1.2 Algebra

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Question 26

A physical experiment measures the spectral intensity $I$ of a pulsed laser relative to its frequency shift $s$ . The measurements are modeled by the parametric equations

\sin t

\frac{18}{7 + \cos 2t}

where $−π2≤t≤π2-\frac{\pi}{2} \le t \le \frac{\pi}{2}$ .

Show that the relationship between intensity and frequency shift can be expressed as

\frac{144}{(13 - s)(s + 3)} \quad p \le s \le q

where $p$ and $q$ are constants to be found.

[5]

Hence, determine a Cartesian equation for this relationship in the form

\frac{a}{s + b} + \frac{c}{s + d} \quad p \le s \le q

where $a, b, c$ and $d$ are constants.

[3]

1.2 Algebra

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Question 26

A physical experiment measures the spectral intensity $I$ of a pulsed laser relative to its frequency shift $s$ . The measurements are modeled by the parametric equations

\sin t

\frac{18}{7 + \cos 2t}

where $−π2≤t≤π2-\frac{\pi}{2} \le t \le \frac{\pi}{2}$ .

Show that the relationship between intensity and frequency shift can be expressed as

\frac{144}{(13 - s)(s + 3)} \quad p \le s \le q

where $p$ and $q$ are constants to be found.

[5]

Hence, determine a Cartesian equation for this relationship in the form

\frac{a}{s + b} + \frac{c}{s + d} \quad p \le s \le q

where $a, b, c$ and $d$ are constants.

[3]

1.2 Algebra

Question 26

Markscheme

1.2 Algebra

Question 26

Markscheme

1.2 Algebra

Question 26

1.2 Algebra Questions

1.2 Algebra

Question 26

1.2 Algebra Questions