IB Maths AA HL 1.10 Counting and extended binomial theorem Question Bank

Practise IB Mathematics HL 1.10 by applying counting and extended binomial theorem methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[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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AHL 1.10 (HL)—Counting and extended binomial theorem question 1

Question (a)

Question (i)

Question (ii)