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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 116

The altitude hhh of a surveying drone, measured in decameters relative to a reference level, is modeled by the function y=f(x)y = \mathrm{f}(x)y=f(x), where xxx represents the horizontal displacement from a base station. The graph of this function, curve CCC, is characterized by the following properties:

  • It has a single maximum turning point at (5,12.5)(5, 12.5)(5,12.5).
  • It intersects the coordinate axes at exactly two points: (0,7.5)(0, 7.5)(0,7.5) and (15,0)(15, 0)(15,0).
  • It has a single horizontal asymptote with equation y=2.5y = 2.5y=2.5 as x→−∞x \rightarrow -\inftyx→−∞.
a.

State the equation of the asymptote to the curve with equation y=f(−x)y = \mathrm{f}(-x)y=f(−x).

[1]
b.

State the coordinates of the turning point on the curve with equation y=f(2.5x)y = \mathrm{f}(2.5x)y=f(2.5x).

[1]
c.

Given that the line with equation y=ky = ky=k, where kkk is a constant, intersects CCC at exactly one point,

state the possible values for kkk.

[2]
d.

The curve CCC is transformed to a new curve that passes through the origin.

(i) Given that the new curve has equation y=f(x)−ay = \mathrm{f}(x) - ay=f(x)−a, state the value of the constant aaa.

(ii) Write down an equation for another single transformation of CCC that also passes through the origin.

[2]
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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