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10
C(5,3)=10.
A Level · English Medium · Cambridge · Mathematics
Ratio, proportion and algebra
Use binomial coefficients, sequences and functions beyond substitution.
About this lesson and its coverage
Original Kidemy A Level progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
A binomial expansion tracks both coefficient choices and powers. An infinite geometric sum needs |r|<1. Function composition and inverse questions require attention to domains as well as formulas.
Worked example
The coefficient of x² in (1+3x)^4 is C(4,2)×9=54. For sum a/(1−r), |r|<1 is essential.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
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12
C(3,2)×4=12.
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12
9/(3/4).
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f⁻¹(x)=√x for x≥0.
Retain the nonnegative input/output ranges.
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The combination counts ways to choose factors; the selected term’s coefficient is multiplied for each choice.
Use a concrete term from an expansion.
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Notebook challenge, sources and further study
Apply the idea
Compare a finite expansion and an infinite series, stating the conditions for each.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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