Skip to content

Course home

1.5 B: Algebra and functions

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354
Question 189

The efficiency rating of an industrial turbine, EEE, is modeled as a function of the intake pressure x x\,x by

E(x)=5x+8x−2,x>2 E(x) = \frac{5x + 8}{x - 2}, \quad x > 2 E(x)=x−25x+8​,x>2
a.

Find an expression for E−1(x)E^{-1}(x)E−1(x).

[3]
b.

Show that the composite function EE(x)EE(x)EE(x) can be written in the form

EE(x)=ax+bcx+d EE(x) = \frac{ax + b}{cx + d} EE(x)=cx+dax+b​

where a,b,c a, b, c\,a,b,c and d d\,d are integers to be found.

[4]
c.

The point P(6,9.5)P(6, 9.5)P(6,9.5) lies on the curve with equation y=E(x)y = E(x)y=E(x).

Find the coordinates of the point to which P P\,P is mapped when the curve is transformed to y=4E(0.5x)−7y = 4E(0.5x) - 7y=4E(0.5x)−7.

[3]
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.

Question bank