Skip to content
MathsGenie logo
Open app

Course home

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

Algebraic Methods

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194
Question 89

The fuel consumption rate S(t)S(t)S(t) (in kg/s) of a prototype hypersonic engine, where ttt is the time in minutes since ignition, is modelled by the polynomial S(t)=2t3+Pt2+Qt−20S(t) = 2t^3 + Pt^2 + Qt - 20S(t)=2t3+Pt2+Qt−20, where PPP and QQQ are constants.

It is given that:

  • when S(t)S(t)S(t) is divided by (t−1)(t - 1)(t−1), the remainder is RRR
  • when S(t)S(t)S(t) is divided by (t+2)(t + 2)(t+2), the remainder is 2R+62R + 62R+6
a.

Show that P−2Q=3P - 2Q = 3P−2Q=3.

[4]
b.

Given also that (2t−5)(2t - 5)(2t−5) is a factor of S(t)S(t)S(t),

Find the value of PPP and the value of QQQ.

[3]
c.

Hence find the quadratic expression g(t)g(t)g(t) such that S(t)=(2t−5)g(t)S(t) = (2t - 5)g(t)S(t)=(2t−5)g(t).

[2]

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) 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