Find an expression for \(m\) in terms of \(p\). Give your answer in its simplest form. [4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\(x\)
\(y\)
−5
−4
2.5
11
2
B1 for one correct
Mark scheme (b)
Answer
Marks
Part marks and guidance
\(y = 5(x - 4)\) oe
or
\(x \to \boxed{-\,4} \to \boxed{\times 5} \to y\)
2
M1 for correct operations in correct order but poor notation eg \(y = x - 4 \times 5\) or \(5(x - 4)\) oe \(\to \boxed{-\,4} \to \boxed{\times 5} \to\) (as minimum allow \(-4\), \(\times 5\) if intent clear)
or for correct operations in reverse order eg implied by \(y = 5x - 4\) \(x \to \boxed{\times 5} \to \boxed{-\,4} \to y\)
For 2 marks and M1 condone \(x\) and \(y\) transposed in algebraic expression or transposed in flow diagram.
M0 for wrong order and poor notation \(\to \boxed{\times 5} \to \boxed{-\,4} \to\)
Mark right-to-left flow diagrams in a similar way
Condone correct flow diagram followed by incorrect algebra or vice-versa
Mark scheme (c)
Answer
Marks
Part marks and guidance
\(5p - 3\) as final answer
4
M1 for \(2p + 4 - 4\) soi M1 for their \(2p \times 5\) soi M1 for their \(10p \div 2\) M1 for their \(5p - 3\) Maximum 3 marks if answer incorrect
Output of function A is \(10p\) implies first M1M1
Alternative method: M1 for \(2(m + 3)\) soi
Use of function A
M1 for \(\dfrac{\mathit{their}\,2(m + 3)}{5} + 4\) soi
Use of function B with output of A
M1 for their \(\dfrac{2(m + 3)}{5} + 4 = 2p + 4\) or better
Equating their output of B with \(2p + 4\)
M1FT for rearranging their equation to isolate \(m\)
Maximum 3 marks if answer incorrect
Their equation must be of form \(\dfrac{am + b}{5} + 4 = 2p + 4\) oe where \(a \ne 0\) and \(b \ne 0\), leading to (\(m =\)) \(\dfrac{10p - b}{a}\) and then simplified if possible
Accept another letter used consistently for \(m\) or \(p\) but not \(m\) and \(p\) interchanged
