Powers, Roots & Standard FormEdexcel IGCSE Maths: Subtopic test

1. 1
   An astronomer is comparing the sizes of a cube-shaped satellite component and the distances between planets, using powers, roots and standard form.

   (a)

   A cube has volume $125\ \text{cm}^3$. What is the length of one edge of the cube?

   [1 mark]

   • A$5$ cm
   • B$25$ cm
   • C$15$ cm
   • D$41.67$ cm

   (b)

   Simplify $x^7 \div x^3$.

   [1 mark]

   • A$x^{21}$
   • B$x^{10}$
   • C$x^4$
   • D$x^{2.33}$

   (c)

   The average distance from Earth to the Sun is $149\,600\,000$ km. Which of the following correctly writes this in standard form?

   [1 mark]

   • A$1.496 \times 10^7$ km
   • B$14.96 \times 10^7$ km
   • C$1.496 \times 10^9$ km
   • D$1.496 \times 10^8$ km

   Total for question 1: 3 marks

2. 2
   A microbiologist is tracking the growth of a bacteria colony over time, recording population sizes in standard form.

   (a)

   A bacteria colony has a population of $6.4 \times 10^5$ at the start of an experiment. After a week the population has grown to $3.2 \times 10^7$. Calculate how many times bigger the population has become, giving your answer as an ordinary number.

   [2 marks]

   (b)

   Calculate $6.4 \times 10^5 + 3.2 \times 10^7$, giving your answer in standard form.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An engineer is designing a pair of cube-shaped storage tanks of different sizes and needs to compare their volumes and surface areas using index laws.

   (a)

   A cube-shaped storage tank has edge length $x$ metres and volume $V = x^3$. A second, similar tank has edge length $2x$. Show that the volume of the second tank is 8 times the volume of the first tank.

   [3 marks]

   (b)

   The surface area of the first cube-shaped tank is $S = 6x^2$. If $x = 2.5$ metres, calculate the surface area, and then calculate the surface area of the second tank (edge length $2x$) using the index laws.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A data centre engineer is calculating storage and processing capacity using standard form and index laws, working with very large numbers of bytes processed and stored.

   (a)

   A data centre processes $2.5 \times 10^{10}$ bytes of data per hour. Calculate how many bytes it processes in a standard 24-hour day, giving your answer in standard form.

   [4 marks]

   (b)

   The data centre has storage capacity of $8.0 \times 10^{12}$ bytes. Using your answer to part (a), calculate how many full days of data (at $6.0 \times 10^{11}$ bytes per day) the storage capacity can hold, rounding down to the nearest whole day.

   [4 marks]

   (c)

   The data centre plans to upgrade so that its daily processing rate doubles every year. If the current daily rate is $6.0 \times 10^{11}$ bytes, find the daily processing rate after 3 years, giving your answer in standard form correct to 2 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions