Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300
Question 272

The thermal intensity H H\,H of a heating element over a distance x x\,x from its center is modeled by the function

H(x)=A−∣5x−B∣ H(x) = A - |5x - B| H(x)=A−∣5x−B∣

where A A\,A and B B\,B are positive constants, with A>BA > BA>B.

a.

Find, giving your answers in terms of A A\,A and BBB: (i) the coordinates of the maximum point of the graph of H(x)H(x)H(x), (ii) the coordinates of the point of intersection of the graph with the yyy-axis, (iii) the coordinates of the points of intersection of the graph with the xxx-axis.

[5]
b.

Sketch the graph of H(x)H(x)H(x) and, on the same axes, add the graph with equation G(x)=2∣x∣−5G(x) = 2|x| - 5G(x)=2∣x∣−5.

[2]
c.

Given that the graphs of H(x)H(x)H(x) and G(x)G(x)G(x) intersect at the points where x=−1x = -1x=−1 and x=3x = 3x=3,

find the value of A A\,A and the value of BBB.

[5]

1.5 B: Algebra and functions Questions

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

Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank