Skip to content

Course home

1.5 B: Algebra and functions

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354
Question 320
a.

(i) Find the binomial expansion of (1+3x)−1(1 + 3x)^{-1}(1+3x)−1 up to and including the term in x2x^2x2.

(ii) Show that the first three terms in the binomial expansion of

15−2x \frac{1}{5 - 2x} 5−2x1​

form a geometric sequence and state the common ratio.

[5]
b.

It is given that

85x(1+3x)(5−2x)≡P5−2x+Q1+3x \frac{85x}{(1 + 3x)(5 - 2x)} \equiv \frac{P}{5 - 2x} + \frac{Q}{1 + 3x} (1+3x)(5−2x)85x​≡5−2xP​+1+3xQ​

where PPP and QQQ are integers. Find the value of PPP and the value of QQQ.

[3]
c.

(i) In a structural model, the stress SSS on a beam at distance xxx from the support is given by S(x)=17x(1+3x)(5−2x)S(x) = \frac{17x}{(1 + 3x)(5 - 2x)}S(x)=(1+3x)(5−2x)17x​. Using your answers to parts (a) and (b), find the binomial expansion of S(x)S(x)S(x) up to and including the term in x2x^2x2.

(ii) Determine the range of values of xxx for which the binomial expansion of S(x)S(x)S(x) is valid.

[5]
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