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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 174

A roller coaster engineer uses a polynomial function h(x)h(x)h(x) to model the height, in decametres, of a section of track relative to a horizontal distance xxx.

The function h(x)h(x)h(x) is defined for all x∈Rx \in \mathbb{R}x∈R. The profile of the track has the following features:

  • It touches the horizontal axis at a local minimum turning point at (2,0)(2, 0)(2,0).
  • It has a local maximum turning point at (−2,8)(-2, 8)(−2,8).
  • It crosses the vertical axis at the point (0,4)(0, 4)(0,4).
  • The graph behaves like a positive cubic, falling to the left and rising to the right.

On separate diagrams, sketch the curve with the following transformed equations:

i.

y=0.5h(x+2)y = 0.5h(x + 2)y=0.5h(x+2)

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]
ii.

y=h(2x)−5y = h(2x) - 5y=h(2x)−5

On each sketch, show clearly the coordinates of:

  • the point where the curve crosses the yyy-axis
  • any maximum or minimum turning points
[4]
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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