4MA0 Higher June 2015 Paper 3 Q13
13
L is a line parallel to the line with equation \(4x + 2y = 13\)
L passes through the point with coordinates (3, −1)
| Scheme | Marks |
|---|---|
| \(6x + 6y = 18\) \(12x + 6y = 39\) \((6x = 21)\) or \(12x + 12y = 36\) \(12x + 6y = 39\) \((6y = -3)\) | M1 |
| \(x = 3.5\) or \(y = -0.5\) | A1 |
| \(4 \times 3.5 + 2y = 13\) | M1 |
| \(x = 3.5\) oe, \(y = -0.5\) oe | A1 |
| (4) |
Notes
M1: M1 for appropriate multiplication to get coefficients of \(x\) or \(y\) the same (condone one arithmetic error) with the correct operation to eliminate one variable or for correct rearrangement of one equation followed by substitution in the other (condone one arithmetic error).
NB: Could work with \(x + y = 3\) throughout rather than \(3x + 3y = 9\)
A1: (dep on M1)
M1: (dep) for substituting into an equation to find the second variable or for a fully correct method to find second variable
A1: Award 4 marks for correct values if at least first M1 scored
| Scheme | Marks |
|---|---|
\(y = \dfrac{-4x + 13}{2}\) or \(y = -2x + 6.5\) or line L has gradient −2 eg. L has equation \(2y = -4x + k\) \(k \ne 13\) | M1 |
| \(-1 = -2 \times 3 + k\) or \(y - -1 = -2(x - 3)\) | M1 |
| \(y = -2x + 5\) | A1 |
| (3) |
Notes
M1: M1 \(4x + 2y = p\)
M1: M1 \(4 \times 3 + 2 \times -1 = p\)
NB: \(4 \times 3 + 2 \times -1 = 10\) gets no marks unless clearly part of a complete method
A1: oe eg. \(4x + 2y = 10\)
NB: \(L = -2x + 5\) gets M2 A0