the mass of the empty plane is 800 kg, to the nearest 100 kg
the mass of fuel is 190 kg, to the nearest 5 kg
the mass of the passengers is 163 kg, to the nearest kg
The total mass of a plane is calculated by adding these three masses.
The maximum mass for the plane to take off safely is 1200 kg
Can this plane definitely take off safely?
Tick a box.
Yes
No
Show working to support your answer. [4 marks]
(b) A different plane travels 1250 miles in 2 hours 30 minutes at a constant speed.
On the grid, draw a speed/time graph to represent this information. [3 marks]
Mark scheme (a)
Answer
Mark
Comments
Alternative method 1: uses the upper bounds
750 or 850 or 187.5 or 192.5 or 162.5 or 163.5
B1
condone 849.99… for 850
condone 192.49… for 192.5
condone 163.49… for 163.5
850 and 192.5 and 163.5
B1
(800, 900] + (190, 195] + (163, 164]
M1
1206 and No
A1
oe 6 kg too heavy and No
Alternative method 2: uses other values
Correct sum of three possible values that exceeds 1200 and No
B4
possible values must lie between the bounds, on the lower bound or on the upper bound eg \(849 + 192 + 163 = 1204\) and No
Additional guidance
Units not required
850 and 195 and 163.5 with answer 1208.5
B1B0M1A0
900 and 195 and 164 with answer 1259
B0B0M1A0
There are no part marks for Alt method 2
Mark to the Alt method which favours the student eg 849 and 192 and 163.5 with answer 1204.5 and ‘No’ could score B1B0M1A0 using Alt method 1, but scores B4 using Alt method 2
\(845 + 194 + 163 = 1202\) and No does not score using either Alt method
Mark scheme (b)
Answer
Mark
Comments
(Speed =) 500
B1
implied by 500 as highest point plotted or marked accept 8.33… with correct units miles per minute stated or implied
Vertical axis labelled ‘Speed’ with a linear scale to at least their 500 and Horizontal axis labelled ‘Time’ with a linear scale to at least 2 hours 30 minutes or 150 minutes
B1ft
ft their 500 which must not be 1250 accept their speed as the only value on the vertical axis and 2 hours 30 minutes as the only value on the horizontal axis ignore all units shown on their graph
Horizontal line from (0, their 500) stopping at (2 hours 30 minutes, their 500) or (150 minutes, their 500)
B1ft
ft their 500 which must not be 1250 ignore any vertical line at 2 hours 30 minutes
Additional guidance
‘Speed’ and ‘Time’ are the only acceptable labels
Use of a distance/time graph is a maximum of B1 for 500 seen
1250/150 = 8.33… miles per minute and correctly plotted with correct labelling and scales
B1B1ftB1ft
\(1250 \div 2.3 = 543\ldots\), with horizontal line from (0, 543) to (2 hours 30 minutes, 543) with correct labelling and scales
