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VICMath MethodsQuick questions
Unit 1
Quick questions on Algebra, indices and equations: VCE Math Methods Unit 1 Year 11
15short 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 inverse relationship?Show answer
$\log_a(a^x) = x$ and $a^{\log_a x} = x$.
What is common factor?Show answer
$6 x^3 - 9 x^2 = 3 x^2 (2 x - 3)$.
What is grouping?Show answer
$x^3 + 2 x^2 - x - 2 = x^2(x + 2) - (x + 2) = (x + 2)(x^2 - 1) = (x + 2)(x - 1)(x + 1)$.
What is quadratic factorisation?Show answer
$x^2 + 5x + 6 = (x + 2)(x + 3)$. Use sum-and-product (looking for two numbers that sum to the middle coefficient and multiply to the constant).
What is quadratic formula?Show answer
$a x^2 + b x + c = 0$ has solutions $x = (-b \pm \sqrt{b^2 - 4ac}) / (2a)$.
What is difference of squares?Show answer
$a^2 - b^2 = (a - b)(a + b)$.
What is sum and 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 or simple multi-step manipulation.
What is quadratic?Show answer
Factor first, then use the null factor law ($AB = 0 \implies A = 0$ or $B = 0$). Or use the quadratic formula.
What is polynomial?Show answer
Factor where possible. Look for rational roots first; then use polynomial division or grouping.
What is exponential?Show answer
Bring to common base if possible, then equate exponents. Otherwise take logarithms.
What is logarithmic?Show answer
Combine logs using laws; convert to exponential form. Always check domain (logs require positive arguments).
What is index law inversion?Show answer
$a^{-n} = 1/a^n$, not $-a^n$.
What is log of a negative?Show answer
Logs of negative numbers and zero are undefined in the real numbers. Always check.
What is wrong factorisation?Show answer
$a^2 - b^2 = (a - b)(a + b)$ is the difference of squares. $a^2 + b^2$ does not factor over the reals.