CAIE IGCSE Additional Math 7.4 Transform Relationships to Straight Line Form Questions

Practise Cambridge IGCSE Additional Mathematics by transforming variables to straight-line graphs, estimating constants and predicting values.

Exam points

Linearise exponential and power relationships by plotting transformed variables.
Use gradient and intercept to estimate model constants and predict unknown values.
Interpret logarithmic graph scales, straight-line equations and stated rounding requirements.

[Maximum number: 4]

Variables x and y are such that when $\ln y$ is plotted against x, a straight-line graph is obtained.
The line passes through the points $(1,\ln 15)$ and $(2,\ln 75)$ .
Show that $y=Ab^x$ , where A and b are integers to be found.

$\ln y=mx+c$ soi
Correct method to find m, e.g. $m=\frac{\ln 75-\ln 15}{2-1}$ oe, or $-m=\ln 15-\ln 75$ oe, or $m=\ln 5$ oe.
M1 FT their c if necessary.
Correct method to find c, e.g. $\ln 15=(\text{their }\ln 5)(1)+c$ oe, $\ln 75=(\text{their }\ln 5)(2)+c$ oe, or $c=\ln 3$ oe, soi.
M1 FT their m if necessary.
$y=3\times 5^x$ nfww, mark final answer

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CAIE IGCSE Additional Math 7.4 Transform Relationships to Straight Line Form Questions question 1