Real-Life and Conversion Graphs

Find £24 on the horizontal axis. Each small square across is £4.

This time start on the euros axis. Check what one small square is worth on each axis.

Go up from 3 hours to the line, then across to the charge axis.

The gradient tells you how much the vertical quantity changes for each 1 unit across.

Each small square up is not 10 litres. Work out what it is worth first.

Look at where the line meets the vertical axis. How far has the taxi gone there?

1. The fixed charge is paid even for a journey of 0 miles.
2. At 0 miles the line starts at £4 on the charge axis.
3. The fixed charge is £4.

Start on the vertical axis this time, at 40, then go across to the line.

1. Find 40 on the battery charge axis.
2. Go across to the line, then down to the time axis.
3. The battery charge is 40\% after 6 hours.

The first number of a coordinate goes with the horizontal axis and the second with the vertical axis.

1. In (3, 18) the first number, 3, is on the horizontal axis: the time is 3 hours.
2. The second number, 18, is on the vertical axis: the cost is £18.
3. So it costs £18 to hire a bike for 3 hours.

For (b), use your answer to (a): how many lots of 11 lb make 33 lb?

Part (a)

1. 1 kg is 2.2 lb, so 10 kg is 10\times2.2=22 lb.

Part (b)

1. 10 kg is 22 lb, so 5 kg is 11 lb.
2. 33=22+11, so 33 lb is 10+5=15 kg.

Start at £9 on the cost axis. Check what each small square across is worth.

1. Find £9 on the cost axis and go across to the line.
2. Then go down to the weight axis. Each small square across is 0.25 kg.
3. Kai buys 1.5 kg of cherries.

Change one of the distances so that both are in the same units.

1. Change 40 km into miles: go across from 40 on the kilometres axis to the line, then down.
2. 40 km is 25 miles.
3. 25 miles is more than 22 miles, so the 40 km walk is longer.

£200 is off the graph. Which amount on the graph could you multiply up to get £200?

1. The graph only goes up to £50, so change £50 first.
2. Go up from £50 to the line, then across: £50 is 65 dollars.
3. £200 is 4\times £50, so £200 is 4\times65=260 dollars.

For (b), count on to the next hour first, then add the minutes that are left.

Part (a)

1. Go across from 30 cm to the line, then down to the time axis.
2. Each small square across is 5 minutes. It takes 45 minutes.

Part (b)

1. 10 minutes after 10:50 is 11:00.
2. There are 45-10=35 more minutes, so the pool is full at 11:35.

Find how much the volume goes up, and how many minutes that takes. Don't forget the water that was there at the start.

1. At 0 minutes there are 10 litres. At 8 minutes there are 90 litres.
2. In 8 minutes the volume goes up by 90-10=80 litres.
3. 80\div8=10 litres per minute.

Each small square up is £20. For (b), the joining fee is only paid once.

Part (a)

1. The joining fee is the cost at 0 months, where the line meets the cost axis.
2. The joining fee is £40.

Part (b)

1. After 12 months the total cost is £280.
2. Take off the joining fee: £280 - £40 = £240 for 12 months.
3. £240 \div12= £20 for each month.

Work out the sale price in euros first, then use the graph to change it into pounds.

Part (a)

1. 30\% of €100 is €30, so the sale price in France is €100 - €30 = €70.
2. On the euros axis, €70 is halfway between €60 and €80. Trace across to the line, then down to the pounds axis.

3. Each small interval on the pounds axis is £4. The guide is two intervals beyond £48, so it reads £48 + £8 = £56.
4. £56 is less than £60, so the trainers are cheaper in France.

Part (b)

1. The trainers cost £56 in France and £60 in the UK.
2. £60 - £56 = £4 cheaper in France.

Find where the cost is £110, then think about whole numbers of hours. Rounding to the nearest hour is not enough.

1. Go across from £110 to the line, then down. The line reaches £110 between 5 and 6 hours.
2. Check with the graph: 5 hours costs £100 and 6 hours costs £115.
3. £115 is more than £110, so the greatest number of whole hours is 5.

For (b), the steeper part of the graph shows both taps together.

Part (a)

1. In the first 10 minutes the volume goes from 0 to 30 litres.
2. 30\div10=3 litres per minute.

Part (b)

1. From 10 to 20 minutes the volume goes from 30 to 110 litres: 80 litres in 10 minutes.
2. With both taps on, 80\div10=8 litres a minute go in.
3. Tap A gives 3 litres a minute of that, so tap B gives 8-3=5 litres per minute.

Company B's charge is not on the graph: work it out from the words.

Part (a)

1. Go up from 7 hours to the line, then across to the cost axis.
2. Company A charges £110.

Part (b)

1. 7\times £13 = £91.
2. £25 + £91 = £116.

Part (c)

1. Company A charges £110 and Company B charges £116.
2. £116 - £110 = £6, so Company A is cheaper by £6.

For (b), the number of painters must be a whole number, and the time must not go over 5 hours.

Part (a)

1. Go up from 3 painters to the graph, then across to the time axis.
2. It takes 8 hours.

Part (b)

1. Go across from 5 hours. The curve is at 5 hours between 4 and 5 painters.
2. 4 painters take 6 hours, which is too long. 5 painters take less than 5 hours.
3. You can't have part of a painter, so the least number is 5 painters.