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

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Study AHL 1.10 (HL)—Counting and extended binomial theorem conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

Question 1

[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 .

Question (a)

(a)

Find the total number of possible codes

[ 4 ]

Question (i)

(i)

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

[ 2 ]

Question (ii)

(ii)

assuming that no value is repeated.

Let P(x)=x3+ax2+bx+cP(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 (x2+3x+2)\left(x^{2}+3 x+2\right).

[ 2 ]
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