IB Diploma DP1 / Mathematics / Curriculum
Geometry and trigonometry: structured theory, worked examples, answered practice, and a mastery checklist for IB Diploma DP1.
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 “Trigonometric functions” and which conditions must be checked.
The answer should show not only which rule is used for “Trigonometric functions”, but also why it is valid here.
Geometry and trigonometry
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
A 8 cm by 6 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 28 cm, A = 48 cm².
A triangle has base 12 cm and height 3 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 12 · 3 = 18 cm².
Two angles in a triangle are 70° and 50°. Find the third.
Triangle angles sum to 180°.
60°.
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
Use a²+b²=c².
10 cm.
A circle has radius 4 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 8π cm, A = 16π cm².
Scale 1:900. What real length in metres does 6 cm represent?
Multiply in cm, then convert to metres.
6 · 900 = 5400 cm = 54 m.
A cuboid is 5 cm × 3 cm × 8 cm. Find its volume.
V = lwh.
V = 120 cm³.
Points A(0,0) and B(8,5). Find AB.
AB = √(Δx²+Δy²).
AB = √89.
Geometry and trigonometry
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: A 4 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 12 cm, A = 8 cm².
Homework 2: A triangle has base 28 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 28 · 4 = 56 cm².
Homework 3: Two angles in a triangle are 30° and 60°. Find the third.
Triangle angles sum to 180°.
90°.
Homework 4: A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
Use a²+b²=c².
15 cm.
Homework 5: A circle has radius 5 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 10π cm, A = 25π cm².
Homework 6: Scale 1:500. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 500 = 1000 cm = 10 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 9 cm by 2 cm rectangle: find perimeter and area.
2 балловP = 22 cm, A = 18 cm².
2. A triangle has base 20 cm and height 4 cm. Find its area.
3 балловA = 1/2 · 20 · 4 = 40 cm².
3. Two angles in a triangle are 80° and 60°. Find the third.
3 баллов40°.
4. A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
4 баллов15 cm.
5. A circle has radius 5 cm. Find circumference and area in terms of π.
4 балловC = 10π cm, A = 25π cm².
6. Scale 1:300. What real length in metres does 2 cm represent?
4 баллов2 · 300 = 600 cm = 6 m.
7. A cuboid is 6 cm × 4 cm × 10 cm. Find its volume.
5 балловV = 240 cm³.
8. Points A(0,0) and B(9,6). Find AB.
5 балловAB = √117.
9. Similar shapes have length scale factor 1:3. If the small area is 5 cm², find the large area.
5 баллов5 · 3² = 45 cm².
10. Explain which givens and theorem are needed for a complete argument about “Vectors introduction where applicable”.
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
IB Diploma DP1: 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.
