German Gymnasium Klasse 8 / Mathematics / Curriculum
Funktionen und Zuordnungen: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 8.
CHAPTER PLAN
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Estimated active study time
209 minutes
Objectives, key ideas, and structured theory.
Open →Worked examples that explain every step.
Open →Graded tasks with hints and answer guidance.
Open →Assignments from core work to challenge.
Open →A timed, marked test with solution guidance.
Open →Progress is stored only in this browser and does not require AI credits.
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.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Follow the method step by step and check why every step is valid.
For f(x) = 4x - 3, find f(2) and the x-intercept.
f(2) = 5, x-intercept = 3/4
Before calculating, explain the key idea from “Proportionale Funktionen” and which conditions must be checked.
The answer should show not only which rule is used for “Proportionale Funktionen”, but also why it is valid here.
Funktionen und Zuordnungen
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Solve 5x + 2 = 12.
Subtract 2 from both sides, then divide by 5.
x = 2.
Expand and simplify 8(x + 4) - 4x.
Multiply every term inside the bracket.
8x + 32 - 4x = 4x + 32.
Factorise 4x + 24.
Take out the common factor 4.
4(x + 6).
For f(x) = 7x + 3, find f(10) and solve f(x) = 24.
Substitute, then solve the equation.
f(10) = 73; x = 3.
A sequence starts 5, 8, 11. Find its nth term and 10th term.
The common difference is 3.
3n + 2; term 10 = 32.
Solve 6x + 2 > 14.
Use equation steps; the coefficient of x is positive.
x > 2.
Solve x + y = 13, x - y = 5.
Add the two equations.
x = 9, y = 4.
A learner writes 5(x + 6) = 5x + 6. Identify and correct the error.
The outside factor multiplies every term.
5(x + 6) = 5x + 30.
Funktionen und Zuordnungen
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Solve 8x + 3 = 27.
Subtract 3 from both sides, then divide by 8.
x = 3.
Homework 2: Expand and simplify 4(x + 5) - 5x.
Multiply every term inside the bracket.
4x + 20 - 5x = -1x + 20.
Homework 3: Factorise 7x + 14.
Take out the common factor 7.
7(x + 2).
Homework 4: For f(x) = 3x + 4, find f(7) and solve f(x) = 16.
Substitute, then solve the equation.
f(7) = 25; x = 4.
Homework 5: A sequence starts 6, 12, 18. Find its nth term and 10th term.
The common difference is 6.
6n + 0; term 10 = 60.
Homework 6: Solve 9x + 3 > 30.
Use equation steps; the coefficient of x is positive.
x > 3.
50 minutes / 40 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Solve 6x + 3 = 21.
2 marksx = 3.
2. Expand and simplify 9(x + 5) - 5x.
3 marks9x + 45 - 5x = 4x + 45.
3. Factorise 5x + 10.
3 marks5(x + 2).
4. For f(x) = 8x + 4, find f(12) and solve f(x) = 36.
4 marksf(12) = 100; x = 4.
5. A sequence starts 6, 10, 14. Find its nth term and 10th term.
4 marks4n + 2; term 10 = 42.
6. Solve 7x + 3 > 24.
4 marksx > 3.
7. Solve x + y = 8, x - y = -2.
5 marksx = 3, y = 5.
8. A learner writes 6(x + 2) = 6x + 2. Identify and correct the error.
5 marks6(x + 2) = 6x + 12.
9. Model this: 4 tickets cost x euros each plus a fixed 9 euros. Write the cost and find it for x = 13.
5 marksC = 4x + 9; C(13) = 61.
10. Represent “Lineare Funktionen” as an equation, a graph, and a verbal description of the same model.
5 marksExample y = 5x + 6: a line with gradient 5, intercept 6, meaning “starts at 6 and rises by 5 per unit”.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Keep each unit in GR/DE: concept, German term, example, exercise, recap.
The structure follows the official textbook layout and is used to organise study.
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.
