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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 310

The output power level PPP of a specific amplifier, in decibels, depends on the signal strength sss according to the function:

P(s)=5+2ln⁡s,s>0 P(s) = 5 + 2\ln s, \quad s > 0 P(s)=5+2lns,s>0

The signal strength SSS produced by a sensor over time ttt (in seconds) is given by:

S(t)=12t−182t+3,t>1.5 S(t) = \frac{12t - 18}{2t + 3}, \quad t > 1.5 S(t)=2t+312t−18​,t>1.5
a.

Determine the value of P−1(9)P^{-1}(9)P−1(9).

[2]
b.

Use differentiation to show that SSS is an increasing function for all t>1.5t > 1.5t>1.5.

[3]
c.

Find an expression for the inverse function S−1(x)S^{-1}(x)S−1(x).

[3]
d.

Determine the range of the composite function PSPSPS.

[3]
Markscheme

1.5 B: Algebra and functions Questions

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

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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