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Skill Checklist
Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.
5 Skills Available
Track your progress:
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Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Pascal's Triangle and nCr
4 skills
Factorials
SL AA 1.9
Factorials are shortcut used to express decreasing products of integers such as
5⋅4⋅3⋅2⋅1=5!
The definition is
n!=n×(n−1)×⋯×2×1🚫
Fractions of factorials as partial products
SL AA 1.9
k!n!=n×(n−1)×⋯×(k+2)×(k+1)
Binomial Coefficient nCr
SL AA 1.9
The number of ways to choose r items from a set of n items can be expressed as (nr), nCr or nCr. The number of combinations can be calculated using the formula
nCr=r!(n−r)!n!📖
Pascal's Triangle
SL AA 1.9
Pascal's triangle is a triangular array where each number is the sum of the two directly above it, beautifully revealing the coefficients of binomial expansions. Each term corresponds to a specific value of nCr. Its symmetry and simple construction make it a powerful tool for exploring combinatorial relationships and probability.
Binomial Theorem
1 skill
The expansion of (a+b)ⁿ
SL AA 1.9
The binomial theorem allows us expand expressions of the form (a+b)n:
(a+b)n=an+nC1an−1b1+nC2an−2b2+⋯📖
or in summation form:
(a+b)n=r=0∑n(nr)an−rbr🚫