Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 1.10—perms and Combs, Binomial with Negative and Fractional Indices with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.10—perms and Combs, Binomial with Negative and Fractional Indices and mirrors Paper 1, 2, 3 style where relevant.
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Consider the -letter word "ALGEBRA".
Find how many distinct -letter arrangements can be formed from the letters of "ALGEBRA" if no letter is repeated.
Find how many distinct -letter arrangements can be formed if the arrangement must start with "A", excluding those that end with "E". No repetition of letters is assumed.
Let .
Show algebraically that
Hence evaluate
Consider the function .
Use the binomial theorem to expand up to and including the term in .
State the values of for which the expansion is valid.
Use the expansion in part (a) to estimate , giving your answer to significant figures.
Now consider the function .
Find the coefficient of in the expansion of .
Find the first three non-zero terms in the expansion of .
A student needs to complete five different homework assignments: Math, Physics, Chemistry, English, and History.
Find in how many different orders the student can complete all five assignments.
If the student decides that Math must be completed first, find in how many different orders the remaining assignments can be completed.
A community organization is forming a volunteer committee of 5 members from a pool of 6 men and 4 women.
Calculate in how many ways this committee can be formed if it must include at least 2 women.