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QLDMath MethodsQuick questions

Unit 1: Algebra, statistics and functions

Quick questions on Index and log laws, polynomial equations: QCE Math Methods Unit 1 Year 11

11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is common factor?
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6x3−9x2=3x2(2x−3)6x^3 - 9x^2 = 3x^2(2x - 3).
What is quadratic?
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x2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x + 2)(x + 3).
What is quadratic formula?
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x=(−b±b2−4ac)/(2a)x = (-b \pm \sqrt{b^2 - 4ac})/(2a).
What are difference of squares?
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a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).
What are sum/difference of cubes?
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a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a+b)(a^2 - ab + b^2). a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a-b)(a^2 + ab + b^2).
What is linear?
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Single-step manipulation.
What is polynomial?
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Factor where possible. Find rational roots first; polynomial division for higher degree.
What is exponential?
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Bring to common base, equate exponents. Otherwise take logs.
What is logarithmic?
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Combine logs using laws; convert to exponential form. Always check domain.
What is log of negative?
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Undefined; always check domain.
What is wrong factorisation?
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a2−b2a^2 - b^2 factors; a2+b2a^2 + b^2 does not (over reals).

All Math MethodsQ&A pages