4MA0 Higher June 2012 Paper 3 Q9

EdexcelHigherOld spec7 marksAlgebraic Fractions Solving Simple Equations

(a) Solve \(3(2x - 1) = 6\)
Show clear algebraic working. (3)

(b) Solve \(\dfrac{2y + 1}{3} = \dfrac{y - 2}{4}\)
Show clear algebraic working. (4)

Mark scheme (a)

Scheme	Marks
\(6x - 3 = 6\) or \(2x - 1 = 2\)	M1
\(6x = 6 + 3\) or \(6x = 9\) or \(6x - 9 = 0\) or \(2x = 2 + 1\) or \(2x = 3\) or \(2x - 3 = 0\)	M1
\(1\frac{1}{2}\) oe	A1
	(3)

Notes

M1: for correct expansion (\(6x - 3\) seen)
or correct division of both sides by 3
(\(2x - 1 = 2\))
May be implied by second M1

M1: for correct rearrangement
Also award for \(6x = 6 + 1\) or \(6x = 7\) or \(6x - 7 = 0\) if preceded by \(6x - 1 = 6\)

A1: Award 3 marks if answer is correct and at least one method mark scored

Mark scheme (b)

Scheme	Marks
\(4(2y + 1) = 3(y - 2)\)	M1
\(8y + 4 = 3y - 6\)	M1
\(5y = -6 - 4\) or \(8y - 3y = -10\) or \(5y = -10\) or \(-5y = 6 + 4\) or \(3y - 8y = 10\) or \(-5y = 10\) or \(5y + 10 = 0\)	M1
−2 oe	A1
	(4)
	(Total 7 marks)

Notes

M1: for clear intention to multiply both sides by 12 or by a multiple of 12

eg \(4(2y + 1) = 3(y - 2)\)

\(2y + 1 \times 4 = y - 2 \times 3\)

\(12 \times \dfrac{2y + 1}{3} = 12 \times \dfrac{y - 2}{4}\)

May be implied by second M1

or by \(8y + 1 = 3y - 2\)

or \(8y + 4 = 3y - 2\)

or \(8y + 1 = 3y - 6\)

Also award this mark for \(\dfrac{4(2y + 1)}{12} = \dfrac{3(y - 2)}{12}\)

M1: for correct expansion of brackets or correct rearrangement of correct terms

eg \(8y - 3y = -6 - 4\), \(\dfrac{8y + 4}{12} = \dfrac{3y - 6}{12}\)

M1: for correct rearrangement with \(y\) terms on one side and numbers on the other AND collection of terms on at least one side or for \(5y + 10 = 0\) oe or for \(\dfrac{5y + 10}{12} = 0\) oe

A1: Award 4 marks if answer is correct and at least one method mark scored

Alternative method

Scheme	Marks
\(\frac{2}{3}y + \frac{1}{3} = \frac{1}{4}y - \frac{1}{2}\)	M1
\(\frac{2}{3}y - \frac{1}{4}y = -\frac{1}{2} - \frac{1}{3}\)	M1
\(\frac{5}{12}y = -\frac{5}{6}\)	M1
−2 oe	A1

M1: for correct expansion
M1: for correct rearrangement of correct terms
M1: for correct collection of correct terms on both sides
A1: Award 4 marks if answer is correct and at least one method mark scored