Higher June 2025 Paper 2 Q16
16 Two jars are mathematically similar.
(a) Work out the height, \(h\) cm, of the smaller jar.
Give your answer correct to 1 decimal place. (4)
Give your answer correct to 1 decimal place. (4)
The surface area of the smaller jar is \(A\) cm2
The surface area of the larger jar is \(pA\) cm2
(b) Find the exact value of \(p\). (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 4.9 | P1 | for beginning to work with scale factors eg \(\left(\dfrac{h}{12}\right)^3\) or \(\left(\dfrac{12}{h}\right)^3\) or \(\dfrac{90}{1350}\ \left(= \dfrac{1}{15}\right)\) or \(\dfrac{1350}{90}\ (= 15)\) or 90 : 1350 oe |
| P1 | for equating scale factors eg \(\left(\dfrac{h}{12}\right)^3 = \dfrac{90}{1350}\) or \(\left(\dfrac{12}{h}\right)^3 = \text{``}15\text{''}\) or for finding the linear scale factor, eg \(\sqrt[3]{\dfrac{90}{1350}}\) or \(\sqrt[3]{\text{``}15\text{''}}\ (= 2.46(6\ldots))\) | |
| P1 | for a complete method eg \(\sqrt[3]{12^3 \times \dfrac{90}{1350}}\) or \(12 \times \sqrt[3]{\dfrac{90}{1350}}\) or \(\dfrac{12}{\text{``}\left(\sqrt[3]{\text{``}15\text{''}}\right)\text{''}}\) | |
| A1 | for answers in the range 4.8 to 4.9 |
| Answer | Mark | Mark scheme |
|---|---|---|
| \((15)^{\frac{2}{3}}\) | B1 | for \(15^{\frac{2}{3}}\) or \(\left(\sqrt[3]{15}\right)^2\) or \(\sqrt[3]{15^2}\) or \(225^{\frac{1}{3}}\) |
Additional guidance
If given in an acceptable form, then given as a decimal, isw and award