Question 1
3 marksTable shows how a blockage (%) in a coronary artery affects blood flow (cm3/min):
0% ? 100
10% ? 64
20% ? 42
50% ? 8
80% ? 2
Estimate the blood flow (in cm3/min) when the coronary artery is 35% blocked. Show clearly how you work out your answer.
Model answer
Approximately 25 cm3/min. Linear interpolation between 20% (42) and 50% (8): change = 8 - 42 = -34 over 30% ? slope ˜ -34/30 ˜ -1.13 cm3·min-1 per 1%. At 35% (15% above 20%): 42 + 15×(-1.13) ˜ 42 - 17 ˜ 25 cm3/min.
Explanation
Use linear interpolation between the two nearest table points. Between 20% and 50% blockage blood flow falls from 42 to 8 (a drop of 34) over 30 percentage points, giving a fall of about 1.13 cm3/min per 1% blockage. Thirty-five percent is 15% above 20%, so the flow is about 42 - 15×1.13 ˜ 25 cm3/min.
Mark scheme
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1 mark
Identify the correct interval to interpolate (between 20% and 50%)
Award if student states they use the 20%–50% pair or uses values 42 and 8.
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1 mark
Calculate gradient / rate of change: (8 - 42) / (50 - 20) ˜ -34/30 ˜ -1.13 cm3·min-1 per 1%
Allow equivalent correct fractions or decimals.
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1 mark
Compute flow at 35% ˜ 42 + 15×(-1.13) ˜ 25 cm3/min (allow ˜ 24–26)
Accept answers ˜24–26 cm3/min with supporting working.