Mathematics · Oct / Nov 2021 · Paper 41 · Question 4

10 3 or 1 33 or 3.33[3…] [3]

M1 for 42 – 12x = 3x – 8 oe or for 7 – 2x = 3 x − 8 oe 6 6

M1 for reaching ax = b correctly FT their first step

1 5 –2.5 or − 2 2 or − 2 [3]

M1 for 3 × 2x = 2(x – 5) oe

M1 for reaching ax = b correctly FT their first step

2(x + 12y)(x – 12y) final answer [3]

B2 for (2x + 24y)(x – 12y) or (2x – 24y)(x + 12y) or for 2(x + 12y)(x – 12y) seen OR

M2 for k(x + 12y)(x – 12y)

or M1 for 2(x2 – 144y2)

(5x – 8) (x + 5) final answer [2]

M1 for 5x(x + 5) – 8(x + 5) or x (5x – 8)+ 5(5x – 8) or for (5x + a)(x + b) where ab = – 40 or a + 5b = 17

4x2 – 17x + 9 [= 0] oe 2 [ −− ]17 ± ( [ ]17 − ) − 4 4 ( )( ) 9 2 × 4 0.62 and 3.63 cao [8]

B1 B2 FT their 3 term quadratic 2 B1FT for ( [ ]17 − ) − 4 4) 9 ( ( ) ) or better 2 2 ( ) 17 [ ] − 17 − 4 4 ( )( ) 9 or x − oe or 8 4 or better and B1FT for [ −− ]17 + q or 2(4) [ −− ]17 − q or better 2(4) or 17 145 oe or 17 145 + − oe or 8 64 8 64 [ −− ]17 [ −− ]17 + q − q 2 2 or 4 4

B2 B1 for each

SC1 for 0.6[0] or 0.619 to 0.620 and 3.6[0] or 3.6301 to 3.6302 or 0.62 and 3.63 seen in working or –0.62 and–3.63 as final answers