y 1 3 y 1 9 y 3 or or M1 for ( ) or [...]( )( ) 2 − − + 3 9 y 1 3 y 1 3 y 1 if 0 scored

SC1 for an otherwise correctly completely factorised expression but with fractions within the brackets

( )( ) 2 − + p m k final answer [2]

M1 for ( ) ( ) + − + 2 m k p m k ( ) ( ) − + − or m 2 p k 2 p

1 − oe nfww 2 [11]

− =+ 5 B4 8 x 4 oe nfww − − x 2 8 x 5 =

or B3 for ( 1 or better )( ) − + x 1 x 1 OR 2 − − B2 x 8 x 5

or M1 for ( )( ) ( ) − − − + x 1 x 1 6 x 1 or better B1 ( )( ) − + x 1 x 1 as full denominator or on the right hand side

( ) ( ) ()( ) −− ± − 2 − − 3 3 4 4 2 oe × 2 4 2 3 3 2 ± + or oe 8 8 4 −0.43 and 1.18 final ans cao [6]

M2 M1 for ( ) ()( ) − 2 − − 3 4 4 2 or for ( ) q or ( ) −− + −− − 3 3 q () () 2 4 2 4 2 3 − or for [4]

x 8

B1 for each

A2 SC1 for −0.4 ,–0.42 or −0.425.... and 1.2 or 1.17 or 1.175.... or answers 0.43 and −1.18 or −0.43 and 1.18 seen in working

− 4 m 4 m =− = k k or − 1 pm pm 1 final answer [4]

M1 for clearing fractions

M1 for collecting terms in k

M1 for factorising

M1 for dividing by bracket Maximum 3 marks if answer incorrect