4MA0 Higher January 2018 Paper 4R Q7
7
(a) Factorise \(4ab + 7a^2 - a\) (2)
(b) Solve the inequality \(4 - 8p > 11\) (2)
(c) Expand and simplify \((x + 3)(x - 6)\) (2)
(d) Simplify \(\dfrac{y^{12}}{y^4}\) (1)
(e) Simplify \((3e)^2\) (2)
| Scheme | Marks |
|---|---|
| \(a(4b + 7a - 1)\) | B2 |
| (2) |
Notes
B2: B1 for factors which, when expanded and simplified, give three terms, at least one of which is correct.
| Scheme | Marks |
|---|---|
| \(4 > 11 + 8p\) or \(-8p > 11 - 4\) or \(-8p > 7\) or \(8p \lt 4 - 11\) or \(8p \lt -7\) | M1 |
| \(p \lt \dfrac{-7}{8}\) | A1 |
| (2) |
Notes
M1: Accept \(4 = 11 + 8p\) or
\(-8p = 11 - 4\) or \(\dfrac{-7}{8}\) or \(8p = 4 - 11\)
A1: Condone \(p \lt -0.875\)
Mark the final answer
| Scheme | Marks |
|---|---|
| \(x^2 + 3x - 6x - 18\) | M1 |
| \(x^2 - 3x - 18\) | A1 |
| (2) |
Notes
M1: For 3 correct terms or
For 4 correct terms ignoring signs or
For \(x^2 - 3x + c\) for any non-zero value of \(c\) or
For ... \(- 3x - 18\)
| Scheme | Marks |
|---|---|
| \(y^8\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(9e^2\) | B2 |
| (2) | |
| (9 marks) |
Notes
B2: B1 for 9 or \(e^2\) as part of a product or for \(3^2 \times e^2\)