1. 1
   An architect calculates the area of a square courtyard as $144$ m$^2$.

   (a)

   (a) What is the length of one side of the courtyard?

   [1 mark]

   • A12 m
   • B72 m
   • C24 m
   • D14.4 m

   (b)

   (b) The architect also needs to express $1,000,000$ in standard form for a report. Which is correct?

   [1 mark]

   • A$1 \times 10^5$
   • B$1 \times 10^6$
   • C$10 \times 10^5$
   • D$1 \times 10^7$

   (c)

   (c) The volume of a storage cube is $27$ m$^3$. What is the length of one edge?

   [1 mark]

   • A13.5 m
   • B9 m
   • C6 m
   • D3 m

   Total for question 1: 3 marks

2. 2
   A scientist records the mass of a virus particle as $2.4 \times 10^{-8}$ grams. In an experiment, she studies a sample containing $5 \times 10^{6}$ of these particles.

   (a)

   (a) Calculate the total mass of the sample, giving your answer in standard form.

   [2 marks]

   (b)

   (b) The scientist's calculator displays the total mass as $\text{1.2E-1}$. Explain what this calculator display means, giving the value as an ordinary (non-standard-form) number.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A designer is working with the exact value $\sqrt{50}$ for the diagonal length of a tile, in centimetres, and wants to express it in its simplest surd form.

   (a)

   (a) Show that $\sqrt{50}$ simplifies to $5\sqrt{2}$.

   [3 marks]

   (b)

   (b) The designer also needs to rationalise the denominator of $\frac{10}{\sqrt{2}}$, which represents another measurement in centimetres. Show that this simplifies to $5\sqrt{2}$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A laboratory dilutes a chemical solution repeatedly. The concentration starts at $c_0 = 8 \times 10^{4}$ parts per million (ppm) and is multiplied by $10^{-2}$ at each dilution stage.

   (a)

   (a) Calculate the concentration after one dilution stage, giving your answer in standard form.

   [4 marks]

   (b)

   (b) Calculate the concentration after two dilution stages, giving your answer in standard form.

   [4 marks]

   (c)

   (c) The lab needs the concentration to fall below $1$ ppm. Using the pattern from parts (a) and (b), find the minimum whole number of dilution stages required, and justify your answer using powers of $10$.

   [5 marks]

   Total for question 4: 13 marks

End of questions