| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Sketch exponential graphs |
| Difficulty | Moderate -0.8 This is a straightforward C2 question testing basic exponential graph sketching (recognizing 0.2^x as a decreasing exponential through (0,1)), routine logarithm manipulation to solve an equation, and identifying that 0.2^x = 5^(-x) represents a reflection in the y-axis. All parts require standard recall and technique with no problem-solving or novel insight. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | Graph with one y-intercept marked as 1 or coordinates (0,1) stated or 'y = 1 when x = 0' | B1 |
| (a) | Correct graph having no other 'crossing point' on either axis. | B1 |
| (b) | \(x \log 0.2 = \log 4\) | M1 |
| (b) | \((x =) -0.861(35...) = -0.861\) (to 3sf) | A1 |
| (c) | Reflection in the y-axis. | E1 |
| Total | 5 |
(a) | Graph with one y-intercept marked as 1 or coordinates (0,1) stated or 'y = 1 when x = 0' | B1 |
(a) | Correct graph having no other 'crossing point' on either axis. | B1 | 2 marks
(b) | $x \log 0.2 = \log 4$ | M1 | OE eg $(x =) \log_{0.2} 4$
(b) | $(x =) -0.861(35...) = -0.861$ (to 3sf) | A1 | 2 marks | Condone > 3sf, rounded or truncated. If use of logarithms not explicitly seen then score 0/2
(c) | Reflection in the y-axis. | E1 | 1 mark | OE. E0 if more than one transformation
| **Total** | **5** |
**OEs for (b):** $-x \log 5 = \log 4$; $x \log 2 = \log 4 + x \log 10$; $x(1 - \log_c 10) = 2$; $(x - 2) \log 2 = x \log 10$
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\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = ( 0.2 ) ^ { x }$, indicating the value of the intercept on the $y$-axis.
\item Use logarithms to solve the equation $( 0.2 ) ^ { x } = 4$, giving your answer to three significant figures.
\item Describe the geometrical transformation that maps the graph of $y = ( 0.2 ) ^ { x }$ onto the graph of $y = 5 ^ { x }$.\\[0pt]
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2016 Q2 [5]}}