Specialist Mathematics syllabus, dot point by dot point
Every dot point in the SA Specialist Mathematics subject outline, in syllabus order, with a focused answer for each. Open any dot point for the answer, exam-style questions and links to related points.
Topic 1: Mathematical Induction
Topic overview →How can we prove that a statement is true for every positive integer without checking infinitely many cases?
Topic 2: Complex Numbers
Topic overview →How do we add, multiply and divide numbers that involve the square root of minus one, and how do we picture them?
How does writing a complex number by its modulus and angle make multiplication, division and powers easy?
Why does a complex number have exactly n distinct nth roots, and how are they arranged?
Topic 3: Functions and Sketching Graphs
Topic overview →How do the zeros of a numerator and denominator dictate the shape of a rational function's graph?
How does taking the absolute value reshape a graph, and how do we solve equations and inequalities involving it?
When can a function be reversed, and how do composition and inversion interact with domain and range?
Topic 4: Vectors in Three Dimensions
Topic overview →How does the dot product measure the angle between two vectors and detect perpendicularity?
How do we find a vector perpendicular to two others, and what does its length tell us?
How do vector and cartesian equations describe lines and planes, and how do we find where they meet?
Topic 5: Integration Techniques
Topic overview →How does splitting a rational function into simpler fractions make it integrable?
How does reversing the product rule let us integrate products such as x times e to the x?
How does reversing the chain rule let us integrate composite functions?
Topic 6: Rates of Change and Differential Equations
Topic overview →How do we solve a differential equation by separating the two variables onto opposite sides?
How do we translate a real situation into a differential equation and interpret its solution?