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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
14short 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?Show answer
$6x^3 - 9x^2 = 3x^2(2x - 3)$.
What is grouping?Show answer
$x^3 + 2x^2 - x - 2 = x^2(x + 2) - (x + 2) = (x + 2)(x^2 - 1)$.
What is quadratic?Show answer
$x^2 + 5x + 6 = (x + 2)(x + 3)$.
What is quadratic formula?Show answer
$x = (-b \pm \sqrt{b^2 - 4ac})/(2a)$.
What is difference of squares?Show answer
$a^2 - b^2 = (a-b)(a+b)$.
What is sum/difference of cubes?Show answer
$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$. $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$.
What is linear?Show answer
Single-step manipulation.
What is polynomial?Show answer
Factor where possible. Find rational roots first; polynomial division for higher degree.
What is exponential?Show answer
Bring to common base, equate exponents. Otherwise take logs.
What is logarithmic?Show answer
Combine logs using laws; convert to exponential form. Always check domain.
What is sign on negative exponent?Show answer
$a^{-n} = 1/a^n$, not $-a^n$.
What is log of negative?Show answer
Undefined; always check domain.
What is wrong factorisation?Show answer
$a^2 - b^2$ factors; $a^2 + b^2$ does not (over reals).
What is missing log domain check?Show answer
Solutions that produce negative log arguments must be rejected.