1. 1
   A survey of 500 students records the fraction, decimal and percentage of students who chose each of three lunch options: pasta, salad and soup.

   (a)

   Convert $\frac{3}{5}$ to a decimal.

   [1 mark]

   • A$0.6$
   • B$0.35$
   • C$0.53$
   • D$1.67$

   (b)

   $0.6$ students chose pasta as a decimal fraction of the survey. Convert $0.6$ to a percentage.

   [1 mark]

   • A$6\%$
   • B$60\%$
   • C$0.6\%$
   • D$16.7\%$

   (c)

   Convert the terminating decimal $0.65$ to a fraction in its simplest form.

   [1 mark]

   • A$\frac{5}{8}$
   • B$\frac{65}{100}$
   • C$\frac{13}{25}$
   • D$\frac{13}{20}$

   Total for question 1: 3 marks

2. 2
   A drinks manufacturer blends orange and mango juice in a jug, and records the mixture using decimals and fractions.

   (a)

   A jug contains 2.5 litres of juice, and $0.375$ of the juice is orange flavour. Convert $0.375$ to a fraction in its simplest form.

   [2 marks]

   (b)

   Using your answer to part (a), calculate the volume of orange juice in the 2.5 litre jug, giving your answer in litres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A mathematics teacher is showing students how to convert recurring decimals into fractions using algebraic methods.

   (a)

   A recurring decimal is defined as $x = 0.\dot{4}\dot{5}$ (i.e. $0.454545\ldots$). Show that $x$ can be written as the fraction $\frac{5}{11}$.

   [3 marks]

   (b)

   Using a similar method, convert the recurring decimal $y = 0.\dot{2}7\dot{3}$ (i.e. $0.273273273\ldots$, with block '273' recurring) into a fraction in its simplest form.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A factory quality control manager is analysing the fraction, decimal and percentage of components passing inspection each day, across several stages of production.

   (a)

   A factory produces 4800 identical components per day. $\frac{7}{12}$ of the components pass a quality check on the first attempt. Convert $\frac{7}{12}$ to a decimal, giving your answer to 3 decimal places, and find the number of components that pass on the first attempt.

   [4 marks]

   (b)

   Of the components that failed the first check, $\frac{3}{5}$ are repaired and pass on a second check. Calculate the number of components that pass on the second check, and hence find the total percentage of the day's 4800 components that eventually pass (first or second check), to 1 decimal place.

   [4 marks]

   (c)

   The factory's target is for at least $87.5\%$ of components to eventually pass. Express $87.5\%$ as a fraction in its simplest form, and determine, with working, whether the factory met its target based on the percentage calculated in part (b).

   [5 marks]

   Total for question 4: 13 marks

End of questions