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)=20−4tfor t≤5The 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)=C2for C=0The 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.
Find an expression for H(t)H(t)H(t).
Find the domain of HHH.
Show that H−1(x)=5−1x2H^{-1}(x) = 5 - \frac{1}{x^2}H−1(x)=5−x21.
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.