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1.5 B: Algebra and functions

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Question 197

The voltage VVV (in mV) in a biological sensor over time ttt (in ms) is modeled by the function V=V(t)V = V(t)V=V(t). The curve C C\,C with equation V=V(t)V = V(t)V=V(t) is described by the following features:

  • It has a single turning point, a maximum, at (4,12)(4, 12)(4,12).
  • It crosses the vertical axis at (0,7)(0, 7)(0,7) and the horizontal axis at (10,0)(10, 0)(10,0).
  • It has a horizontal asymptote with equation V=3V = 3V=3 as t→−∞t \to -\inftyt→−∞.
a.

State the equation of the horizontal asymptote to the curve with equation y=V(−t)y = V(-t)y=V(−t).

[1]
b.

State the coordinates of the maximum turning point on the curve with equation y=V(2t)y = V(2t)y=V(2t).

[2]
c.

Given that the horizontal line V=kV = kV=k, where k k\,k is a constant, intersects C C\,C at exactly one point:

Determine the possible values for kkk.

[2]
d.

The curve C C\,C is transformed to a new curve that passes through the origin.

(i) Given that the new curve has equation y=V(t)−cy = V(t) - cy=V(t)−c, state the value of the constant ccc.

(ii) Write down an equation for another single transformation of C C\,C that also results in a curve passing through the origin.

[2]

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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