Higher June 2025 Paper 6 Q5
5 A teacher asks their class which of the following values is the smallest.
\(2^{-1} \qquad 4^{-3} \qquad 10^{-2}\)
One student says
\(2^{-1}\) is the smallest because 2 is smaller than 4 and 10.
Explain the error made by the student in their reasoning and write down the smallest value. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| They have ignored the [negative] powers oe | 1 | See Appendix | |
| \(10^{-2}\) or 0.01 or \(\frac{1}{100}\) | 1 | ||
Appendix: Question 5
| Response | Mark |
|---|---|
| They have ignored the negative powers | 1 |
| That he ignored the small numbers next to the number | 1 implies ignore indices |
| They have ignored the negative powers, it is actually the largest number as it is a fraction | 1bod, not contradicted |
| They have only compared the whole numbers | 1bod |
| They thought the smallest base number would give the smallest answer | 1bod |
| They have treated the powers as positive / They have done \(2^1, 4^3, 10^2\) | 0 not a comment on the student’s reasoning |
| The larger the number, the lower the reciprocal | 0 true but not a comment on the student’s reasoning |
| The power -1 is bigger than the power -2 | 0 not always true |
| \(10^{-2}\) is the smallest as it is closer to 0 | 0 |
| They haven’t simplified the indices / They haven’t calculated them | 0 |
| You need to pick the one with the highest negative power | 0 |
| Assumed all the powers were the same | 0 not if powers are negative |
| They didn’t take the other numbers into account | 0 |
| They have ignored the negative powers, the number with the largest negative power will be smallest | 0 Second part is incorrect |
| The student didn’t calculate the actual value of each number (the three answers given as decimals) | 0 |