Numeracy Higher June 2018 Unit 1 Q11
11. During a chemistry experiment, it was found that a particle lost \(\boldsymbol{\dfrac{3}{4}}\) of its mass every second.
The initial mass of the particle was 160 mg.
(a) Calculate the mass of the particle after 4 seconds.
Circle your answer. [1]
Circle your answer. [1]
2·5 mg 0·15625 mg 40 mg 0·625 mg 0·875 mg
(b) Write down a formula for the mass \(m\), in milligrams, of the particle after \(t\) seconds. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 0·625 mg | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(m = 160 \times 0{\cdot}25^{t}\) or \(m = \dfrac{160}{4^{t}}\) or \(m = 160 \times (^{1}/_{4})^{t}\) or equivalent | B3 | B2 for \(160 \times 0{\cdot}25^{t}\) or \(\dfrac{160}{4^{t}}\) or \(160 \times (^{1}/_{4})^{t}\) or or \(m = (160 \times 0{\cdot}25)^{t}\) or \(m = 160 \times \dfrac{1^{t}}{4}\) B1 for sight of \(0{\cdot}25^{t}\) or \(4^{t}\) or \((^{1}/_{4})^{t}\) or \(160 \times \dfrac{1^{t}}{4}\) or \((160 \times 0{\cdot}25)^{t}\) B0 for \(\dfrac{1^{t}}{4}\) only If no marks awarded: SC2 for \(m = 160{\times}0{\cdot}75^{t}\) or \(m = 160{\times}(^{3}/_{4})^{t}\) SC1 for \(160{\times}0{\cdot}75^{t}\) or \(160{\times}(^{3}/_{4})^{t}\) or \(m = 160 \times \dfrac{3^{t}}{4}\) |