Edexcel IGCSE Math A 1.8.HA bounds problems

Practise bounds-problem questions by choosing which variables need upper or lower bounds in formulae such as D, G, T or acceleration.

Exam points

Choose upper or lower bounds for each variable in formulae before substituting.
Calculate bounds for areas, distances or speeds before giving a rounded final answer.
Use measurements and formula structure to maximise or minimise a length or value.

[Maximum number: 5]

$24 D=\frac{n}{p-q}$
n=10.3 correct to 1 decimal place
p=7.24 correct to 2 decimal places
q=4.39 correct to 2 decimal places
By considering bounds, work out the value of D to a suitable degree of accuracy. Show your working clearly.

Bounds:
$10.25\le n<10.35,\quad 7.235\le p<7.245,\quad 4.385\le q<4.395$
For $D=\frac{n}{p-q}$ :
$D_{\mathrm{UB}}=\frac{10.35}{7.235-4.395}=3.644\ldots$ $D_{\mathrm{LB}}=\frac{10.25}{7.245-4.385}=3.583\ldots$
Both bounds round to:
3.6

Final answer:
$D=3.6\text{ to 1 decimal place}$

B2 for all six correct bounds. M1 for a correct upper or lower bound method. M1 for both bounds. A1 for 3.6.

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1.8.HA Upper- and lower-bound problems question 1