Higher June 2018 Paper 1R Q14
14
(a) Simplify \((2e^2f^3)^3\) (2)
(b) Expand and simplify \((3x - 4y)(x + 3y)\) (2)
\(\dfrac{\sqrt{a} \times a}{a^{-2}}\) can be written in the form \(a^k\)
(c) Find the value of \(k\). (2)
(d) Simplify \(\dfrac{2^n - 1}{4^n - 1}\) (2)
| Scheme | Marks |
|---|---|
| \(8e^6f^9\) | B2 |
| (2) |
Notes
B2: B1 for 2 correct terms in a product of 3 terms
| Scheme | Marks |
|---|---|
| \(3x^2 + 9xy - 4yx - 12y^2\) | M1 |
| \(3x^2 + 5xy - 12y^2\) | A1 |
| (2) |
Notes
M1: M1 for 3 correct terms out of 4
or for 4 correct terms ignoring signs
or for \(3x^2 + 5xy + c\) for any non zero value of \(c\)
or for \(d + 5xy - 12y^2\) for any non zero value of \(d\)
| Scheme | Marks |
|---|---|
\(a^{\frac{1}{2}} \times a = a^{\frac{3}{2}}\) or \(\dfrac{a}{a^{-2}} = a^3\) or \(\dfrac{a^{\frac{1}{2}}}{a^{-2}} = a^{\frac{5}{2}}\) | M1 |
| \(\dfrac{7}{2}\) | A1 |
| (2) |
Notes
M1: for one correct step
A1: oe
| Scheme | Marks |
|---|---|
| \(\dfrac{2^n - 1}{(2^n - 1)(2^n + 1)}\) | M1 |
| \(\dfrac{1}{2^n + 1}\) | A1 |
| (2) | |
| (8 marks) |
Notes
M1: for \((2^n - 1)(2^n + 1)\)