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SingaporeAdditional Mathematics

Algebra: Surds, Indices and Polynomials

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

How do the laws of indices let us simplify expressions with positive, negative, zero and fractional powers?

Apply the laws of indices to simplify expressions involving positive, negative, zero and fractional powers and to solve simple exponential equations
A focused answer to the O-Level A-Maths outcome on indices. The laws of exponents, the meaning of zero, negative and fractional powers, and using them to simplify and to solve simple index equations.
8 min answer →

How do the remainder and factor theorems let us find remainders and factors of a polynomial without long division?

Use the remainder theorem to find the remainder on division by a linear factor and the factor theorem to identify and extract factors of a polynomial
A focused answer to the O-Level A-Maths outcome on polynomials. Polynomial division, the remainder theorem, and the factor theorem for finding and extracting linear factors of cubics and higher polynomials.
9 min answer →

How do we solve a cubic equation by combining the factor theorem with factorisation of the resulting quadratic?

Solve cubic and higher polynomial equations by factorising fully and applying the zero-product principle to find all real roots
A focused answer to the O-Level A-Maths outcome on solving polynomial equations. Using the factor theorem to find a root, factorising fully, and applying the zero-product principle to list every real root.
8 min answer →

How do we simplify expressions containing square roots and remove surds from a denominator?

Simplify surds, perform the four operations on surds, and rationalise denominators including those of the form a plus root b
A focused answer to the O-Level A-Maths outcome on surds. Simplifying surds, adding and multiplying them, and rationalising denominators including conjugate surds of the form a plus root b.
8 min answer →