Skip to content

Course home

Sign up

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

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319
Question 87
a.

Find the binomial expansion of (1−2x)−1(1 - 2x)^{-1}(1−2x)−1 up to and including the term in x2x^2x2.

[2]
b.

It is given that

8x(1−2x)(3+2x)≡P1−2x+Q3+2x\displaystyle \frac{8x}{(1 - 2x)(3 + 2x)} \equiv \frac{P}{1 - 2x} + \frac{Q}{3 + 2x}(1−2x)(3+2x)8x​≡1−2xP​+3+2xQ​

where P P\,P and Q Q\,Q are integers.

Find the value of P P\,P and the value of QQQ.

[3]
c.

Using your answers to parts (a) and (b), find the binomial expansion of

8x(1−2x)(3+2x)\displaystyle \frac{8x}{(1 - 2x)(3 + 2x)}(1−2x)(3+2x)8x​

up to and including the term in x2x^2x2.

[2]
d.

Find the range of values of x x\,x for which the expansion in part (c) is valid.

[1]
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