4MA0 Higher June 2016 Paper 3R Q12
12
(a) Simplify fully \(\dfrac{a^{11}}{a^2 \times a^5}\) (2)
(b) Make \(p\) the subject of \(p + 4q = 3p + 5\) (2)
(c) Expand and simplify \((2y + 3)(4y - 1)\) (2)
(d) Simplify \((8a^6b^3)^{\frac{1}{3}}\) (2)
| Scheme | Marks |
|---|---|
| e.g. \(\dfrac{a^{11}}{a^7}\) or \(\dfrac{a^6}{a^2}\) or \(\dfrac{a^9}{a^5}\) oe | M1 |
| \(a^4\) | A1 |
| (2) |
Notes
M1: For \(\dfrac{a^{11}}{a^7}\) or any index law used correctly
| Scheme | Marks |
|---|---|
| \(4q - 5 = 3p - p\) oe eg \(-2p = 5 - 4q\) | M1 |
| \(p = \dfrac{4q - 5}{2}\) | A1 |
| (2) |
Notes
M1: For correctly collecting terms in \(p\) one side and other terms on the other side
A1: oe, eg \(p = 2q - 2.5\)
| Scheme | Marks |
|---|---|
| \(8y^2 - 2y + 12y - 3\) | M1 |
| \(8y^2 + 10y - 3\) | A1 |
| (2) |
Notes
M1: For any three correct terms
or for 4 correct terms ignoring signs
or for \(8y^2 + 10y + k\) for any non-zero value of \(k\) or for \(\ldots + 10y - 3\)
| Scheme | Marks |
|---|---|
| \(2a^2b\) | B2 |
| (2) |
Notes
B2: B1 for two of 2 or \(a^2\) or \(b\) as part of a product