Metric units, money and dimensional conversion

(a) 3600 m

1. 1 km = 1000 m.
2. Multiply by 1000: 3.6 $\times$ 1000 = 3600 m.

• B1 Correct answer: 3600 m

(a) $3500$ m

1. $1$ km $= 1000$ m, so $3.5 \times 1000 = 3500$ m.

• B1 The correct answer, $3500$ m.

(b) $2.45$ kg

1. $1000$ g $= 1$ kg, so $2450 \div 1000 = 2.45$ kg.

• B1 The correct answer, $2.45$ kg.

(c) £5.52

1. Write every amount in pounds: 85p £$=$0.85.
2. $3.60 + 0.85 + 1.07 = 5.52$, so £5.52.

• M1 Converting 85p to £0.85 (or everything to pence: $360 + 85 + 107$).
• A1 £5.52 (or 552p).

(a) $23500$ cm²

1. $$2.35\times 100^{2}$$
2. 1 m = 100 cm, so 1 $m^{2}$ = $100^{2}$ = 10 000 cm².
3. 2.35 $\times$ 10 000 = 23 500.

• M1 Establishing $2.35\times 100^{2}$ or an equivalent valid method.
• A1 Correct answer: $23500$ cm²

(a) $1.31$ litres

1. $$8\times 180$$
2. $$2.75-1.44$$
3. Use matching units: eight cups use 8 $\times$ 180 = 1440 ml = 1.44 litres.
4. The amount remaining is 2.75 $-$ 1.44 = 1.31 litres.

• P1 Establishing $8\times 180$ or an equivalent valid method.
• P1 Establishing $2.75-1.44$ or an equivalent valid method.
• A1 Correct answer: $1.31$ litres

(a) $360$

1. Convert the tile side to metres and square it.
   $$0.2^{2}$$
2. Divide the floor area by the area of one tile.
   $$4.5\times 3.2/0.04$$
3. Therefore $360$.

• P1 Convert the tile side to metres and square it.
• P1 Divide the floor area by the area of one tile.
• A1 Correct answer: $360$

(b) $23$

1. Divide by the pack size and round upwards.
   $$360/16$$
2. Therefore $23$.

• M1 Divide by the pack size and round upwards.
• A1 Correct answer: $23$

(a) $120$ litres

1. Convert the first length to centimetres and multiply all three dimensions.
   $$60\times 50\times 40$$
2. Convert cubic centimetres to litres.
   $$120000/1000$$
3. Therefore $120$ litres.

• P1 Convert the first length to centimetres and multiply all three dimensions.
• P1 Convert cubic centimetres to litres.
• A1 Correct answer: $120$ litres

(b) $150$ seconds

1. Convert the capacity to ml and divide by the filling rate.
   $$120\times 1000/800$$
2. Therefore $150$ seconds.

• P1 Convert the capacity to ml and divide by the filling rate.
• A1 Correct answer: $150$ seconds

(a) $720$ cm²

1. One square metre is ten thousand square centimetres.
   $$0.072\times 10000$$
2. Therefore $720$ cm².

• M1 One square metre is ten thousand square centimetres.
• A1 Correct answer: $720$ cm²

(b) $\frac{1}{8}$

1. Compare the two areas in the same units.
   $$90/720$$
2. Therefore $\frac{1}{8}$.

• M1 Compare the two areas in the same units.
• A1 Correct answer: $\frac{1}{8}$

(a) $2$ hours

1. Use centimetres for every length.
   $$120 \times 80 \times 50 = 480\,000 \text{ cm}^3$$
2. Convert to litres.
   $$480\,000 \div 1000 = 480 \text{ litres}$$
3. $$480 \div 4 = 120 \text{ minutes} = 2 \text{ hours}$$

• P1 Finding the volume in one unit: $480\,000\ \text{cm}^3$ or $0.48\ \text{m}^3$.
• P1 Converting to 480 litres.
• P1 Dividing by 4 to get 120 minutes.
• A1 The correct answer, $2$ hours.

(b) 1 hour 20 minutes

1. $\frac{1}{4}$ of 480 litres is 120 litres.
2. $$120 \div 1.5 = 80 \text{ minutes} = 1 \text{ hour } 20 \text{ minutes}$$

• M1 Finding 120 litres and dividing by 1.5.
• A1 1 hour 20 minutes.