Bounds for the area of a square tile
Bounds for the area of a square tile
IP 1
7 marks
The side of a square tile is measured as \(8.4\text{ cm}\), correct to \(1\) decimal place.
- Write down the lower and upper bounds of the side length.[1]
- Find the lower and upper bounds of the area of the tile.[2]
- Explain why the area cannot be given as \(70.6\text{ cm}^2\) correct to \(3\) significant figures, and state the area to the greatest accuracy that is certain.[2]
- The side of another square is \(n\text{ cm}\), correct to the nearest whole number, where \(n\ge1\). Show that its true area differs from \(n^2\text{ cm}^2\) by less than \(\left(n+\dfrac14\right)\text{ cm}^2\).[2]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \(8.35\text{ cm}\le\text{side}<8.45\text{ cm}\) (b) \(69.7225\text{ cm}^2\le\text{area}<71.4025\text{ cm}^2\) (c) bounds give \(69.7\) and \(71.4\) to \(3\) s.f.; area \(=70\text{ cm}^2\) to \(1\) s.f. (d) \(\left(n+\dfrac12\right)^2-n^2=n+\dfrac14\) and \(n^2-\left(n-\dfrac12\right)^2=n-\dfrac14\)
Need help? Join our IP Math tuition programme.
Learn more