Input-output relationship
A function maps each allowed input to one output. Formula, table, and graph are different representations of the same relationship.
Panhellenic Exams / Mathematics / Curriculum
Κεφάλαιο 1: Όριο - Συνέχεια συνάρτησης: structured theory, worked examples, answered practice, and a mastery checklist for Panhellenic Exams.
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) = 2x - 4, find f(3) and the x-intercept.
Mathematics
Panhellenic strategy: theory, methodology, timing, grading, and continuous correction.
The structure follows the official textbook layout and is used to organise study.
f(3) = 2, x-intercept = 4/2
Before calculating, explain the key idea from “Πραγματικοί αριθμοί” and which conditions must be checked.
The answer should show not only which rule is used for “Πραγματικοί αριθμοί”, but also why it is valid here.
Κεφάλαιο 1: Όριο - Συνέχεια συνάρτησης
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Πραγματικοί αριθμοί”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Πραγματικοί αριθμοί”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Συναρτήσεις”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Συναρτήσεις”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Μονοτονία”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Μονοτονία”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Ακρότατα”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Ακρότατα”, shows equivalent steps, and includes a final check.
The areas that usually create mistakes or need extra revision.
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.