Higher November 2024 Paper 2 Q19

EdexcelCurrent spec5 marksUpper & Lower Bounds

19 \(T = \dfrac{w}{a - c}\)

\(w = 435\) correct to the nearest 5
\(a = 9.8\) correct to 2 significant figures.
\(c = 2.5\) correct to 2 significant figures.

By considering bounds, calculate the value of \(T\) to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer. (5)

Mark scheme

Answer	Mark	Mark scheme
60 and reason	B1	for 432.5 or 437.5 or 9.75 or 9.85 or 2.45 or 2.55
	M1	for a correct process to find a bound for \(T\) eg [LB of \(w\)] \(\div\) [UB of \(a\) – LB of \(c\)] where \(432.5 \leqslant\) [LB of \(w\)] \(\lt 435\) and \(9.8 \lt \) [UB of \(a\)] \(\leqslant 9.85\) and \(2.45 \leqslant\) [LB of \(c\)] \(\lt 2.5\) or [UB of \(w\)] \(\div\) [LB of \(a\) – UB of \(c\)] where \(435 \lt \) [UB of \(w\)] \(\leqslant 437.5\) and \(9.75 \leqslant\) [LB of \(a\)] \(\lt 9.8\) and \(2.5 \lt \) [UB of \(c\)] \(\leqslant 2.55\)
	M1	for a correct process to find both LB and UB bound for \(T\) eg [LB of \(w\)] \(\div\) [UB of \(a\) – LB of \(c\)] where \(432.5 \leqslant\) [LB of \(w\)] \(\lt 435\) and \(9.8 \lt \) [UB of \(a\)] \(\leqslant 9.85\) and \(2.45 \leqslant\) [LB of \(c\)] \(\lt 2.5\) and [UB of \(w\)] \(\div\) [LB of \(a\) – UB of \(c\)] where \(435 \lt \) [UB of \(w\)] \(\leqslant 437.5\) and \(9.75 \leqslant\) [LB of \(a\)] \(\lt 9.8\) and \(2.5 \lt \) [UB of \(c\)] \(\leqslant 2.55\)
	A1	(dep on all previous marks) for 58.44(5...) and 60.76(3...) with both values clearly coming from working with correct values
	C1	for 60 from 58.44... and 60.76... and statement that both LB and UB round to 60

Additional guidance

Letter	Given	LB	UB
\(w\)	435	432.5	437.5
\(a\)	9.8	9.75	9.85
\(c\)	2.5	2.45	2.55

Letter	Given	LB	UB
\(w\)	435	432.5	437.5
\(a\)	9.8	9.75	9.85
\(c\)	2.5	2.45	2.55

Letter	Given	LB	UB
\(w\)	435	432.5	437.5
\(a\)	9.8	9.75	9.85
\(c\)	2.5	2.45	2.55

Accept bounds rounded or truncated to at least 4 sf