IGCSE Year 11 / Mathematics / Curriculum
Vectors, statistics and probability: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 11.
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, 5, 9, 7, 7, find the mean and range.
Mean 6.4, range 5.
Before calculating, explain the key idea from “Column vectors” and which conditions must be checked.
The answer should show not only which rule is used for “Column vectors”, but also why it is valid here.
Vectors, statistics and probability
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Data: 4, 4, 4, 4. Find mean and range.
Mean = sum/count.
mean = 4.0, range = 0.
Order 13, 7, 42, 6, 7 and find the median.
The median is the middle ordered value.
6, 7, 7, 13, 42; median = 7.
A bag contains 3 blue and 3 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 3/6.
In 150 trials, an outcome occurred 30 times. Find relative frequency and percentage.
Divide frequency by number of trials.
30/150 = 0.2 = 20%.
Values 9, 2 have frequencies 2, 9. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(9·2 + 2·9)/11 = 3.27.
Two samples have the same mean but ranges 5 and 20. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 5 is more consistent because its values are less spread out.
Choose a suitable graph for “Scatter graphs” 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.
Vectors, statistics and probability
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: Data: 7, 5, 7, 5. Find mean and range.
Mean = sum/count.
mean = 6.0, range = 2.
Homework 2: Order 5, 3, 6, 2, 3 and find the median.
The median is the middle ordered value.
2, 3, 3, 5, 6; median = 3.
Homework 3: A bag contains 6 blue and 4 yellow counters. Find P(blue).
Favourable outcomes / total outcomes.
P = 6/10.
Homework 4: In 270 trials, an outcome occurred 54 times. Find relative frequency and percentage.
Divide frequency by number of trials.
54/270 = 0.2 = 20%.
Homework 5: Values 5, 3 have frequencies 3, 5. Find the weighted mean.
Sum value×frequency and divide by total frequency.
(5·3 + 3·5)/8 = 3.75.
Homework 6: Two samples have the same mean but ranges 8 and 40. Which is more consistent and why?
Lower spread means greater consistency.
The sample with range 8 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: 5, 5, 5, 5. Find mean and range.
2 балловmean = 5.0, range = 0.
2. Order 10, 8, 16, 2, 8 and find the median.
3 баллов2, 8, 8, 10, 16; median = 8.
3. A bag contains 4 blue and 4 yellow counters. Find P(blue).
3 балловP = 4/8.
4. In 210 trials, an outcome occurred 42 times. Find relative frequency and percentage.
4 баллов42/210 = 0.2 = 20%.
5. Values 3, 3 have frequencies 3, 3. Find the weighted mean.
4 баллов(3·3 + 3·3)/6 = 3.00.
6. Two samples have the same mean but ranges 6 and 30. Which is more consistent and why?
4 балловThe sample with range 6 is more consistent because its values are less spread out.
7. Choose a suitable graph for “Scatter graphs” 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 “Tree diagrams”: 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 “Conditional probability introduction” 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
IGCSE Year 11: 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.
