IB Maths AA HL Ahl 1 10 Hl Counting and Extended Binomial Theorem Questions

Practise IB Mathematics HL 1.10 by applying counting and extended binomial theorem methods to questions from the Question Bank.

Exam points

Apply counting principles and combinations in extended binomial-theorem problems.
Determine specified coefficients or terms of extended binomial expansions using complete evidence.

[Maximum number: 4]

Consider a three-digit code a b c, where each of a, b and c is assigned one of the values 1,2,3,4 or 5 .

(a)

Find the total number of possible codes

[ 4 ]

(i)

assuming that each value can be repeated (for example, 121 or 444);

[ 2 ]

$5^{3}$
=125

(ii)

assuming that no value is repeated.

Let $P(x)=x^{3}+a x^{2}+b x+c$ , where each of a, b and c is assigned one of the values 1,2,3,4 or 5 . Assume that no value is repeated.

Consider the case where P(x) has a factor of $\left(x^{2}+3 x+2\right)$ .

[ 2 ]

$\quad{ }^{5} P_{3}=5 \times 4 \times 3$
=60

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IB Maths AA HL Ahl 1 10 Hl Counting and Extended Binomial Theorem Questions question 1

Question (a)

Question (i)

Question (ii)