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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 224

The profit function ppp for a project and the efficiency function qqq are defined by

p(t)=81−t2t∈R,t≥0 p(t) = 81 - t^2 \quad t \in \mathbb{R}, t \ge 0 p(t)=81−t2t∈R,t≥0 q(v)=125v+2v∈R,v≥0 q(v) = \frac{12}{5v + 2} \quad v \in \mathbb{R}, v \ge 0 q(v)=5v+212​v∈R,v≥0
a.

Determine the range of the function ppp.

[1]
b.

Calculate the value of pq(0.2)pq(0.2)pq(0.2).

[2]
c.

Determine the inverse function q−1(x)q^{-1}(x)q−1(x) and state its domain.

[4]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 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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