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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 215

A precision laser-cutting head moves along a path C C\,C in a vertical plane. Its horizontal displacement sss (cm) and vertical height hhh (cm) are modelled by the parametric equations

s=5+3sin⁡θ s = 5 + 3 \sin \theta s=5+3sinθ h=167+cos⁡2θ h = \frac{16}{7 + \cos 2\theta} h=7+cos2θ16​

for −π2≤θ≤π2-\frac{\pi}{2} \le \theta \le \frac{\pi}{2}−2π​≤θ≤2π​.

a.

Show that the path C C\,C has the Cartesian equation

h=72(11−s)(s+1)p≤s≤q h = \frac{72}{(11 - s)(s + 1)} \quad p \le s \le q h=(11−s)(s+1)72​p≤s≤q

where p p\,p and q q\,q are constants to be found.

[6]
b.

Hence, find a Cartesian equation for C C\,C in the form

h=as+b+cs+dp≤s≤q h = \frac{a}{s + b} + \frac{c}{s + d} \quad p \le s \le q h=s+ba​+s+dc​p≤s≤q

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

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Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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