(a) Below is part of the map showing City A and City B.
Heidi is planning to walk from City A to City B for charity.
Heidi measures the straight-line distance on the map from City A to City B accurately as 5 cm. Heidi says she will walk from City A to City B at an average speed of 2.5 km / h for 10 hours per day.
(i) Use this information to work out how many days Heidi needs to complete the walk from City A to City B. [4]
(ii) Explain why the information used in part (i) is likely to give an underestimate for the number of days Heidi needs to complete the walk. [1]
(b) Yoshi writes the scale of the map, 1 cm represents 150 km, as the ratio 1 : 150.
Explain Yoshi’s error and write the scale correctly in the form 1 : \(n\). [2]
Mark scheme (a)
Answer
Marks
Part marks and guidance
(i) 30 nfww
4
Not from 150 ÷ 5 A correct answer in working, subsequently spoilt, scores max M1M1
M1 for 5 × 150 implied by 750 [km]
M2 for their 750 ÷ (2.5 × 10) oe or M1 for 2.5 × 10 implied by 25
Their 750 from attempt at 5 × 150; condone 150 for their 750
OR
M1 for 5 × 150 implied by 750 [km]
M2 for their 750 ÷ 2.5 ÷ 10 oe or M1 for their 750 ÷ 2.5 implied by 300
Their 750 from attempt at 5 × 150; condone 150 for their 750
(ii) Correct reason indicating roads/paths unlikely to be straight oe
1
See Appendix
Appendix: Question 4(a)(ii)
Reason
Mark
Reason
In real life Heidi will not be able to walk in a straight line
1
Implies distance increases
Roads aren’t straight
1
Implies distance increases
She doesn’t consider buildings in the way of the straight line distance
1
Implies “not a straight line”
The km are estimated as 750 where it is not in real life
0
Correct but does not reference using a direct distance
She may have to go a different route
0
Doesn’t say that the overall distance may be greater (than calculated)
Do not accept
Average speed is just an estimate
0
Do not address error in method of using straight-line distance
Because it’s a decimal so doesn’t give an exact number of days
0
Do not address error in method of using straight-line distance
Because it seems unrealistic
0
Do not address error in method of using straight-line distance
She will get tired/slow down/toilet stops
0
Do not address error in method of using straight-line distance
There is not enough information
0
Do not address error in method of using straight-line distance
Rounded down
0
Do not address error in method of using straight-line distance
Mark scheme (b)
Answer
Marks
Part marks and guidance
The units are not the same oe
1
1 : 15 000 000
1
See Appendix eg should have multiplied by 100 000 or one is cm and the other is km Condone: • poorly placed zero separators e.g. 150, 000, 00 • correct other forms • inclusion of units
Appendix: Question 4(b)
Reason
Mark
Reason
Kilometres is not the same as cm
1
BOD recognises the different units
Not converting km to cm
1
Not converting to the same units
1
“Not converting the units” is not enough
The 1 and 150 aren’t both cm
1
BOD implies different units
They are in different measurements
1
BOD condone “measurements” oe for “units”
He hasn’t used units making it seem 1 cm = 150 cm
1
BOD the missed out “the same” as explained by the example. The words before 1 cm...are not enough
If it was 1 : 150 then 1 cm would be 1.5 metres
1
Shows statement is incorrect
There are 1000 cm in 1 km so he didn’t convert
1
Incorrect factor but recognises no conversion and does link cm and km implying “between them” (The incorrect factor penalised by wrong 15 000 000)
You can’t have two different measurements in the same ratio
1
BOD condone “measurements” oe for “units”
It needs to be in cm
1
BOD “The ratio” needs to be “all” in cm
He did not convert the km to cm correctly
1
BOD references km and cm and conversion
He did not use scale correctly and so has made 150 cm and not 150 km
1
BOD Implies not in same units
He wrote it as 1 cm to 150 cm not km
1
BOD Implies not in same units
Because cm and km are / are not the same scale
0
Incorrect use of scale and the meaning is unclear
He did not convert the units
0
Needs to say “to the same units”
He undervalues the 150 km in the ratio
0
Doesn’t explain how or why
It doesn’t show the units so it would be inaccurate
