Mathematics · May / June 2023 · Paper 42 · Question 9

27x6y12 final answer [2]

B1 for two terms correct in answer e.g. 27x6yk or 27xky12 or kx6y12 or for correct answer seen then spoilt

24 12 x y final answer 64 [3]

B2 for final answer with two correct elements 64− 1 64 or final answer or or − − x 24 y 12 x 24 y 12 better or for correct answer seen

or B1 for 64 or x24 or y12 seen in final answer k or final answer − − x 24 y 12

or M1 for first correct step seen 3 [ ] − 3 x y 16 8 2 4 eg or or 16 8 4 x y − 1 4096 2 48 24 x y

(x + 3)(x – 3) final answer [1]

+ x 3 final answer + 2 y 5 [3]

M2 for (x – 3)(2y + 5)

or M1 for 2y(x – 3) + 5(x – 3) or x (2y + 5) – 3( 2y + 5)

5x2 + 4x – 20 [= 0] oe or 5y2 – 78y + 221 [= 0] oe () −± 2 − − 4 4 4(5)( 20) oe 2(5) or 2 4 4 − ± 4 + oe 10 10 x = 1.64 y = 3.72 and x = – 2.44 y = 11.88 [9]

M2 M1 for 7 – 2x = 5x2 + 2x – 13 oe seen − 2 − 7 y 7 y = + − or y 5 2 13 oe seen 2 2 M2 FT their 3-term quadratic 2 − −

or M1 for (4)

4(5)( 20) or better −+ −− or for 4 q or 4 q × × 2 5 2 5 2 4 + or for x oe 10

B2 B1 for one correct pair or both x-values correct or both y – values correct