Sec 2 E Math Mock Paper 2-Q07 - Quadratic drone path and a crane cable

Sec 2 E Math Mock Paper 2-Q07 - Quadratic drone path and a crane cable

Secondary 2
TGM Original Questions

An inspection drone crosses a construction site. Its height is modelled by \(y=12+7x-\tfrac12x^2\), where \(0\le x\le14\). The table gives corresponding values.

  1. Find \(p\).
  2. Draw the quadratic graph on the supplied grid.
  3. Find
    1. its greatest height,
    2. the two \(x\)-values when \(y=30\),
    3. interpret them.
  4. A taut crane cable follows \(y=2.5x\). Draw the line and determine whether the drone meets the cable before the site boundary at \(x=12\).
Drone height values
\(x\)\(0\)\(2\)\(4\)\(6\)\(8\)\(10\)\(12\)\(14\)
\(y\)\(12\)\(24\)\(32\)\(36\)\(36\)\(p\)\(24\)\(12\)

Solution:

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Answer:(a) \(p=32\); (c)(i) \(36.5\) m; (ii) \(x\approx3.39,10.61\); (iii) positions at height 30 m; (d) yes, at \(x\approx11.15<12\).

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