DP Mathematics: Applications and Interpretation Questionbank

AHL 2.10—Scaling large numbers, log-log graphs
Description
[N/A]Directly related questions
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EXN.1.AHL.TZ0.12c.i:
Use your answer to part (b) to write down the value of nn to the nearest integer.
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EXN.1.AHL.TZ0.12b:
Find the equation of the least squares regression line of log10 Plog10P against log10 dlog10d.
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EXN.1.AHL.TZ0.12c.ii:
Find an expression for PP in terms of dd.
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EXN.1.AHL.TZ0.12a:
Explain why this graph indicates that PP is inversely proportional to dndn.
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21N.1.AHL.TZ0.12a:
Use the data in the second table to find the value of mm and the value of bb for the regression line, ln x=m(ln d)+blnx=m(lnd)+b.
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21N.1.AHL.TZ0.12b:
Assuming that the model found in part (a) remains valid, estimate the percentage of trees in stock when d=25d=25.
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SPM.1.AHL.TZ0.18:
The rate, AA, of a chemical reaction at a fixed temperature is related to the concentration of two compounds, BB and CC, by the equation
A=kBxCyA=kBxCy, where xx, yy, k∈R.
A scientist measures the three variables three times during the reaction and obtains the following values.
Find x, y and k.
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EXM.1.AHL.TZ0.13a:
Find the equation of the straight line, giving your answer in the form lnm=ap+b, where a,b∈R.
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EXM.1.AHL.TZ0.15c.i:
find the value of a and of b.
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EXM.1.AHL.TZ0.13b.ii:
the value of m when p=0.
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EXM.1.AHL.TZ0.13b.i:
a formula for m in terms of p.
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EXM.1.AHL.TZ0.15b:
Find the equation of the regression line of ln(T−25) on t.
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EXM.1.AHL.TZ0.14:
It is believed that two variables, v and w are related by the equation v=kwn, where k,n∈R. Experimental values of v and w are obtained. A graph of lnv against lnw shows a straight line passing through (−1.7, 4.3) and (7.1, 17.5).
Find the value of k and of n.
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EXM.1.AHL.TZ0.15a:
Show that ln(T−25)=bt+lna.
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EXM.1.AHL.TZ0.15c.ii:
predict the temperature of the metal rod after 3 minutes.
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22M.2.AHL.TZ2.4c:
(i) the gradient of this line in terms of c;
(ii) the y-intercept of this line in terms of A.
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22M.2.AHL.TZ2.4d:
Find the equation of the regression line for ln k on 1T.
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EXM.3.AHL.TZ0.7a.i:
Use the trapezoidal rule to find an estimate for the area.
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EXM.3.AHL.TZ0.7c.ii:
Find the value of this area.
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EXM.3.AHL.TZ0.7b.ii:
Write down the coefficient of determination.
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EXM.3.AHL.TZ0.7a.ii:
With reference to the shape of the graph, explain whether your answer to part (a)(i) will be an over-estimate or an underestimate of the area.
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EXM.3.AHL.TZ0.7d.i:
Show that lny=qx+lnp.
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EXM.3.AHL.TZ0.7d.iv:
Hence find the area enclosed by the exponential function, the x-axis, the y-axis and the line x=4.4.
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EXM.3.AHL.TZ0.7b.i:
Use all the coordinates in the table to find the equation of the least squares cubic regression curve.
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EXM.3.AHL.TZ0.7d.iii:
By finding the equation of a suitable regression line, show that p=1.83 and q=0.986.
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EXM.3.AHL.TZ0.7c.i:
Write down an expression for the area enclosed by the cubic function, the x-axis, the y-axis and the line x=4.4.
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EXM.3.AHL.TZ0.7d.ii:
Hence explain how a straight line graph could be drawn using the coordinates in the table.