Standard +0.3 This is a straightforward algebraic manipulation requiring factorisation of the numerator by grouping terms and recognising common factors involving surds. While it requires careful algebraic handling of fractional powers and multiple steps, it follows standard A-level techniques without requiring novel insight—slightly easier than average due to being a pure manipulation exercise.
Question 6:
6 | Begins to solve the problem
using an appropriate technique
eg factorising or grouping terms
in numerator or writing y= x
PI if 2 + x or 25 – x or
5 – x1/2 seen
or
5+ x
multiplies by
5+ x | 3.1a | M1 | 1 3
10+5x−2x2−x2 5+ x
×
5− x 5+ x
1 3 3
50+25x−10x2−5x2+10 x+5x x−2x−x2 x
=
25−x
50+23x−x2
=
25−x
(25−x)(2+x)
=
25−x
=2+x
Obtains one correct common
factor in numerator eg 2 + x or
25 – x or 5 – x1/2
or
expands numerator
condone one error
may be unsimplified | 1.1a | M1
Obtains second correct common
factor in numerator
or
obtains correct simplified
numerator and denominator
PI in long division | 1.1a | M1
Completes manipulation by
cancelling common factor to
obtain 2 + x | 1.1b | A1
Total | 4
Q | Marking instructions | AO | Mark | Typical solution