21M.1.SL.TZ2.2

attempt to subtract squares of integers            (M1)

${\left(n+1\right)}^2-n^2$

 

EITHER

correct order of subtraction and correct expansion of ${\left(n+1\right)}^2$, seen anywhere            A1A1

$=n^2+2n+1-n^2 (=2n+1)$

 

OR

correct order of subtraction and correct factorization of difference of squares          A1A1

$=(n+1-n)(n+1+n)(=2n+1)$

 

THEN

$=n+n+1=\text{RHS}$             A1

 

Note: Do not award final A1 unless all previous working is correct.

 

which is the sum of $n$ and $n+1$            AG

 

Note: If expansion and order of subtraction are correct, award full marks for candidates who find the sum of the integers as $2n+1$ and then show that the difference of the squares (subtracted in the correct order) is $2n+1$.

 

[4 marks]

[N/A]