Higher June 2022 Paper 2 Q19
19 \(a = \dfrac{14}{3x - 7}\) \(x = \dfrac{7}{4y - 3}\)
Express \(a\) in the form \(\dfrac{py + q}{ry + s}\) where \(p\), \(q\), \(r\) and \(s\) are integers.
Give your answer in its simplest form.
(3)
| Scheme | Marks |
|---|---|
| \((a =)\;\dfrac{14}{3 \times \dfrac{7}{4y - 3} - 7}\) | M1 |
| \((a =)\;\dfrac{14(4y - 3)}{21 - 7(4y - 3)}\) oe eg \(\dfrac{56y - 42}{21 - 28y + 21}\) | M1 |
| \(\dfrac{4y - 3}{3 - 2y}\) | A1 |
| (3) | |
| (3 marks) |
Notes
M1: For a correct substitution
M1: or for a correct but unsimplified answer in the form \(\dfrac{m}{n}\) ie the denominator should be simplified to remove the fraction
A1: oe but must be simplified
| Scheme | Marks |
|---|---|
\(x = \dfrac{14 + 7a}{3a}\) and \(\dfrac{14 + 7a}{3a} = \dfrac{7}{4y - 3}\) | M1 |
\(a(42 - 28y) = 56y - 42\) oe eg \((a =)\;\dfrac{56y - 42}{21 - 28y + 21}\) | M1 |
| \(\dfrac{4y - 3}{3 - 2y}\) | A1 |
Notes
M1: For rearranging ‘\(x\)’ to be in terms of \(a\) and equating two expressions for \(a\)
M1: or for a correct but unsimplified answer in the form \(\dfrac{m}{n}\)
A1: oe but must be simplified