§-Specialist Mathematics Q&A
SA · SACE Board← Specialist Mathematics
Specialist Mathematics Q&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.
Polar form expresses a complex number by its modulus and argument, and De Moivre's theorem raises it to integer powers.
Find the nth roots of a complex number using polar form and de Moivre's theorem, and represent them geometrically on the Argand plane.
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.
Sketch graphs involving the modulus (absolute value) function and solve equations and inequalities containing modulus expressions.
Sketch graphs of rational functions, identifying intercepts, vertical asymptotes, and horizontal or oblique asymptotes.
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.
Write vector, parametric and cartesian equations of lines and planes in three dimensions and find intersections and angles between them.
Represent vectors in three dimensions, compute magnitudes and unit vectors, and use the dot product to find angles and test for perpendicularity.
Topic 5: Integration Techniques
Evaluate integrals using integration by parts, including choosing u and dv and applying the method more than once where needed.
Evaluate integrals using the method of substitution, including changing the limits for definite integrals.
Decompose rational functions into partial fractions and use the decomposition to integrate them.