IGCSE Year 11 / Mathematics / Curriculum
Graphs and coordinate geometry: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 11.
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 15 cm and 20 cm. Find its hypotenuse and area.
Hypotenuse 25 cm, area 150 cm².
Before calculating, explain the key idea from “Linear graphs” and which conditions must be checked.
The answer should show not only which rule is used for “Linear graphs”, but also why it is valid here.
Graphs and coordinate geometry
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
A 3 cm by 5 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 16 cm, A = 15 cm².
A triangle has base 12 cm and height 2 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 12 · 2 = 12 cm².
Two angles in a triangle are 90° and 40°. Find the third.
Triangle angles sum to 180°.
50°.
A right triangle has legs 18 cm and 24 cm. Find the hypotenuse.
Use a²+b²=c².
30 cm.
A circle has radius 3 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 6π cm, A = 9π cm².
Scale 1:400. What real length in metres does 5 cm represent?
Multiply in cm, then convert to metres.
5 · 400 = 2000 cm = 20 m.
A cuboid is 7 cm × 2 cm × 9 cm. Find its volume.
V = lwh.
V = 126 cm³.
Points A(0,0) and B(3,4). Find AB.
AB = √(Δx²+Δy²).
AB = √25.
Graphs and coordinate geometry
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Homework 1: A 6 cm by 6 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 24 cm, A = 36 cm².
Homework 2: A triangle has base 27 cm and height 3 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 27 · 3 = 40.5 cm².
Homework 3: Two angles in a triangle are 50° and 50°. Find the third.
Triangle angles sum to 180°.
80°.
Homework 4: A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
Use a²+b²=c².
10 cm.
Homework 5: A circle has radius 4 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 8π cm, A = 16π cm².
Homework 6: Scale 1:700. What real length in metres does 6 cm represent?
Multiply in cm, then convert to metres.
6 · 700 = 4200 cm = 42 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 4 cm by 6 cm rectangle: find perimeter and area.
2 балівP = 20 cm, A = 24 cm².
2. A triangle has base 21 cm and height 3 cm. Find its area.
3 балівA = 1/2 · 21 · 3 = 31.5 cm².
3. Two angles in a triangle are 30° and 50°. Find the third.
3 балів100°.
4. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
4 балів10 cm.
5. A circle has radius 4 cm. Find circumference and area in terms of π.
4 балівC = 8π cm, A = 16π cm².
6. Scale 1:500. What real length in metres does 6 cm represent?
4 балів6 · 500 = 3000 cm = 30 m.
7. A cuboid is 8 cm × 3 cm × 11 cm. Find its volume.
5 балівV = 264 cm³.
8. Points A(0,0) and B(4,5). Find AB.
5 балівAB = √41.
9. Similar shapes have length scale factor 1:2. If the small area is 7 cm², find the large area.
5 балів7 · 2² = 28 cm².
10. Explain which givens and theorem are needed for a complete argument about “Midpoint”.
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
IGCSE Year 11: 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.
