or \(k = (\pm)\left(\dfrac{7p - 5}{8 + 3p}\right)^{0.5}\) (condone omission of \(\pm\))
NB: to award A1 we must see \(k = (\pm)\sqrt{\dfrac{7p - 5}{8 + 3p}}\) in working if \((\pm)\sqrt{\dfrac{7p - 5}{8 + 3p}}\) alone is given as an answer
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
