Input-output relationship
A function maps each allowed input to one output. Formula, table, and graph are different representations of the same relationship.
KS3 Year 9 / Mathematics / Curriculum
Graphs and functions: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 9.
Unit
The essential chapter ideas in a clear sequence before practice.
A function maps each allowed input to one output. Formula, table, and graph are different representations of the same relationship.
Parameters change slope, position, amplitude, or rate of change. Read the key features before plotting individual points.
The domain states which inputs are allowed. In a real model, also check whether the output is physically meaningful.
Mathematics
Follow the method step by step and check why every step is valid.
For f(x) = 3x - 6, find f(5) and the x-intercept.
Mathematics
Start from the board specification and work topic by topic before full papers.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
f(5) = 9, x-intercept = 6/3
Before calculating, explain the key idea from “Linear graphs” and which conditions must be checked.
The answer should show not only which rule is used for “Linear graphs”, but also why it is valid here.
Graphs and functions
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Linear graphs”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Linear graphs”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Gradient and intercept”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Gradient and intercept”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Quadratic graphs introduction”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Quadratic graphs introduction”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Reciprocal graphs introduction”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Reciprocal graphs introduction”, shows equivalent steps, and includes a final check.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.