IB Diploma DP1 / Mathematics / Curriculum
Geometry and trigonometry: structured theory, worked examples, answered practice, and a mastery checklist for IB Diploma DP1.
Розділ
Ключові ідеї глави у зрозумілій послідовності перед практикою.
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
Дотримуйтесь методу крок за кроком і перевіряйте обґрунтування.
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
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
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
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
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 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. A 9 cm by 2 cm rectangle: find perimeter and area.
2 балівP = 22 cm, A = 18 cm².
2. A triangle has base 20 cm and height 4 cm. Find its area.
3 балівA = 1/2 · 20 · 4 = 40 cm².
3. Two angles in a triangle are 80° and 60°. Find the third.
3 балів40°.
4. A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
4 балів15 cm.
5. A circle has radius 5 cm. Find circumference and area in terms of π.
4 балівC = 10π cm, A = 25π cm².
6. Scale 1:300. What real length in metres does 2 cm represent?
4 балів2 · 300 = 600 cm = 6 m.
7. A cuboid is 6 cm × 4 cm × 10 cm. Find its volume.
5 балівV = 240 cm³.
8. Points A(0,0) and B(9,6). Find AB.
5 балівAB = √117.
9. Similar shapes have length scale factor 1:3. If the small area is 5 cm², find the large area.
5 балів5 · 3² = 45 cm².
10. Explain which givens and theorem are needed for a complete argument about “Vectors introduction where applicable”.
5 балівFull response: a labelled diagram, givens, an applicable theorem with its conditions, and a logically derived conclusion.
Розділ
Джерела програми; порядок тем уточнюйте у школі та викладача.
Mathematics
IB Diploma DP1: 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.
