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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?
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log⁡a(ax)=x\log_a(a^x) = x and alog⁡ax=xa^{\log_a x} = x.
What is common factor?
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6x3−9x2=3x2(2x−3)6 x^3 - 9 x^2 = 3 x^2 (2 x - 3).
What is quadratic factorisation?
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x2+5x+6=(x+2)(x+3)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?
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ax2+bx+c=0a x^2 + b x + c = 0 has solutions 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 and 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 or simple multi-step manipulation.
What is quadratic?
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Factor first, then use the null factor law (AB=0  ⟹  A=0AB = 0 \implies A = 0 or B=0B = 0). Or use the quadratic formula.
What is polynomial?
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Factor where possible. Look for rational roots first; then use polynomial division or grouping.
What is exponential?
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Bring to common base if possible, then equate exponents. Otherwise take logarithms.
What is logarithmic?
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Combine logs using laws; convert to exponential form. Always check domain (logs require positive arguments).
What is log of a negative?
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Logs of negative numbers and zero are undefined in the real numbers. Always check.
What is wrong factorisation?
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a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b) is the difference of squares. a2+b2a^2 + b^2 does not factor over the reals.
What is q1?
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Solve 23x+1=322^{3x + 1} = 32. [2 marks]
What is q2?
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A population is modelled by P=500(1.04)tP = 500 (1.04)^t (tt in years). Find, to one decimal place, when P=900P = 900. [3 marks]

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