Proven Potential TMUA Sample Paper 1 · Question 2

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Proven Potential TMUA Sample Paper 1 · Q2

Paper 1ProbabilityGeometryFunctions & graphs

The function $f(x)$ is defined piecewise by

f(x)=\begin{cases}x^2,&0\le x<\sqrt[3]{k+1},\\ \sqrt{x},&\sqrt[3]{k+1}\le x\le1,\\0,&\text{otherwise}.\end{cases}

The probability that the variable lies between two values of $x$ is given by the area under the graph of $f(x)$ between those values. Given that the total probability is 1, find the value of $k$ .

k=0

k=2+2\sqrt2

k=2-2\sqrt2

k=\sqrt2

k=-\sqrt2

k=8

k=2

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