Skip to content

Course home

1.5 B: Algebra and functions

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354
Question 173

The altitude hhh of a surveying drone, measured in decameters relative to a reference level, is modeled by the function y=f(x)y = \mathrm{f}(x)y=f(x), where xxx represents the horizontal displacement from a base station. The graph of this function, curve CCC, is characterized by the following properties:

  • It has a single maximum turning point at (5,12.5)(5, 12.5)(5,12.5).
  • It intersects the coordinate axes at exactly two points: (0,7.5)(0, 7.5)(0,7.5) and (15,0)(15, 0)(15,0).
  • It has a single horizontal asymptote with equation y=2.5y = 2.5y=2.5 as x→−∞x \rightarrow -\inftyx→−∞.
a.

State the equation of the asymptote to the curve with equation y=f(−x)y = \mathrm{f}(-x)y=f(−x).

[1]
b.

State the coordinates of the turning point on the curve with equation y=f(2.5x)y = \mathrm{f}(2.5x)y=f(2.5x).

[1]
c.

Given that the line with equation y=ky = ky=k, where kkk is a constant, intersects CCC at exactly one point,

state the possible values for kkk.

[2]
d.

The curve CCC is transformed to a new curve that passes through the origin.

(i) Given that the new curve has equation y=f(x)−ay = \mathrm{f}(x) - ay=f(x)−a, state the value of the constant aaa.

(ii) Write down an equation for another single transformation of CCC that also passes through the origin.

[2]
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