German Gymnasium Klasse 8 / Mathematics / Curriculum
Daten und Zufall: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 8.
ПЛАН ГЛАВЫ
Следуйте шагам по порядку или переходите к нужному разделу.
—/5
завершено
Примерное активное время
209 мин
Цели, основные идеи и структурированная теория.
Открыть →Решённые примеры с объяснением шагов.
Открыть →Задания разного уровня с подсказками и ответами.
Открыть →Задания от базового уровня до сложных.
Открыть →Тест с таймером, баллами и решениями.
Открыть →Прогресс хранится только в этом браузере и не требует AI-кредитов.
Раздел
Ключевые идеи главы в понятной последовательности перед практикой.
Before calculating, identify what each value measures, the population, and whether the sample is representative.
Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.
A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
State what each value measures, organise it in a table or graph, then choose the appropriate statistic. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
For the data 4, 6, 10, 8, 7, find the mean and range.
Mean 7.0, range 6.
Before calculating, explain the key idea from “Mehrstufige Zufallsexperimente” and which conditions must be checked.
The answer should show not only which rule is used for “Mehrstufige Zufallsexperimente”, but also why it is valid here.
Daten und Zufall
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Data: 6, 5, 6, 5. Find mean and range.
Mean = sum/count.
mean = 5.5, range = 1.
Order 11, 9, 18, 2, 9 and find the median.
The median is the middle ordered value.
2, 9, 9, 11, 18; median = 9.
A bag contains 5 blue and 4 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 5/9.
In 240 trials, an outcome occurred 48 times. Find relative frequency and percentage.
Divide frequency by number of trials.
48/240 = 0.2 = 20%.
Values 4, 3 have frequencies 3, 4. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(4·3 + 3·4)/7 = 3.43.
Two samples have the same mean but ranges 7 and 35. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 7 is more consistent because its values are less spread out.
Choose a suitable graph for “Baumdiagramme introduction” and justify axes, scale, and title.
Decide whether data are categorical, discrete, or continuous.
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
Explain why correlation between two variables does not prove causation.
A third factor or reverse relationship may exist.
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
Daten und Zufall
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: Data: 9, 6, 9, 6. Find mean and range.
Mean = sum/count.
mean = 7.5, range = 3.
Homework 2: Order 8, 5, 15, 3, 5 and find the median.
The median is the middle ordered value.
3, 5, 5, 8, 15; median = 5.
Homework 3: A bag contains 8 blue and 5 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 8/13.
Homework 4: In 40 trials, an outcome occurred 8 times. Find relative frequency and percentage.
Divide frequency by number of trials.
8/40 = 0.2 = 20%.
Homework 5: Values 7, 4 have frequencies 4, 7. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(7·4 + 4·7)/11 = 5.09.
Homework 6: Two samples have the same mean but ranges 3 and 18. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 3 is more consistent because its values are less spread out.
50 минут / 40 баллов
Полный тест с таймером, баллами и образцами ответов.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Data: 7, 6, 7, 6. Find mean and range.
2 балловmean = 6.5, range = 1.
2. Order 6, 3, 9, 3, 3 and find the median.
3 баллов3, 3, 3, 6, 9; median = 3.
3. A bag contains 6 blue and 5 yellow counters. Find P(blue).
3 балловP = 6/11.
4. In 90 trials, an outcome occurred 18 times. Find relative frequency and percentage.
4 баллов18/90 = 0.2 = 20%.
5. Values 5, 4 have frequencies 4, 5. Find the weighted mean.
4 баллов(5·4 + 4·5)/9 = 4.44.
6. Two samples have the same mean but ranges 8 and 48. Which is more consistent and why?
4 балловThe sample with range 8 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Baumdiagramme introduction” and justify axes, scale, and title.
5 балловA full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
8. Explain why correlation between two variables does not prove causation.
5 балловCorrelation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Mittelwerte”: population, sample, variables, and possible bias.
5 балловA complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Relative Häufigkeit” using sample size, spread, and limitations.
5 балловThe evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Раздел
Источники программы; порядок тем уточняйте в школе и у преподавателя.
Mathematics
German Gymnasium Klasse 8: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.
Структура следует учебнику и помогает организовать изучение темы.
Темы, где чаще возникают ошибки или нужна дополнительная практика.
С чего начать: учебник, daily material, PDFs, videos и worked examples.
Целевая практика перед full tests, чтобы coverage было понятным.
Как измерять прогресс по главе и когда включать ее в общий mock.
Что делать после главы и как она связана со следующим разделом.
Примечание: официальную экзаменационную программу каждого года всегда уточняйте в школе, у преподавателя и по текущим официальным источникам.
