IGCSE Year 11 / Mathematics / Curriculum
Geometry and trigonometry: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 11.
Раздел
Ключевые идеи главы в понятной последовательности перед практикой.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
A right triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse and area.
Hypotenuse 15 cm, area 54 cm².
Before calculating, explain the key idea from “Similarity” and which conditions must be checked.
The answer should show not only which rule is used for “Similarity”, but also why it is valid here.
Geometry and trigonometry
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
A 9 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 22 cm, A = 18 cm².
A triangle has base 20 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 20 · 4 = 40 cm².
Two angles in a triangle are 80° and 60°. Find the third.
Triangle angles sum to 180°.
40°.
A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
Use a²+b²=c².
15 cm.
A circle has radius 5 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 10π cm, A = 25π cm².
Scale 1:300. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 300 = 600 cm = 6 m.
A cuboid is 6 cm × 4 cm × 10 cm. Find its volume.
V = lwh.
V = 240 cm³.
Points A(0,0) and B(9,6). Find AB.
AB = √(Δx²+Δy²).
AB = √117.
Geometry and trigonometry
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: A 5 cm by 3 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 16 cm, A = 15 cm².
Homework 2: A triangle has base 40 cm and height 5 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 40 · 5 = 100 cm².
Homework 3: Two angles in a triangle are 40° and 20°. Find the third.
Triangle angles sum to 180°.
120°.
Homework 4: A right triangle has legs 12 cm and 16 cm. Find the hypotenuse.
Use a²+b²=c².
20 cm.
Homework 5: A circle has radius 6 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 12π cm, A = 36π cm².
Homework 6: Scale 1:600. What real length in metres does 3 cm represent?
Multiply in cm, then convert to metres.
3 · 600 = 1800 cm = 18 m.
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. A 3 cm by 3 cm rectangle: find perimeter and area.
2 балловP = 12 cm, A = 9 cm².
2. A triangle has base 30 cm and height 5 cm. Find its area.
3 балловA = 1/2 · 30 · 5 = 75 cm².
3. Two angles in a triangle are 90° and 20°. Find the third.
3 баллов70°.
4. A right triangle has legs 12 cm and 16 cm. Find the hypotenuse.
4 баллов20 cm.
5. A circle has radius 6 cm. Find circumference and area in terms of π.
4 балловC = 12π cm, A = 36π cm².
6. Scale 1:400. What real length in metres does 3 cm represent?
4 баллов3 · 400 = 1200 cm = 12 m.
7. A cuboid is 7 cm × 5 cm × 12 cm. Find its volume.
5 балловV = 420 cm³.
8. Points A(0,0) and B(3,2). Find AB.
5 балловAB = √13.
9. Similar shapes have length scale factor 1:4. If the small area is 6 cm², find the large area.
5 баллов6 · 4² = 96 cm².
10. Explain which givens and theorem are needed for a complete argument about “Area of triangle”.
5 балловFull response: a labelled diagram, givens, an applicable theorem with its conditions, and a logically derived conclusion.
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.
