1. 1
   A paint mixer combines blue and yellow paint in the ratio $5:3$ to make green paint. A customer orders $32$ litres of green paint.

   (a)

   (a) How many litres of blue paint are needed to make the $32$ litres of green paint?

   [1 mark]

   • A20 litres
   • B12 litres
   • C15 litres
   • D24 litres

   (b)

   (b) Express the volume of blue paint as a fraction of the volume of yellow paint.

   [1 mark]

   • A$\frac{3}{5}$
   • B$\frac{5}{3}$
   • C$\frac{5}{8}$
   • D$\frac{3}{8}$

   (c)

   (c) If only $9$ litres of yellow paint are available, what is the maximum volume of green paint (blue and yellow in the ratio $5:3$) that can be made?

   [1 mark]

   • A45 litres
   • B15 litres
   • C24 litres
   • D9 litres

   Total for question 1: 3 marks

2. 2
   A metal cube has volume $64$ cm$^3$ and mass $563.2$ g. Separately, a hydraulic press applies a force of $450$ N over a contact area of $0.03$ m$^2$.

   (a)

   (a) Calculate the density of the metal, in g/cm$^3$.

   [2 marks]

   (b)

   (b) Calculate the pressure applied by the press, in Pa.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A supermarket sells olive oil in two sizes: a $750$ ml bottle for $£6.30$, and a $1.5$ litre bottle for $£11.70$.

   (a)

   (a) Show that the larger bottle offers better value for money per ml.

   [3 marks]

   (b)

   (b) A shopper needs exactly $3$ litres of oil. Show that buying $2$ large bottles is cheaper than buying $1$ large bottle and $2$ small bottles (which also gives exactly $3$ litres).

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A runner mixes an electrolyte drink from powder and water in the ratio $1:9$ by volume, making up bottles of $600$ ml each for a race. Separately, race organisers record that she completes the first $8$ km of the race in $42$ minutes, then completes the remaining $13.4$ km in $67$ minutes.

   (a)

   (a) The runner needs to prepare $9$ bottles for the race. Calculate the total volume of powder and the total volume of water required.

   [4 marks]

   (b)

   (b) Calculate the runner's average speed, in km/h, for the whole race (total distance $\div$ total time).

   [4 marks]

   (c)

   (c) Calculate the runner's pace (in min/km) for each of the two sections separately, and state which section she ran faster.

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A map has a scale of $1:25{,}000$. On the map, the distance between two villages is $8.4$ cm.

   (a)

   (a) What is the actual distance between the two villages, in km?

   [1 mark]

   • A21 km
   • B210 km
   • C0.21 km
   • D2.1 km

   (b)

   (b) A field has an actual area of $6.25$ km$^2$. What would its area be on this map, in cm$^2$?

   [1 mark]

   • A100 cm$^2$
   • B10 cm$^2$
   • C1{,}000 cm$^2$
   • D0.01 cm$^2$

   (c)

   (c) A second map uses a scale of $1:50{,}000$. What distance on this map would represent the same $2.1$ km real distance between the villages?

   [1 mark]

   • A8.4 cm
   • B4.2 cm
   • C2.1 cm
   • D16.8 cm

   Total for question 5: 3 marks

6. 6
   A courier is paid $£0.35$ per parcel delivered, plus a fixed rate of $£12$ per hour. In one $6$-hour shift she delivers $140$ parcels.

   (a)

   (a) Calculate the courier's total pay for the shift.

   [2 marks]

   (b)

   (b) Calculate her overall rate of pay, in £ per hour, for this shift (total pay $\div$ hours worked), correct to 2 decimal places.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   The cost, $C$ (in £), of hiring a cement mixer is directly proportional to the number of days, $d$, it is hired for. Hiring for $4$ days costs $£86$.

   (a)

   (a) Find the formula for $C$ in terms of $d$, and use it to find the cost of hiring the mixer for $11$ days.

   [3 marks]

   (b)

   (b) A customer hires the mixer for $13$ days and is quoted $£275.50$. Show that this quote is not consistent with the direct proportion established in part (a), and state the correct cost.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   A delivery van travels from its depot to a client, a distance of $180$ km, at an average speed of $60$ km/h. On the return journey, due to traffic, the average speed is only $45$ km/h. The van's diesel is blended with an additive in the ratio $2:23$ (additive : diesel) by volume, and its tank holds $60$ litres of the blended fuel.

   (a)

   (a) Calculate the total time taken for the round trip, and hence find the average speed for the whole round trip (total distance $\div$ total time), correct to 2 decimal places.

   [4 marks]

   (b)

   (b) Calculate the volume of additive and the volume of diesel in a full $60$-litre tank of the blended fuel.

   [4 marks]

   (c)

   (c) The van uses fuel at a rate of $0.28$ litres per km. Using the round-trip distance from part (a), calculate the total fuel used, and determine whether one full $60$-litre tank is enough for the round trip.

   [5 marks]

   Total for question 8: 13 marks

End of questions