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Algebra and Functions

Algebra and Functions involves knowing about:

Laws of indices;

Surd manipulation;

Quadratic functions and their graphs including the discriminant, real and repeated roots, completing the square and solution of quadratic equations.

Solve simultaneous equations by elimination and substitution;

Solve linear and quadratic inequalities and interpret such inequalities graphically;

Express solutions using set notation;

Manipulate polynomials algebraically including algebraic division and factor theorem;

Understand and use graphs of functions, proportional relationships and the modulus of a linear function and inverse graphs;

Understand and use composite functions, inverse functions and their graphs;

Understand the effect of simple transformations on the graph of y=f(x) including sketching y=af(x), y=f(x)+a, y=f(x+a), yf(ax) and combinations of these transformations;

Decompose rational functions into partial fractions;

Use functions in modelling including consideration of limitations and refinements of the models.

Q102 Indices

A video on using indices with an unknown quantity and using lots of knowledge to determine what that quantity is.