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1.3 Functions

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Question 67

The temperature, V V\,V degrees Celsius, of a chemical reaction chamber over a period of time t t\,t minutes is modelled by the function

V(t)=∣kt−30∣−12,t≥0 V(t) = |kt - 30| - 12, \quad t \ge 0 V(t)=∣kt−30∣−12,t≥0

where k k\,k is a positive constant.

The graph of y=V(t)y = V(t)y=V(t) intersects the vertical axis at the point C C\,C and has a minimum point at MMM.

a.

(i) Write down the V V\,V coordinate of CCC. (ii) Find, in terms of kkk, the t t\,t coordinate of MMM.

[2]
b.

Find, in terms of kkk, the range of values of t t\,t for which V(t)<0V(t) < 0V(t)<0.

[3]
c.

A cooling phase is defined by the linear function L(t)=6−2tL(t) = 6 - 2tL(t)=6−2t.

Given that the line y=L(t)y = L(t)y=L(t) intersects the graph y=V(t)y = V(t)y=V(t) at two distinct points, find the range of possible values for kkk.

[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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