Standard formIB MYP Maths Standard: Subtopic test

1. 1
   The Earth is about $150\,000\,000$ km from the Sun. Light travels at $3\times10^{5}$ km per second.

   (a)

   Write the distance from the Earth to the Sun in standard form.

   [1 mark]

   • A$15\times10^{7}$ km
   • B$1.5\times10^{7}$ km
   • C$1.5\times10^{9}$ km
   • D$1.5\times10^{8}$ km

   (b)

   Find the time, in seconds, that light takes to travel from the Sun to the Earth.

   [1 mark]

   • A$4.5\times10^{13}$ s
   • B$2\times10^{-3}$ s
   • C$5\times10^{2}$ s
   • D$5\times10^{3}$ s

   (c)

   Mars is $2.28\times10^{8}$ km from the Sun. Find how many times further from the Sun Mars is than the Earth. Give your answer to 2 significant figures.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A red blood cell has a diameter of about $7\times10^{-6}$ m. A hydrogen atom has a diameter of about $1.06\times10^{-10}$ m.

   (a)

   Which of these is the diameter of a red blood cell written as an ordinary decimal, in metres?

   [1 mark]

   • A$0.00007$
   • B$0.000007$
   • C$0.0000007$
   • D$7\,000\,000$

   (b)

   How many times larger is the diameter of the red blood cell than the diameter of the atom? Give your answer to 2 significant figures.

   [1 mark]

   • A$6.6\times10^{4}$
   • B$6.6\times10^{-4}$
   • C$1.5\times10^{-5}$
   • D$6.6\times10^{3}$

   (c)

   A bacterium has a length of $2.5\times10^{-6}$ m. Without a calculator, find the total length of $4000$ of these bacteria placed end to end. Give your answer in standard form, in metres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lorry carries $2.5\times10^{3}$ kg of rice. One kilogram of rice contains about $5\times10^{4}$ grains.

   (a)

   Without a calculator, find the number of grains of rice on the lorry. Give your answer in standard form.

   [3 marks]

   (b)

   A mill processes $4\times10^{6}$ grains of rice per day. Use your answer to (a) to find how many days the mill needs to process all the rice on the lorry. Give a whole number of days.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In computing, data is measured in bytes. One kilobyte (KB) is $10^{3}$ bytes, one megabyte (MB) is $10^{6}$ bytes, one gigabyte (GB) is $10^{9}$ bytes and one terabyte (TB) is $10^{12}$ bytes.

   (a)

   (i) Write the number of bytes in $5$ KB, $5$ MB and $5$ GB in standard form.
   (ii) Describe the pattern in the powers of ten as the unit gets larger.
   (iii) Use the pattern to predict the number of bytes in $5$ TB, and verify your prediction using the definition of a terabyte.

   [6 marks]

   (b)

   A phone has $128$ GB of storage. A video uses $6\times10^{8}$ bytes per minute and a photo uses $4\times10^{6}$ bytes.
   (i) Find the number of complete minutes of video that fit in the storage.
   (ii) Eve says that the phone can hold $200$ minutes of video and $5000$ photos at the same time. Justify whether she is correct.

   [6 marks]

   Total for question 4: 12 marks

End of questions