4MA0 Higher January 2017 Paper 3R Q16
16
(a) Solve \(\;\dfrac{3x + 1}{5} - \dfrac{x - 4}{3} = 2\)
Show clear algebraic working. (3)
Show clear algebraic working. (3)
(b) Make \(p\) the subject of the formula \(\;t = \dfrac{7 - 2p}{3p + 1}\) (4)
| Scheme | Marks |
|---|---|
e.g. \(3(3x + 1) - 5(x - 4) = 2 \times 15\) or \(\dfrac{3(3x + 1)}{15} - \dfrac{5(x - 4)}{15} = 2\) or \(\dfrac{3(3x + 1) - 5(x - 4)}{15} = 2\) | M1 |
| e.g. \(9x + 3 - 5x + 20 = 30\) | M1 |
| 1.75 oe | A1 |
| (3) |
Notes
M1: deals with fractions eg. finds common denominator (15 or a multiple of 15) or multiplies by common multiple in a correct equation.
M1: Expands brackets and multiplies by common denominator in a correct equation
A1: dep on M1
| Scheme | Marks |
|---|---|
| \(t(3p + 1) = 7 - 2p\) | M1 |
| \(3pt + 2p = 7 - t\) | M1 |
| \(p(3t + 2) = 7 - t\) | M1 |
| \(p = \dfrac{7 - t}{3t + 2}\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: multiplies by \(3p + 1\) must have brackets
M1: isolates terms in \(p\)
M1: takes \(p\) out as a common factor
A1: or \(p = \dfrac{t - 7}{-3t - 2}\) oe with \(p\) as the subject