1.1 Scientific notationIB Maths: Applications and Interpretation HL: Subtopic test

1. 1
   The mass of the Earth is $5.97\times10^{24}$ kg and the mass of the Moon is $7.35\times10^{22}$ kg.

   (a)

   Find how many times heavier the Earth is than the Moon. Give your answer in the form $a\times10^{k}$, where $1\le a<10$ and $k$ is an integer, correct to 3 significant figures.

   [1 mark]

   • A$8.12\times10^{2}$
   • B$1.23\times10^{-2}$
   • C$8.12\times10^{1}$
   • D$8.12\times10^{46}$

   (b)

   Find the total mass of the Earth and the Moon. Give your answer in the form $a\times10^{k}$, where $1\le a<10$, correct to 3 significant figures.

   [1 mark]

   • A$6.04\times10^{24}$ kg
   • B$6.71\times10^{24}$ kg
   • C$1.33\times10^{25}$ kg
   • D$1.33\times10^{47}$ kg

   (c)

   Write down the mass of the Earth in grams, in the form $a\times10^{k}$ where $1\le a<10$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A red blood cell has a diameter of $7.5\times10^{-6}$ m. An adult body contains approximately $2.4\times10^{13}$ red blood cells.

   (a)

   Write the diameter of a red blood cell in millimetres, in the form $a\times10^{k}$ where $1\le a<10$.

   [1 mark]

   • A$7.5\times10^{-9}$ mm
   • B$7.5\times10^{-4}$ mm
   • C$7.5\times10^{-6}$ mm
   • D$7.5\times10^{-3}$ mm

   (b)

   Suppose all the red blood cells in an adult body were placed in a straight line, touching one another. Find the length of the line in metres.

   [1 mark]

   • A$1.8\times10^{7}$ m
   • B$1.8\times10^{8}$ m
   • C$3.1\times10^{-19}$ m
   • D$1.8\times10^{19}$ m

   (c)

   Find the number of red blood cells needed to make a line of length 1 m. Give your answer in the form $a\times10^{k}$ where $1\le a<10$, correct to 3 significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Light travels at $3.00\times10^{8}$ m s$^{-1}$. The star Proxima Centauri is approximately $4.0\times10^{16}$ m from the Sun.

   (a)

   Find the time, in days, that light takes to travel from Proxima Centauri to the Sun. Give your answer in the form $a\times10^{k}$, where $1\le a<10$, correct to 3 significant figures. (There are $8.64\times10^{4}$ seconds in one day.)

   [3 marks]

   (b)

   One light-year is the distance that light travels in $3.15\times10^{7}$ seconds. Find the length of a light-year in metres, and hence find the distance of Proxima Centauri from the Sun in light-years. Give the first answer in the form $a\times10^{k}$ where $1\le a<10$, and both answers to 3 significant figures.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A data centre has a storage capacity of $4.8\times10^{15}$ bytes. An average photo file uses $3.2\times10^{6}$ bytes and an average video file uses $2.5\times10^{9}$ bytes.

   (a)

   (i) Find the number of photos that can be stored if only photos are stored.
   (ii) Find the number of videos that can be stored if only videos are stored.
   (iii) Find how many times larger a video file is than a photo file.
   Give each answer in the form $a\times10^{k}$ where $1\le a<10$, correct to 3 significant figures.

   [6 marks]

   (b)

   The centre stores $4.0\times10^{5}$ video files and the remaining capacity is used for photos.
   (i) Find the number of bytes used by the videos.
   (ii) Find the capacity that remains.
   (iii) Find the number of photos that can be stored in the remaining capacity.
   Give each answer in the form $a\times10^{k}$ where $1\le a<10$, correct to 3 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions