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1.3 Functions

1.3 Functions

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Question 127

A signal processor monitors the power P P\,P in milliwatts of an oscillating beam over time t t\,t milliseconds. The power output is modeled by the function

P(t)=30−5∣4−t∣,t≥0 P(t) = 30 - 5|4 - t|, \quad t \ge 0 P(t)=30−5∣4−t∣,t≥0
a.

Determine the value of PP(2)PP(2)PP(2).

[2]
b.

Solve the equation P(t)=5tP(t) = 5tP(t)=5t.

[2]
c.

Given that the equation P(t)=kP(t) = kP(t)=k has exactly two roots, state the range of possible values for the constant kkk.

[2]
d.

The power signal is adjusted such that the new power output Q(t)Q(t)Q(t) is given by Q(t)=aP(t−b)Q(t) = aP(t - b)Q(t)=aP(t−b). The maximum power of the new signal is 6 mW and occurs at t=12t = 12t=12. Find the value of the constants a a\,a and bbb.

[3]
Markscheme

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 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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