Moderate -0.5 This is a standard logarithmic graph question requiring students to recognize that ln y = ln A + n ln x gives a straight line with gradient n and y-intercept ln A. Students must read values from the graph and perform basic calculations. While it requires understanding of the logarithmic transformation technique, it's a routine application with no novel problem-solving required, making it slightly easier than average.
2
\includegraphics[max width=\textwidth, alt={}, center]{9275a3ed-8820-481b-9fc8-28c21b81dbed-2_559_789_513_678}
Two variable quantities \(x\) and \(y\) are related by the equation \(y = A x ^ { n }\), where \(A\) and \(n\) are constants. The diagram shows the result of plotting \(\ln y\) against \(\ln x\) for four pairs of values of \(x\) and \(y\). Use the diagram to estimate the values of \(A\) and \(n\).
Equate estimate of \(\ln y\)-intercept to \(\ln A\)
M1
Obtain value \(A\) between 1.97 and 2.03
A1
Calculate the gradient of the line of data points
M1
Obtain value \(n = 0.25\), or equivalent
A1
Total: [5]
State or imply that $\ln y = \ln A + n \ln x$ | B1 |
Equate estimate of $\ln y$-intercept to $\ln A$ | M1 |
Obtain value $A$ between 1.97 and 2.03 | A1 |
Calculate the gradient of the line of data points | M1 |
Obtain value $n = 0.25$, or equivalent | A1 |
**Total: [5]**
---
2\\
\includegraphics[max width=\textwidth, alt={}, center]{9275a3ed-8820-481b-9fc8-28c21b81dbed-2_559_789_513_678}
Two variable quantities $x$ and $y$ are related by the equation $y = A x ^ { n }$, where $A$ and $n$ are constants. The diagram shows the result of plotting $\ln y$ against $\ln x$ for four pairs of values of $x$ and $y$. Use the diagram to estimate the values of $A$ and $n$.
\hfill \mbox{\textit{CAIE P3 2005 Q2 [5]}}