17N.1.SL.TZ0.T_3

pestleMathematicsAASLPaper 117N· sl-1-1-using-standard-formsource ↗

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.

[3]

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 $k \in \mathbb{Z}$ .

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$\frac{{149600000}}{{300000 \times 60}}$ (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]

Examiners’ report

[N/A]