Цели обучения
- Recognise, explain, and apply “Averages”.
- Recognise, explain, and apply “Range”.
- Recognise, explain, and apply “Frequency tables”.
- Recognise, explain, and apply “Pie charts”.
- Recognise, explain, and apply “Scatter diagrams”.
IGCSE Year 10 / Mathematics / Curriculum
Probability and statistics
Probability and statistics: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 10.
Ключевые идеи и проверки
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- Every solution or explanation for “Probability and statistics” should include a method, justification, and final check.
Раздел
Основная теория
Ключевые идеи главы в понятной последовательности перед практикой.
Data and population
Before calculating, identify what each value measures, the population, and whether the sample is representative.
Statistic with interpretation
Mean, median, range, and probability answer different questions. Give the value together with a contextual interpretation.
Scale and probability check
A graph needs a valid scale and a probability must lie from 0 to 1. These checks immediately expose inconsistent answers.
Averages
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.
Range
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.
Frequency tables
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.
Pie charts
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.
Scatter diagrams
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
Разобранные примеры
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
Worked data example
For the data 3, 3, 6, 5, 6, find the mean and range.
- 1Sum = 23 and count = 5.
- 2Mean = 23/5.
- 3Range = maximum - minimum.
Mean 4.6, range 3.
Reasoning example
Before calculating, explain the key idea from “Averages” and which conditions must be checked.
- 1Define the idea in one clear sentence.
- 2Connect it to a representation, law, or formula.
- 3State a restriction, unit, or final check that makes the solution valid.
The answer should show not only which rule is used for “Averages”, but also why it is valid here.
Probability and statistics
Практика с ответами
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Базовый навык4 минут
Data: 6, 2, 6, 2. Find mean and range.
Подсказка
Mean = sum/count.
Ответ
mean = 4.0, range = 4.
Базовый навык5 минут
Order 13, 9, 36, 4, 9 and find the median.
Подсказка
The median is the middle ordered value.
Ответ
4, 9, 9, 13, 36; median = 9.
Применение6 минут
A bag contains 5 blue and 6 yellow counters. Find P(blue).
Подсказка
Favourable outcomes / total outcomes.
Ответ
P = 5/11.
Применение7 минут
In 120 trials, an outcome occurred 24 times. Find relative frequency and percentage.
Подсказка
Divide frequency by number of trials.
Ответ
24/120 = 0.2 = 20%.
Обоснование8 минут
Values 4, 5 have frequencies 5, 4. Find the weighted mean.
Подсказка
Sum value×frequency and divide by total frequency.
Ответ
(4·5 + 5·4)/9 = 4.44.
Обоснование9 минут
Two samples have the same mean but ranges 7 and 14. Which is more consistent and why?
Подсказка
Lower spread means greater consistency.
Ответ
The sample with range 7 is more consistent because its values are less spread out.
Экзаменационный10 минут
Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
Подсказка
Decide whether data are categorical, discrete, or continuous.
Ответ
A full response matches graph type to the data, labels axes and units, uses an even scale, and includes a clear title.
Экзаменационный12 минут
Explain why correlation between two variables does not prove causation.
Подсказка
A third factor or reverse relationship may exist.
Ответ
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
Частые ошибки
- Using the mean when outliers distort the result.
- Using the wrong denominator in a probability.
- Drawing a graph without title, units, or consistent scale.
Проверка понимания
- I choose an appropriate statistic.
- I calculate and interpret probabilities.
- I check sample and graph quality.
Probability and statistics
Домашняя работа по главе
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Базовый8 минут
Homework 1: Data: 9, 3, 9, 3. Find mean and range.
Подсказка
Mean = sum/count.
Ответ
mean = 6.0, range = 6.
Базовый10 минут
Homework 2: Order 10, 5, 25, 5, 5 and find the median.
Подсказка
The median is the middle ordered value.
Ответ
5, 5, 5, 10, 25; median = 5.
Углубленный12 минут
Homework 3: A bag contains 8 blue and 2 yellow counters. Find P(blue).
Подсказка
Favourable outcomes / total outcomes.
Ответ
P = 8/10.
