Higher January 2020 Paper 2R Q21
21
(a) Simplify fully \(\;\dfrac{10x^2 + 23x + 12}{4x^2 - 9}\) (3)
\[2^{2y} \times 2^{3y + 2} = \dfrac{8^{5y}}{4^n}\]
(b) Find an expression for \(n\) in terms of \(y\).
Show clear algebraic working and simplify your expression. (4)
Show clear algebraic working and simplify your expression. (4)
| Scheme | Marks |
|---|---|
| Factorising numerator as \((5x + 4)(2x + 3)\) | M1 |
| Factorising denominator as \((2x + 3)(2x - 3)\) | M1 |
| \(\dfrac{5x + 4}{2x - 3}\) | A1 |
| (3) |
| Scheme | Marks |
|---|---|
| (\(8^{5y}\) =) \(2^{15y}\) or (\(4^n\) =) \(2^{2n}\) or \(2^{5y + 2}\) | M1 |
| \(2^{5y + 2} = 2^{15y - 2n}\) oe | M1 |
| \(5y + 2 = 15y - 2n\) oe | M1 |
| Working required Answer: \(n = 5y - 1\) | A1 |
| (4) | |
| (7 marks) |
Notes
M1: e.g. \(2^{2n} = 2^{15y - 5y - 2}\)
M1: Correct equation using the powers
A1: Dep on M2 (accept \(5y - 1\))