Skip to content

Course home

3.2 Algebra and Functions (A-level only)

3.2 Algebra and Functions (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161
Question 130

The output power level PPP of a specific amplifier, in decibels, depends on the signal strength sss according to the function:

P(s)=5+2ln⁡s,s>0 P(s) = 5 + 2\ln s, \quad s > 0 P(s)=5+2lns,s>0

The signal strength SSS produced by a sensor over time ttt (in seconds) is given by:

S(t)=12t−182t+3,t>1.5 S(t) = \frac{12t - 18}{2t + 3}, \quad t > 1.5 S(t)=2t+312t−18​,t>1.5
a.

Determine the value of P−1(9)P^{-1}(9)P−1(9).

[2]
b.

Use differentiation to show that SSS is an increasing function for all t>1.5t > 1.5t>1.5.

[3]
c.

Find an expression for the inverse function S−1(x)S^{-1}(x)S−1(x).

[3]
d.

Determine the range of the composite function PSPSPS.

[3]
Markscheme

3.2 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Algebra and Functions (A-level only)

216 exam-style questions on WJEC A Level Maths 3.2 Algebra and Functions (A-level only), covering 3.2.1 Algebra and Functions (A-level only), 3.2.2 Algebra and Functions (A-level only), 3.2.3 Algebra and Functions (A-level only), 3.2.4 Algebra and Functions (A-level only), 3.2.5 Algebra and Functions (A-level only), 3.2.6 Algebra and Functions (A-level only), and 3.2 Algebra and Functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank