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1.3 Functions

1.3 Functions

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Question 102

The strength of a radio signal SSS, measured in microvolts, is modelled by the function

S(t)=32∣2t−10∣+4,t⩾0 S(t) = \frac{3}{2}|2t - 10| + 4, \quad t \geqslant 0 S(t)=23​∣2t−10∣+4,t⩾0

where t t\,t is the time in seconds after a broadcast begins. The minimum signal strength occurs at point VVV.

a.

Determine the coordinates of VVV.

[2]
b.

Solve the equation S(t)=t+7S(t) = t + 7S(t)=t+7.

[3]
c.

An interference signal is modelled by the equation

S(t)=mt+1 S(t) = mt + 1 S(t)=mt+1

where m m\,m is a constant. Given that the broadcast signal and the interference signal have equal strength at exactly two distinct times,

find the range of possible values for mmm.

[4]
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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