Mathematics · Oct / Nov 2023 · Paper 42 · Question 11
0580
As printed in the paper
The question as text
( )x x 1 3 f = - ( ) ( ) x x 1 g 2 = - ( ) , x x x 3 0 h ! =
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Show the answer and mark scheme
11(a)[1]
4 [1]
11(b)[2]
7 – 3x final answer [2]
M1 for 1 – 3(x – 2)
11(c)[2]
−x oe final answer 1 3 [2]
M1 for x = 1 – 3y or y – 1 = –3x or 1 – y y 1 = − = 3x or x 3 3
11(d)[5]
a = 2, b = 5, c = –1 [5]
B4 for two correct values only after correct substitution seen i.e. (1 – 3x – 1)2 – (x – 1)2(1 – 3x) or for correct unsimplified expansion or a correct simplified expansion. OR
M1 for (1 – 3x – 1)2 – (x – 1)2(1 – 3x)
B2 for correct expansion of [–](x – 1)2(1 – 3x) [–]( x2 – x – x + 1 – 3x3 + 3x2 + 3x2 – 3x) or better
or B1 for expansion of one pair of brackets ( x − 1) 2 = x 2 − x − x + 1 or better or [ (x – 1)(1 – 3x) =] – 3x2 + x + 3x – 1
11(e)[3]
− + 2 3 x 3 x final answer x [2]
− − 3
B1 for 3 x (1 3 ) x or better
B1 for common denominator x isw
11(f)[1]
–7 [1]
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