| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | log(y) vs x: convert and interpret |
| Difficulty | Standard +0.3 This is a standard data transformation question requiring students to linearise an exponential relationship using logarithms, plot points, identify an outlier, and find parameters from a line of best fit. While it involves multiple steps (7 marks total), each component is routine AS-level work: taking logs is straightforward calculation, plotting is mechanical, the outlier is visually obvious, and finding k and b from gradient/intercept follows a standard method taught explicitly in the specification. Slightly easier than average due to the structured guidance through each step. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form2.02c Scatter diagrams and regression lines |
| \(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(y\) | 14 | 45 | 130 | 1100 | 1300 | 3400 |
| \(\log_{10} y\) |
| Answer | Marks |
|---|---|
| 10(a) | Obtains (at least four) correct |
| Answer | Marks | Guidance |
|---|---|---|
| plotted | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Plots all points correctly | AO1.1b | A1 |
| (b) | Identifies y 1100 and gives | |
| correct reason | AO2.2b | B1 |
| Answer | Marks |
|---|---|
| (c) | Uses laws of logs. |
| Answer | Marks | Guidance |
|---|---|---|
| logs were used there) | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| gradient | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 0.45< ‘their’ gradient < 0.51 | AO1.1b | A1F |
| Answer | Marks | Guidance |
|---|---|---|
| 0.6 ‘their’ intercept 0.8 | AO1.1b | A1F |
| Total | 7 | |
| Q | Marking Instructions | AO |
Question 10:
--- 10(a) ---
10(a) | Obtains (at least four) correct
log y values, in table or
10
plotted | AO1.1a | M1 | (1, 1.1) (2, 1.7) (3, 2.1) (4, 3.0)
(5, 3.1) (6, 3.5)
(Points above plotted on grid)
Plots all points correctly | AO1.1b | A1
(b) | Identifies y 1100 and gives
correct reason | AO2.2b | B1 | (4, 1100), as it is not on the line that
the other points are close to
(c) | Uses laws of logs.
(May earn in part (a) if laws of
logs were used there) | AO1.1a | M1 | log y log kxlog b
10 10 10
Vertical intercept c = 0.68 (=log k)
10
Therefore
from intercept: k 100.68
Gradient m = 0.48 = log b
10
Therefore
from gradient:b100.48
k = 4.8
b = 3.0
Draws straight line
and
calculates/measures the vertical
intercept c and attempts 10c
or
calculates/measures gradient m
and attempts 10m
Alternatively
uses regression line from
calculator to get intercept and
gradient | AO1.1a | M1
Finds correct value of b from
‘their’ gradient, provided
0.45< ‘their’ gradient < 0.51 | AO1.1b | A1F
Finds correct value of k from
‘their’ intercept, provided
0.6 ‘their’ intercept 0.8 | AO1.1b | A1F
Total | 7
Q | Marking Instructions | AO | Marks | Typical SolutionA student conducts an experiment and records the following data for two variables, $x$ and $y$.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$y$ & 14 & 45 & 130 & 1100 & 1300 & 3400 \\
\hline
$\log_{10} y$ & & & & & & \\
\hline
\end{tabular}
The student is told that the relationship between $x$ and $y$ can be modelled by an equation of the form $y = kb^x$
\begin{enumerate}[label=(\alph*)]
\item Plot values of $\log_{10} y$ against $x$ on the grid below. [2 marks]
\includegraphics{figure_10}
\item State, with a reason, which value of $y$ is likely to have been recorded incorrectly. [1 mark]
\item By drawing an appropriate straight line, find the values of $k$ and $b$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 Q10 [7]}}