Date | May 2021 | Marks available | 4 | Reference code | 21M.1.SL.TZ2.2 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Show that | Question number | 2 | Adapted from | N/A |
Question
Consider two consecutive positive integers, n and n+1.
Show that the difference of their squares is equal to the sum of the two integers.
Markscheme
attempt to subtract squares of integers (M1)
(n+1)2-n2
EITHER
correct order of subtraction and correct expansion of (n+1)2, seen anywhere A1A1
=n2+2n+1−n2 (=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=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]