June 2024 Paper 1 Q5
5
(a) Make \(y\) the subject of the formula \(\log_{10}(y-k) = x\log_{10}2\), where \(k\) is a positive constant. [2]
(b) Sketch the graph of \(y\) against \(x\). [3]
| Scheme | Marks | AO |
|---|---|---|
| \(\log_{10}(y-k) = \log_{10}2^x\) | M1 | 1.1 |
| \(y = k + 2^x\) | A1 | 1.1 |
| [2] |
Notes
M1: Correct use of one of the laws of logs – award if \(2^x\) seen or if \((y-k) = 10^{x\log 2}\)
A1: LHS must be \(y =\)
Allow \(y = k + 10^{x\log 2}\)
| Scheme | Marks | AO |
|---|---|---|
 | B1 B1 B1 | 1.2 1.1 1.1 |
| [3] |
Notes
B1: General shape correct. Positive and negative values of \(x\) should be seen used. FT their exponential (a)
B1: \(y\)-intercept at \(k+1\) on positive \(y\)-axis. FT their exponential (a) provided in terms of \(k\)
B1: Asymptote at \(k\). Horizontal line need not been seen provided the intention is clear