German Gymnasium Klasse 10 / Mathematics Thüringen / Curriculum
Stochastik: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 10.
Розділ
Ключові ідеї глави у зрозумілій послідовності перед практикою.
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 Thüringen
Дотримуйтесь методу крок за кроком і перевіряйте обґрунтування.
For the data 5, 3, 8, 5, 8, find the mean and range.
Mean 5.8, range 5.
Before calculating, explain the key idea from “Mehrstufige Experimente” and which conditions must be checked.
The answer should show not only which rule is used for “Mehrstufige Experimente”, but also why it is valid here.
Stochastik
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
Data: 9, 2, 9, 2. Find mean and range.
Mean = sum/count.
mean = 5.5, range = 7.
Order 9, 5, 20, 4, 5 and find the median.
The median is the middle ordered value.
4, 5, 5, 9, 20; median = 5.
A bag contains 8 blue and 6 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 8/14.
In 60 trials, an outcome occurred 12 times. Find relative frequency and percentage.
Divide frequency by number of trials.
12/60 = 0.2 = 20%.
Values 7, 5 have frequencies 5, 7. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(7·5 + 5·7)/12 = 5.83.
Two samples have the same mean but ranges 3 and 6. 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.
Choose a suitable graph for “Baumdiagramme” 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.
Stochastik
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Homework 1: Data: 5, 3, 5, 3. Find mean and range.
Mean = sum/count.
mean = 4.0, range = 2.
Homework 2: Order 13, 8, 40, 5, 8 and find the median.
The median is the middle ordered value.
5, 8, 8, 13, 40; median = 8.
Homework 3: A bag contains 4 blue and 2 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 4/6.
Homework 4: In 140 trials, an outcome occurred 28 times. Find relative frequency and percentage.
Divide frequency by number of trials.
28/140 = 0.2 = 20%.
Homework 5: Values 3, 6 have frequencies 6, 3. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(3·6 + 6·3)/9 = 4.00.
Homework 6: Two samples have the same mean but ranges 6 and 18. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 6 is more consistent because its values are less spread out.
50 хвилин / 40 балів
Повний тест із таймером, балами та зразками відповідей.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Data: 3, 3, 3, 3. Find mean and range.
2 балівmean = 3.0, range = 0.
2. Order 11, 6, 30, 5, 6 and find the median.
3 балів5, 6, 6, 11, 30; median = 6.
3. A bag contains 9 blue and 2 yellow counters. Find P(blue).
3 балівP = 9/11.
4. In 100 trials, an outcome occurred 20 times. Find relative frequency and percentage.
4 балів20/100 = 0.2 = 20%.
5. Values 8, 6 have frequencies 6, 8. Find the weighted mean.
4 балів(8·6 + 6·8)/14 = 6.86.
6. Two samples have the same mean but ranges 4 and 12. Which is more consistent and why?
4 балівThe sample with range 4 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Baumdiagramme” and justify axes, scale, and title.
5 балівA 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 балівCorrelation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Statistische Kennwerte”: population, sample, variables, and possible bias.
5 балівA complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Prüfungsaufgaben” using sample size, spread, and limitations.
5 балівThe evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Розділ
Джерела програми; порядок тем уточнюйте у школі та викладача.
Mathematics Thüringen
German Gymnasium Klasse 10: структурований маршрут з математики та фізики з розділами, практикою і наступними кроками.
Структура відповідає підручнику й допомагає організувати вивчення теми.
Теми, де найчастіше виникають помилки або потрібна додаткова практика.
З чого почати: підручник, daily material, PDFs, videos і worked examples.
Цільова практика перед full tests, щоб coverage було зрозумілим.
Як вимірювати прогрес у главі і коли додавати її до загального mock.
Що робити після глави і як вона пов'язана з наступним розділом.
Примітка: офіційну екзаменаційну програму кожного року завжди уточнюйте у школі, викладача та за поточними офіційними джерелами.
