| Date | November 2017 | Marks available | 3 | Reference code | 17N.1.sl.TZ0.3 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 3 | Adapted from | N/A |
Question
The speed of light is \({\text{300}}\,{\text{000}}\) kilometres per second. The average distance from the Sun to the Earth is 149.6 million km.
A light-year is the distance light travels in one year and is equal to \({\text{9}}\,{\text{467}}\,{\text{280}}\) million km. Polaris is a bright star, visible from the Northern Hemisphere. The distance from the Earth to Polaris is 323 light-years.
Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.
Find the distance from the Earth to Polaris in millions of km. Give your answer in the form \(a \times {10^k}\) with \(1 \leqslant a < 10\) and \(k \in \mathbb{Z}\).
Markscheme
\(\frac{{149600000}}{{300000 \times 60}}\) (M1)(M1)
Note: Award (M1) for dividing the correct numerator (which can be presented in a different form such as \(149.6 \times {10^6}\) or \(1.496 \times {10^8}\)) by \({\text{300}}\,{\text{000}}\) and (M1) for dividing by 60.
\( = 8.31{\text{ }}({\text{minutes}}){\text{ }}(8.31111 \ldots {\text{, 8 minutes 19 seconds}})\) (A1) (C3)
[3 marks]
\(323 \times 9467\,280\) (M1)
Note: Award (M1) for multiplying 323 by \(9\,467\,280\), seen with any power of 10; therefore only penalizing incorrect power of 10 once.
\( = 3.06 \times {10^9}{\text{ ( = }}3.05793 \ldots \times {10^9})\) (A1)(A1) (C3)
Note: Award (A1) for 3.06.
Award (A1) for \( \times {10^9}\)
Award (A0)(A0) for answers of the type: \(30.6 \times {10^8}\)
[3 marks]
