Higher January 2020 Paper 1R Q3
3
(a) Make \(a\) the subject of \(\;d = g + 2ac\) (2)
(b) Factorise fully \(\;9ef - 12f\) (2)
(c) Expand and simplify \(\;(x + 2)(x - 5)\) (2)
(d) Simplify fully \(\;\dfrac{n^4 \times n^7}{n^5}\) (2)
| Scheme | Marks |
|---|---|
e.g. \(d - g = 2ac\) \(\dfrac{d}{2c} = \dfrac{g}{2c} + a\) | M1 |
| \(a = \dfrac{d - g}{2c}\) | A1 |
| (2) |
Notes
M1: for a correct first step eg subtract \(g\) from both sides OR divide all terms by 2 OR divide all terms by \(c\) OR divide all terms by \(2c\)
A1: oe
| Scheme | Marks |
|---|---|
| \(3f(3e - 4)\) | B2 |
| (2) |
Notes
B2: (B1 for \(3(3ef - 4f)\) or \(f(9e - 12)\) or \(3f(ke - 4)\) or \(3f(3e - m)\) where \(k \neq 0\) and \(m \neq 0\))
| Scheme | Marks |
|---|---|
| \(x^2 - 5x + 2x - 10\) | M1 |
| \(x^2 - 3x - 10\) | A1 |
| (2) |
Notes
M1: for any 3 correct terms or for 4 out of 4 correct terms ignoring signs or \(x^2 - 3x \ldots\) or for \(\ldots -3x - 10\)
| Scheme | Marks |
|---|---|
| \(\dfrac{n^{11}}{n^5}\) OR \(n^{-1} \times n^7\) OR \(n^4 \times n^2\) OR \(n^4 \times n^7 \times n^{-5}\) OR \(n^{\text{“}11\text{”}} \div n^5 = n^{(\text{“}11\text{”} - 5)}\) | M1 |
| \(n^6\) | A1 |
| (2) | |
| (8 marks) |
Notes
M1: for simplifying two terms