Higher January 2019 Paper 1R Q15
15
(a) Simplify \((3x^2y^5)^4\) (2)
(b) Expand and simplify \(4n(n - 3)(n + 5)\) (2)
(c) Factorise \(4c^2 - 9d^2\) (1)
(d) Simplify fully \(\dfrac{x^2 - 7x + 12}{4x - x^2}\) (3)
| Scheme | Marks |
|---|---|
| \(81x^8y^{20}\) | B2 |
| (2) |
Notes
B2: (B1 two terms correct in a product of 3 terms)
| Scheme | Marks |
|---|---|
| \(4n(n^2 + 2n - 15)\) or \((4n^2 - 12n)(n + 5)\) or \((4n^2 + 20n)(n - 3)\) | M1 |
| \(4n^3 + 8n^2 - 60n\) | A1 |
| (2) |
Notes
M1: For a correct partial expansion ( may be unsimplified e.g \(4n(n^2 + 5n - 3n - 15)\))
| Scheme | Marks |
|---|---|
| \((2c - 3d)(2c + 3d)\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\dfrac{(4 - x)(3 - x)}{x(4 - x)}\) or \(\dfrac{(x - 4)(x - 3)}{x(4 - x)}\) | M1 |
| M1 | |
| \(\dfrac{3 - x}{x}\) | A1 |
| (3) | |
| (8 marks) |
Notes
M1: for either numerator or denominator factorised correctly
M1: for both numerator and denominator factorised correctly
A1: oe