CAIE IGCSE Additional Mathematics 12.2 General Binomial Term Question Bank

Practise using the general binomial term to find constant terms, specified coefficients and parameter values.

Exam points

write the general term and solve for r when the total power of x is zero
combine only term pairs whose powers add to the requested coefficient
equate coefficient expressions to solve for a positive parameter

[Maximum number: 5]

In the expansion of $(k-2x)^8$ , where k is a constant, the coefficient of $x^4$ divided by the coefficient of $x^2$ is $\frac{5}{8}$ . The coefficient of x is positive. Form an equation and hence find the value of k.

${}^8C_4\times k^4\times(-2)^4[x^4]$
oe, or $1120k^4[x^4]$ soi
B1
${}^8C_2\times k^6\times(-2)^2[x^2]$
oe, or $112k^6[x^2]$ soi
B1
$\frac{1120k^4}{112k^6}=\frac58$
oe, soi
M1 FT providing at least B1 awarded and correct terms attempted
$k^2=16$
soi
A1
For coefficient of x to be positive, k<0, therefore k=-4
A1

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12.2. Use the general binomial term question 1