4MA0 Higher January 2015 Paper 3 Q15
15
Diagram NOT accurately drawn
Zane buys mineral water in large bottles and in small bottles.
The large bottles are mathematically similar to the small bottles.
Large bottles have a height of 32 cm and a volume of 2000 cm3
Small bottles have a volume of 500 cm3
Work out the height of a small bottle.
Give your answer correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
\(\left(\dfrac{h}{32}\right)^3 = \dfrac{500}{2000}\) or \(\sqrt[3]{\dfrac{500}{2000}}\) oe or \(\sqrt[3]{\dfrac{2000}{500}}\) or \(\dfrac{2000}{500}\) or 4 or \(\dfrac{500}{2000}\) or \(\dfrac{1}{4}\) or 500 : 2000 oe or 2000 : 500 oe | M1 |
| Eg \((h =)\sqrt[3]{\dfrac{500}{2000} \times 32^3}\) or \(\sqrt[3]{\dfrac{1}{4} \times 32768}\) or \(\sqrt[3]{8192}\) or \(\sqrt[3]{\dfrac{1}{4}} \times 32\) oe | M1 |
| 20.2 | A1 |
| (3 marks) |
Notes
M1: Accept 1.58(7401052......) or 0.629(9605249......) rounded or truncated to at least 3 SF
M1: for any correct expression for \(h\).
A1: for awrt 20.2