Support · Mathematics Extension 2 11–12 – Year 12 · Introduction to complex numbers
Support Define and calculate the argument of a non-zero complex number z = a + ib as arg(z) = θ, where θ satisfies sinθ = b/(z) and cosθ = a/(z), noting that the argument has multiple values that differ by multiples of 2π
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Prerequisite dot points
Use the product rule to prove that if P(x) has a zero, α, of multiplicity m > 1, then α is a zero of P'(x) of multiplicity m - 1, and use the result to determine the multiplicity of a discovered zero of P(x) and solve related polynomial problems
Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus Draft mapping
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Define α as a repeated zero or multiple zero of a non-zero polynomial P(x) = (x - α)Q(x) when (x - α) is a factor of Q(x), and α as a single zero of P(x) when (x - α) is not a factor of Q(x), for Q(x)≠0
Mathematics Extension 1 11–12 – Year 11 · Polynomials Draft mapping
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Examine the graphs of the composite functions (y = sin)^(- 1)(sinx), (y = cos)^(- 1)(cosx) and (y = tan)^(- 1)(tanx), establish the values of x for which the formulas sin^(- 1)(sinx) = x, cos^(- 1)(cosx) = x and tan^(- 1)(tanx) = x are true, and apply the formulas to solve problems, simplify expressions and prove results
Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions Draft mapping
No checked resources on this prerequisite dot point yet.