| Date | May 2015 | Marks available | 3 | Reference code | 15M.1.sl.TZ2.1 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The distance \(d\) from a point \({\text{P}}(x,{\text{ }}y)\) to the point \({\text{A}}(1,{\text{ }} - 2)\) is given by \(d = \sqrt {{{(x - 1)}^2} + {{(y + 2)}^2}} \)
Find the distance from \({\text{P}}(100,{\text{ }}200)\) to \({\text{A}}\). Give your answer correct to two decimal places.
Write down your answer to part (a) correct to three significant figures.
Write down your answer to part (b) in the form \(a \times {10^k}\), where \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).
Markscheme
\(\sqrt {{{(100 - 1)}^2} + {{(200 + 2)}^2}} \) (M1)
\(\sqrt {50605} \;\;\;( = 224.955 \ldots )\) (A1)
Note: Award (M1)(A1) if \(\sqrt {50605} \) seen.
\({\text{224.96}}\) (A1) (C3)
Note: Award (A1) for their answer given correct to 2 decimal places.
\(225\) (A1)(ft) (C1)
Note: Follow through from their part (a).
\(2.25 \times {10^2}\) (A1)(ft)(A1)(ft) (C2)
Notes: Award (A1)(A0) for \(2.25\) and an incorrect index value.
Award (A0)(A0) for answers such as \(22.5 \times {10^1}\).
