P3.1 - Algebra and functions

Simplification of rational Denominators of rational expressions will be linear or expressions including factorising quadratic, and cancelling, and algebraic 1 ax +b x3 +1 division. e.g.,,. ax + b px2 + qx + r x2 −1.

Use simplification of rational denominators of rational to connect the rule to the data and decision in the question.

This matters because simplification of rational denominators of rational determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply simplification of rational denominators of rational to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Simplification of rational Denominators of rational is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Definition of a function.; Domain The concept of a function as a one-one or many-one and range of functions. mapping from (or a subset of) to.; The notation Composition of functions.; Inverse f: x and f(x) will be used. functions and their graphs. ℝ ℝ ℝ Students should know that fg will mean ‘do g first, then f ’.; Students should know that if f −1 exists, then f −1f(x) = ff −1(x) = x.

Use definition of a function to connect the rule to the data and decision in the question.

This matters because definition of a function determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply definition of a function to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Definition of a function is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The modulus function.; Students should be able to sketch the graphs of y = | ax + b | and the graphs of y = | f(x) | and y = f(| x |), given the graph of y = f(x).; For example, sketch the graph with equation y = | 2x − 1 | and use the graph to solve the equation | 2x − 1 | = x + 5 or the inequality | 2x − 1 | > x + 5.

Use modulus function to connect the rule to the data and decision in the question.

This matters because modulus function determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply modulus function to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: modulus function is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Combine transformations y = af(x), y = f(x) + a, y = f(x + a) and y = f(ax), and sketch the resulting graphs; transformations of the form y = f(ax + b) are not required.

Use combined transformations of functions to connect the rule to the data and decision in the question.

This matters because combined transformations of functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply combined transformations of functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Combined transformations of functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.