IB Maths AA SL 1.9 Binomial theorem Question Bank

Practise IB Maths AA SL 1.9 by expanding binomials, finding coefficients and solving for parameters in algebraic expressions.

Exam points

Expand a binomial to the required power and collect terms in ascending or descending order.
Use the general term to find a specified coefficient or power in a binomial expansion.
Solve for an unknown parameter from a coefficient or term and check all possible values.

[Maximum number: 5]

Consider the expansion of $(x+3)^{10}$ .

(a)

Write down the number of terms in this expansion.

[ 1 ]

(b)

Find the term containing $x^{3}$ .

[ 4 ]

evidence of binomial expansion
eg $\quad\binom{n}{r} a^{n-r} b^{r}$ , attempt to expand
evidence of choosing correct term
eg $\quad 8^{\text {th }}$ term, $r=7,\binom{10}{7},(x)^{3}(3)^{7}$
correct working
eg $\quad\binom{10}{7}(x)^{3}(3)^{7},\binom{10}{3}(x)^{3}(3)^{7}$ ,
$262440 x^{3}$ (accept $262000 x^{3}$ )

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SL 1.9—Binomial theorem question 1

Question (a)

Question (b)