Углубленный15 минут
Homework 4: In 80 trials, an outcome occurred 16 times. Find relative frequency and percentage.
Подсказка
Divide frequency by number of trials.
Ответ
16/80 = 0.2 = 20%.
Сложный18 минут
Homework 5: Values 7, 6 have frequencies 6, 7. Find the weighted mean.
Подсказка
Sum value×frequency and divide by total frequency.
Ответ
(7·6 + 6·7)/13 = 6.46.
Сложный20 минут
Homework 6: Two samples have the same mean but ranges 3 and 9. Which is more consistent and why?
Подсказка
Lower spread means greater consistency.
Ответ
The sample with range 3 is more consistent because its values are less spread out.
50 минут / 40 баллов
Полный тест по главе
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, 3, 7, 3. Find mean and range.
2 балловОтвет
mean = 5.0, range = 4.
2. Order 8, 3, 15, 5, 3 and find the median.
3 балловОтвет
3, 3, 5, 8, 15; median = 5.
3. A bag contains 6 blue and 2 yellow counters. Find P(blue).
3 балловОтвет
P = 6/8.
4. In 180 trials, an outcome occurred 36 times. Find relative frequency and percentage.
4 балловОтвет
36/180 = 0.2 = 20%.
5. Values 5, 6 have frequencies 6, 5. Find the weighted mean.
4 балловОтвет
(5·6 + 6·5)/11 = 5.45.
6. Two samples have the same mean but ranges 8 and 24. Which is more consistent and why?
4 балловОтвет
The sample with range 8 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
5 балловОтвет
A 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 балловОтвет
Correlation shows co-variation, not a controlled mechanism. Establishing causation needs a designed experiment and control of confounders.
9. Design a study about “Range”: population, sample, variables, and possible bias.
5 балловОтвет
A complete design defines population, random/stratified sampling, measurable variables, sample size, and a specific bias with mitigation.
10. Evaluate a conclusion about “Frequency tables” using sample size, spread, and limitations.
5 балловОтвет
The evaluation links the claim to representativeness, uncertainty/spread, and at least one limitation of data collection.
Раздел
Официальные источники
Источники программы; порядок тем уточняйте в школе и у преподавателя.
Mathematics
IGCSE Year 10: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.
Что покрывает глава
Структура следует учебнику и помогает организовать изучение темы.
Averages
Range
Frequency tables
Pie charts
Scatter diagrams
Probability scale
Combined events introduction
Где сфокусироваться
Темы, где чаще возникают ошибки или нужна дополнительная практика.
I choose an appropriate statistic.
I calculate and interpret probabilities.
I check sample and graph quality.
Источники, ежедневные материалы и ресурсы
С чего начать: учебник, daily material, PDFs, videos и worked examples.
Start from the official textbook or specification referenced on the subject page.
Use the notes and examples as support, not as a replacement for the official syllabus.
Check the current syllabus version before exam preparation.
Практика по подтемам
Целевая практика перед full tests, чтобы coverage было понятным.
Data: 6, 2, 6, 2. Find mean and range.
Order 13, 9, 36, 4, 9 and find the median.
A bag contains 5 blue and 6 yellow counters. Find P(blue).
In 120 trials, an outcome occurred 24 times. Find relative frequency and percentage.
Values 4, 5 have frequencies 5, 4. Find the weighted mean.
Two samples have the same mean but ranges 7 and 14. Which is more consistent and why?
Choose a suitable graph for “Combined events introduction” and justify axes, scale, and title.
Explain why correlation between two variables does not prove causation.
Mocks и проверка прогресса
Как измерять прогресс по главе и когда включать ее в общий mock.
Start with untimed practice by subtopic.
Move to a short timed checkpoint only after completing the mastery checklist.
Record each error with the correct method and revisit it after 48 hours.
Следующий шаг
Что делать после главы и как она связана со следующим разделом.
Complete the practice without support.
Explain the core method aloud in under two minutes.
Continue to the next chapter or request targeted tutor support.
Примечание: официальную экзаменационную программу каждого года всегда уточняйте в школе, у преподавателя и по текущим официальным источникам.