\(x = 8.6\) and \(y = 3.2\), each correct to \(1\) decimal place. Calculate the lower bound of \(x - y\).
Question 1 Report
\(x = 8.6\) and \(y = 3.2\), each correct to \(1\) decimal place.
Calculate the lower bound of \(x - y\).
Answer Details
A value given to \(1\) decimal place lies within half of \(0.1\), that is \(0.05\), of the stated figure.
So \(8.55 \leqslant x \lt 8.65\) and \(3.15 \leqslant y \lt 3.25\) [M1].
For a subtraction, the result is smallest when the first number is as small as possible and the number being taken away is as large as possible. That means using the lower bound of \(x\) with the upper bound of \(y\):
\(8.55 - 3.25\) [M1] \(= 5.3\) [A1] cao.
Using \(8.55 - 3.15 = 5.4\) is the common error; that pairing gives neither bound of the difference. As a contrast, the upper bound of \(x - y\) would be \(8.65 - 3.15 = 5.5\), so the true value of \(x - y\) lies between \(5.3\) and \(5.5\).
Exam takeaway: for addition pair like with like, but for subtraction and division the bounds must be crossed over.
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