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Specialist MathematicsQ&A by dot point
A short Q&A bank for every SA Specialist Mathematics syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Topic 1: Mathematical Induction
Topic 2: Complex Numbers
- Complex numbers extend the reals with i where i squared equals minus one, and are represented as points or vectors on the Argand plane.0Q&A pairs
- Polar form expresses a complex number by its modulus and argument, and De Moivre's theorem raises it to integer powers.0Q&A pairs
- Find the nth roots of a complex number using polar form and de Moivre's theorem, and represent them geometrically on the Argand plane.2Q&A pairs
Topic 3: Functions and Sketching Graphs
- Form composite functions and find inverse functions, attending to domain and range and the condition for an inverse to exist.0Q&A pairs
- Sketch graphs involving the modulus (absolute value) function and solve equations and inequalities containing modulus expressions.0Q&A pairs
- Sketch graphs of rational functions, identifying intercepts, vertical asymptotes, and horizontal or oblique asymptotes.1Q&A pairs
Topic 4: Vectors in Three Dimensions
- Compute the cross product of two vectors, interpret its direction and magnitude, and use it to find areas and normals.0Q&A pairs
- Write vector, parametric and cartesian equations of lines and planes in three dimensions and find intersections and angles between them.1Q&A pairs
- Represent vectors in three dimensions, compute magnitudes and unit vectors, and use the dot product to find angles and test for perpendicularity.1Q&A pairs
Topic 5: Integration Techniques
- Evaluate integrals using integration by parts, including choosing u and dv and applying the method more than once where needed.1Q&A pairs
- Evaluate integrals using the method of substitution, including changing the limits for definite integrals.1Q&A pairs
- Decompose rational functions into partial fractions and use the decomposition to integrate them.2Q&A pairs