Skip to content

Course home

Sign up

1.7.1 Binomial expansion

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697
Question 33

The intensity of light LLL measured at a depth rrr inside a specific mineral solution is modeled by the function

L(r)=(4+αr)−2,∣αr∣<4 L(r) = (4 + \alpha r)^{-2}, \quad |\alpha r| < 4 L(r)=(4+αr)−2,∣αr∣<4

where α\alphaα is a non-zero attenuation constant. The series expansion for this model is given by

L(r)=A+Br+Cr2+Dr3+… L(r) = A + Br + Cr^2 + Dr^3 + \dots L(r)=A+Br+Cr2+Dr3+…

where A,B,CA, B, CA,B,C and DDD are constants.

a.

Find the value of AAA.

[1]
b.

Given that C=−9BC = -9BC=−9B

show that α2−24α=0\alpha^2 - 24\alpha = 0α2−24α=0.

[4]
c.

Hence (i) find the value of α\alphaα (ii) find the value of DDD.

[3]
Markscheme

1.7.1 Binomial expansion Questions

  1. A Level
  2. /Maths
  3. /1.7.1 Binomial expansion

144 exam-style questions on AQA A Level Maths 1.7.1 Binomial expansion. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank