| Exam Board | Edexcel |
|---|
| Module | C1 (Core Mathematics 1) |
|---|
| Topic | Indices and Surds |
|---|
- Given that \(2 ^ { x } = \frac { 1 } { \sqrt { 2 } }\) and \(2 ^ { y } = 4 \sqrt { } 2\),
- find the exact value of \(x\) and the exact value of \(y\),
- calculate the exact value of \(2 ^ { y - x }\).
- \(f ( x ) = \frac { \left( x ^ { 2 } - 3 \right) ^ { 2 } } { x ^ { 3 } } , x \neq 0\).
- Show that \(\mathrm { f } ( x ) \equiv x - 6 x ^ { - 1 } + 9 x ^ { - 3 }\).
- Hence, or otherwise, differentiate \(\mathrm { f } ( x )\) with respect to \(x\).
- The sum of an arithmetic series is \(\sum _ { r = 1 } ^ { n } ( 80 - 3 r )\).
- Write down the first two terms of the series.
- Find the common difference of the series.
Given that \(n = 50\), - find the sum of the series.