Functions and straight-line graphs.
Connect rules, variables and graphs, then use straight lines and simple relations to model situations and justify solutions.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Function notation and evaluating rules
Read a function rule, substitute inputs carefully and distinguish an input from its output.
- 02
Dependent and independent variables
Choose which quantity is controlled and which responds, and interpret units and restrictions in a model.
- 03
Domain and range
State allowed inputs and possible outputs, including restrictions caused by formulas and real situations.
- 04
Functions versus relations and the vertical-line test
Distinguish a general relation from a function and test the connection between inputs and outputs.
- 05
Gradient and intercepts
Read slope and axis intercepts from an equation, a table or two points, and explain the units of a gradient.
- 06
Finding a line from points or gradient
Build a line equation from two points, a gradient or intercept information, then check it against the original data.
- 07
Parallel and perpendicular lines
Use gradients and geometric exceptions to identify and construct parallel or perpendicular lines.
- 08
Simultaneous linear equations and intersection models
Find where two linear conditions hold together and interpret intersections, parallel cases and identical models.
- 09
Distance and midpoint
Calculate the length and midpoint of a segment from its endpoints, and use these ideas in geometric arguments.
- 10
Inverse-proportion graphs and asymptotes
Recognise inverse proportion, find its constant and explain the restrictions and asymptotes of its graph.
- 11
Circles and other simple relations
Read and sketch circle relations and connect algebraic restrictions to the visible parts of a graph.
Topic review
Revisit the key ideas, then choose a practice paper.