1. 1
   A science teacher is setting a short quiz on powers and roots for her class, using whole-number examples before moving to a fractional-index question.

   (a)

   Which of these is the value of $6^2$?

   [1 mark]

   • A12
   • B216
   • C18
   • D36

   (b)

   What is the value of $\sqrt[3]{125}$?

   [1 mark]

   • A5
   • B15
   • C25
   • D41.67

   (c)

   What is the value of $16^{\frac{1}{2}}$?

   [1 mark]

   • A2
   • B4
   • C8
   • D256

   Total for question 1: 3 marks

2. 2
   A laboratory records bacteria population growth using powers of 5, since the population multiplies by a factor of 5 at fixed intervals.

   (a)

   Simplify $\dfrac{5^7 \times 5^3}{5^6}$, giving your answer as a single power of 5.

   [2 marks]

   (b)

   Evaluate $27^{-\frac{2}{3}}$, giving your answer as a fraction.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An astronomy student is comparing distances to stars, which are given in standard form because the numbers involved are extremely large.

   (a)

   The distance from Earth to a star is $4.08 \times 10^{16}$ metres and the distance from Earth to a nearer star is $9.6 \times 10^{15}$ metres. Find the difference between the two distances, giving your answer in standard form.

   [3 marks]

   (b)

   A single hydrogen atom has a mass of $1.67 \times 10^{-27}$ kg. Calculate the total mass, in kilograms, of $2.4 \times 10^{20}$ hydrogen atoms. Give your answer in standard form to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   An engineer is designing cube-shaped storage tanks and needs to relate the volume of each tank to its edge length using powers and roots.

   (a)

   A cube-shaped storage tank has a volume of $343$ m$^3$. Show that the length of one edge of the tank is $7$ m.

   [4 marks]

   (b)

   The engineer then designs a larger cube-shaped tank whose edge length is exactly $3$ times the edge length of the first tank. Calculate the volume of the larger tank.

   [4 marks]

   (c)

   The volume of the larger tank, in m$^3$, is written in standard form as $9.261 \times 10^n$. Find the value of $n$, and hence find the volume of $500$ such tanks in standard form, giving your answer to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions