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
Mark scheme (b)
Scheme
Marks
(i) \((y \pm 6)(y \pm 5)\) or \((6 \pm y)(5 \pm y)\) or \(y(y - 6) - 5(y - 6)\) or \(y(y - 5) - 6(y - 5)\)
M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \((y - 6)(y - 5)\)
A1
(2)
(ii) Answer: (\(y\) =) 6, (\(y\) =) 5
B1
(1)
(6 marks)
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 \((y + a)(y + b)\)
(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)
Mark scheme (b)
Scheme
Marks
eg
\(5 - 2x = 18x - 24\)
or
\(\dfrac{5}{6} - \dfrac{2}{6}x = 3x - 4\)
M1
\(5 + 24 = 18x + 2x\) oe or \(29 = 20x\) oe
or
\(\dfrac{5}{6} + 4 = \dfrac{2}{6}x + 3x\) oe
M1ft
Working required Answer: 1.45
A1
(3)
(5 marks)
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
eg \(9x + 6 - 10x - 5 = 15x\) oe or \(1 - x = 15x\) oe
eg \(9x + 6 = 15x + 10x + 5\)
or
\(\dfrac{-x + 1}{15} = \dfrac{15x}{15}\) or \(-\dfrac{16}{15}x = -\dfrac{1}{15}\)
M1
Working required
Answer: \(\dfrac{1}{16}\)
A1
(3)
Notes
M1: Writing fractions over a common denominator or removing denominator or writing each term separately – if student has expanded/multiplied at this stage, then allow one of the 4 terms on the LHS incorrect.
If the student has removed the denominator at this stage then a correct method must be shown or implied
M1: An equation with no brackets or fractions or an equation with a common denominator for all terms with numerators simplified (allow one error for the 4 terms on the LHS only (they may have moved these to the RHS) across the 2 M marks and ft for simplifying)
A1: oe 0.0625 (allow 0.062 or 0.063) dep on M1
Mark scheme (b)
Scheme
Marks
\(f^2 = \dfrac{a + bc}{c - d}\)
M1
eg \(cf^2 - df^2 = a + bc\)
M1
eg \(cf^2 - bc = a + df^2\)
M1
Correct answer scores full marks (unless from obvious incorrect working)
Answer: \(c = \dfrac{a + df^2}{f^2 - b}\)
A1
(4)
(7 marks)
Notes
M1: for squaring both sides in a correct equation
M1: for multiplying by the denominator and expanding in a correct equation
M1: for isolating terms in \(c\) on one side and other terms the other in a correct equation
M1: for expanding with at least 3 correct terms (must see for example, \(8n^2\) and not just \(2n \times 4n\))(can assume that no sign in front of a number is a + if terms written in a list or table)
A1: oe \(2n + 9n^2\) or \(n(9n + 2)\) or \(n(2 + 9n)\)
Mark scheme (c)
Scheme
Marks
eg
\(2x + 5 = 12 - 3x\) or
\(\dfrac{2}{3}x + \dfrac{5}{3} = 4 - x\) oe
M1
eg
\(2x + 3x = 12 - 5\) or \(5x = 7\) or
\(5 - 12 = -3x - 2x\) or \(-7 = -5x\) or
\(\dfrac{2}{3}x + x = 4 - \dfrac{5}{3}\) oe or \(\dfrac{5}{3}x = \dfrac{7}{3}\) oe
M1
Working required
Answer: \(\dfrac{7}{5}\)
A1
(3)
(6 marks)
Notes
M1: for removal of fraction and multiplying out RHS correctly by 3 or separating fraction (LHS) in an equation
M1: ft (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
