Course review
Review each learning objective in this topic, then open its concept explanation or question set.
Learning objective
• Use counting principles, permutations and combinations. • Extend binomial expansion to fractional and negative indices. • Exclude identical-object permutations, circular arrangements and proof of the theorem.
Start with the concept explanation, then practise to create mastery evidence.
Learning objective
• Decompose rational expressions into partial fractions. • Denominators have at most two distinct linear terms; numerator degree is lower than denominator degree.
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Learning objective
• Use i where i^2 = -1 and Cartesian form z=a+bi. • Know real/imaginary parts, conjugate, modulus, argument and the Argand diagram.
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Learning objective
• Use polar form z=r(cos theta + i sin theta)=r cis theta and Euler form z=re^(i theta). • Convert between Cartesian, polar and Euler forms; interpret sums, products and quotients geometrically.
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Learning objective
• Know complex conjugate roots of real-coefficient polynomial equations. • Use De Moivre's theorem for powers and roots of complex numbers. • Include induction proof for positive integer powers; be aware of rational exponent extension.
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Learning objective
• Use proof by mathematical induction and proof by contradiction. • Use counterexamples to disprove statements, with explanation of why the counterexample works.
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Learning objective
• Solve up to three linear equations in three unknowns algebraically and with technology. • Identify unique, infinite or no solutions; find general solutions where appropriate.
Start with the concept explanation, then practise to create mastery evidence.