Notes

M1: for factorising 2 or 3 of the quadratics fully – could be implied by 2 factors cancelled correctly

NB factors must be in the form \((ax + b)\)

NB Substitution of values of \(x\) into the given equation is not an acceptable algebraic method

M1: for factorising all of the quadratics fully – could be implied by 2 factors cancelled correctly

NB factors must be in the form \((ax + b)\)

M1: for inverting the 2^nd fraction (this mark can be awarded at any time and may be awarded with incorrect factorisation if meaning is clear)

A1: oe dep on M3

ALT

Notes

M1: An expansion with only one error

Do not award this mark for
\(4x^2 + 12x + 8x^2 - 20x\)

M1: ft dep on M1
allow one further error

A1: cao dep on M1
Terms may be in any order but must be simplified

ISW correct factorisation
\(8x^3 + 4x^2 - 60x\) must be seen previously to award 3 marks
eg \(4(2x^3 + x^2 - 15x)\)
\(x(8x^2 + 4x - 60)\)

Do not ISW incorrect simplification or further incorrect work following \(8x^3 + 4x^2 - 60x\)
eg \(8x^3 + 4x^2 - 60x = 2x^3 + x^2 - 15x\) gets M2A0

M2 for 3 terms (out of a maximum of 4 terms) from:
\(8x^3 - 20x^2 + 24x^2 - 60x\)
If not M2, then M1 for 2 correct out of a maximum of 4

Notes

M1: for \((y \pm 3)(y \pm 7)\)
or for \((y \pm a)(y \pm b)\) with \(ab = 21\) or \(a + b = -10\)

A1: for correct factors

B1: ft dep on factorising in the form \((y \pm p)(y \pm q)\)

Notes

M1: for correct removal of fraction and expansion of bracket in a correct equation
or
separating fraction (RHS) in an equation

M1ft: (dep on 4 terms) correctly rearranging their 4 term equation for terms in \(x\) on one side of equation and number terms on the other

A1: oe eg 6.75 or \(6\dfrac{3}{4}\), dep on M1

Notes

M1: for \((y \pm 6)(y \pm 5)\) or \((6 \pm y)(5 \pm y)\) or for \((y + a)(y + b)\) where \(ab = 30\) or \(a + b = -11\)
or
\(y(y + a) + b(y + a)\) or
\(y(y + b) + a(y + b)\)
where \(ab = 30\) or \(a + b = -11\)

A1: oe, allow any letter for \(y\)

B1: must ft from their answer in (b)(i) ft from their factors in the form \((y + a)(y + b)\)

Notes

B2: for \(9c(2 - 5d)\) or \(-9c(5d - 2)\)

(B1 for \(9(2c - 5cd)\) or \(c(18 - 45d)\) or \(3c(6 - 15d)\) or \(3(6c - 15cd)\)
or \(9c(p + qd)\) where \(p\) and \(q\) are non-zero integers
or \((2 - 5d)\) as a factor)

Notes

M1: for removal of the fraction and correctly multiplying out RHS by 6 in an equation
or
separating fractions on the LHS in an equation

M1ft: dep on 4 terms
for correctly rearranging their 4 term equation for terms in \(x\) on one side of the equation and number terms on the other

Notes

M1indep: [NB: the two fractions when divided and cancelled give an answer of \(4(2x - 3)\) or \(2(4x - 6)\) or \(8x - 12\) (any one of these gain 2 marks) ]

M2 for any fraction with completely simplified non-linear numerator and non-linear denominator that will cancel to –19

M1: a linear expression that should give the correct value for \(n\)
(this mark implies previous M marks as not all factorising is necessary)

A1: dep on M2

Notes

M1: for \((x \pm 8)(x \pm 3)\) or
\((x + a)(x + b)\) where \(ab = -24\) or
\(a + b = 5\) and, \(a\) and \(b\) are integers

A1: for \((x + 8)(x - 3)\)
Allow any letter for \(x\)

Must be in the form \((x + a)(x + b)\) where \(a\) and \(b\) are integers

B1: must ft from their answer in (a)(i)
ft from their incorrect factors in the form \((x + a)(x + b)\)
Award B0 for –8 and 3 if no marks scored in (a)(i)

Notes

M1: allow use of = or condone incorrect inequality sign

M1: allow use of = or condone incorrect inequality sign