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SingaporeAdditional Mathematics

Binomial Theorem and Partial Fractions

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How does the binomial theorem let us expand a power of a two-term expression without multiplying it out by hand?

Expand expressions of the form a plus b to the power n for a positive integer n using the binomial theorem and binomial coefficients
A focused answer to the O-Level A-Maths outcome on the binomial theorem. Expanding a plus b to a positive integer power using binomial coefficients, Pascal's triangle, and the general structure of the expansion.
8 min answer →

How do we pick out a single term, such as the coefficient of x cubed or the constant term, from a binomial expansion?

Use the general term of a binomial expansion to find a specified term, the coefficient of a given power, or the term independent of x
A focused answer to the O-Level A-Maths outcome on the general term. Using the term formula to find a specified coefficient, a chosen power, or the constant term without writing the whole expansion.
8 min answer →

How do we split a proper rational fraction with distinct linear factors into simpler partial fractions?

Express a proper rational fraction with distinct linear factors in the denominator as a sum of partial fractions
A focused answer to the O-Level A-Maths outcome on partial fractions. Splitting a proper fraction whose denominator factorises into distinct linear factors, and finding the unknown numerators by substitution.
8 min answer →

How does the partial-fraction form change when the denominator has a repeated factor or an irreducible quadratic factor?

Express proper fractions with repeated linear factors or an irreducible quadratic factor as partial fractions, choosing the correct numerator forms
A focused answer to the O-Level A-Maths outcome on harder partial fractions. The correct numerator forms for a repeated linear factor and an irreducible quadratic factor, and finding the constants.
9 min answer →