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Date May 2014 Marks available 2 Reference code 14M.1.sl.TZ2.1
Level SL only Paper 1 Time zone TZ2
Command term Write down Question number 1 Adapted from N/A

Question

The average radius of the orbit of the Earth around the Sun is 150 million kilometres.


The average radius of the orbit of the Earth around the Sun is 150 million kilometres.


Write down this radius, in kilometres, in the form \(a \times {10^k}\), where \(1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}\).

[2]
a.

The Earth travels around the Sun in one orbit. It takes one year for the Earth to complete one orbit.

Calculate the distance, in kilometres, the Earth travels around the Sun in one orbit, assuming that the orbit is a circle.

[2]
b.

Today is Anna’s 17th birthday.

Calculate the total distance that Anna has travelled around the Sun, since she was born.

[2]
c.

Markscheme

\(1.5 \times {10^8}{\text{ (km)}}\)     (A2)     (C2)

 

Notes: Award (A2) for the correct answer.

     Award (A1)(A0) for 1.5 and an incorrect index.

     Award (A0)(A0) for answers of the form \(15 \times {10^7}\).

 

[2 marks]

a.

\(2\pi 1.5 \times {10^8}\)     (M1)

\( = 942\,000\,000{\text{ (km)   (942}}\,{\text{477}}\,{\text{796.1}} \ldots {\text{, }}3 \times {10^8}\pi ,{\text{ }}9.42 \times {10^8})\)     (A1)(ft)     (C2)

 

Notes: Award (M1) for correct substitution into correct formula. Follow through from part (a).

     Do not accept calculator notation \(9.42{\text{E}}8\).

     Do not accept use of \(\frac{{22}}{7}\) or\( 3.14\) for \(\pi\).

 

[2 marks]

b.

\(17 \times 942\,000\,000\)     (M1)

\( = 1.60 \times {10^{10}}{\text{ (km) }}\left( {{\text{1.60221}} \ldots  \times {{10}^{10}}{\text{, 1.6014}} \times {{10}^{10}},{\text{ 16}}\,{\text{022}}\,{\text{122}}\,{\text{530, }}(5.1 \times {{10}^9})\pi } \right)\)     (A1)(ft)     (C2)

 

Note: Follow through from part (b).

 

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 1 - Number and algebra » 1.3 » Expressing numbers in the form \(a \times {10^k}\) , where \(1 \le a < 10\) and \(k\) is an integer.
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