| Date | May 2011 | Marks available | 2 | Reference code | 11M.1.sl.TZ1.15 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Calculate | Question number | 15 | Adapted from | N/A |
Question
Consider the function \(f(x) = 1.25 - {a^{ - x}}\) , where a is a positive constant and \(x \geqslant 0\). The diagram shows a sketch of the graph of \(f\) . The graph intersects the \(y\)-axis at point A and the line \(L\) is its horizontal asymptote.
Find the \(y\)-coordinate of A .
The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Calculate the value of \(a\) .
The point \((2{\text{, }}1)\) lies on the graph of \(y = f(x)\) . Write down the equation of \(L\) .
Markscheme
\(y = 1.25 - {a^0}\) \(1.25 - 1\) (M1)
\(= 0.25\) (A1) (C2)
Note: Award (M1)(A1) for \((0{\text{, }}0.25)\) .
[2 marks]
\(1 = 1.25 - {a^{ - 2}}\) (M1)
\(a = 2\) (A1) (C2)
[2 marks]
\(y = 1.25\) (A1)(A1) (C2)
Note: Award (A1) for \(y =\) “a constant”, (A1) for \(1.25\).
[2 marks]
Examiners report
Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).
Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).
Very few candidates showed working and subsequently lost marks due to this. Many candidates seemed to forget that \({a^0} = 1\) and not \(0\).
