Skip to content

Course home

1.3 Functions

1.3 Functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148
Question 96

The concentration of a chemical CCC in a reaction vessel at time ttt minutes is modelled by the function:

C(t)=20−4tfor t≤5 C(t) = \sqrt{20 - 4t} \quad \text{for } t \le 5 C(t)=20−4t​for t≤5

The rate of reaction RRR relative to the concentration is given by:

R(C)=2Cfor C≠0 R(C) = \frac{2}{C} \quad \text{for } C \ne 0 R(C)=C2​for C=0

The overall system function HHH is defined by the composite function H(t)=R(C(t))H(t) = R(C(t))H(t)=R(C(t)) on the maximum possible domain.

a.

Find an expression for H(t)H(t)H(t).

[1]
b.

Find the domain of HHH.

[2]
c.

Show that H−1(x)=5−1x2H^{-1}(x) = 5 - \frac{1}{x^2}H−1(x)=5−x21​.

[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.

Question bank