Mathematics · May / June 2022 · Paper 42 · Question 8

1 2 or 0.5 oe [1]

− = + 2

M1 for 10 3 11 p 3 p oe or better

2 k = [ m ] oe final answer − c 2 g [3]

M1 for correctly isolating m terms

M1 for correctly factorising

M1 for dividing by a bracket with two terms to the final answer Maximum mark M2 if final answer incorrect

0 4.5 oe [5]

B4 for 2 − = or 9x – 2x2 [= 0] or better 2 x 9 [ 0] x OR

M2 for ( ) ( ) ( )( ) + + − = − + 2 x 3 4 x 3 x 3 2 x 3 or better

or M1 for ( ) ( ) + + − 2 x 3 4 x 3 seen oe or common denominator ( )( ) − + x 3 2 x 3 oe 2 − + −

B1 for 2 x 6 x 3 x 9 or better seen

− + = y 2 10 y 21[ 0] or − − = x 2 4 x 12[ 0] (y – 3)(y – 7) [= 0] or (x + 2)(x – 6) [= 0] x = − 2 y = 7 x = 6 y = 3 [7]

( )

M2 M1 for + − = y 2 5 12 2 y 39 oe ( ) − 2 12 x + = seen oe or 5 x 39 2 2 M1 or for 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

B2 B1 for x = − 2, x = 6 or for y = 7, y = 3 or for one correct pair of x and y values

3 + 2 − + final answer 2 x x 54 x 72 [3]

B2 correct expansion of three brackets unsimplified or for final answer of correct form with 3 out of 4 terms correct or B1 correct expansion of two brackets with at least three terms out of four correct