Skip to content

Course home

Sign up

3 Unit A2 1: Pure Mathematics (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319
Question 73

The height of a laser beam trajectory relative to a datum is modeled by the function H(x)H(x)H(x), where

H(x)=2∣3x−9∣+4,x≥0 H(x) = 2|3x - 9| + 4, \quad x \ge 0 H(x)=2∣3x−9∣+4,x≥0

The minimum point on the beam's path is at the vertex VVV.

a.

Determine the coordinates of VVV.

[2]
b.

Find the values of x x\,x for which H(x)=x+7H(x) = x + 7H(x)=x+7.

[4]
c.

Consider the family of linear paths defined by G(x)=kx+1G(x) = kx + 1G(x)=kx+1, where k k\,k is a constant. Given that the equation H(x)=G(x)H(x) = G(x)H(x)=G(x) has exactly two distinct solutions,

find the range of possible values for kkk.

[4]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3 Unit A2 1: Pure Mathematics (A-level only)

Question bank