Algebra and Functions

The second year turns algebra into the language of functions: what goes in, what comes out, and how to reverse it. Partial fractions and the modulus function are new tools, and both are used heavily in calculus later in the course.

• An Overview — the big idea, the language of functions, the core techniques and the common mistakes

The content statements

• Algebraic and Partial Fractions — simplifying rational expressions, algebraic division, and splitting fractions with linear and repeated linear denominators
• The Modulus Function — the graphs of y = |ax + b| and y = |f(x)|, and solving modulus equations and inequalities
• Composite and Inverse Functions — mappings, domain and range, one-one and many-one functions, composites, and inverses as reflections in y = x
• Combined Transformations — y = af(bx + c) + d, the order of transformations, and the graphs of y = f(|x|) and y = |f(x)|

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.