KS3 Year 9 / Mathematics / Curriculum
Geometry and measure: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 9.
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 “Interior/exterior angles” and which conditions must be checked.
The answer should show not only which rule is used for “Interior/exterior angles”, but also why it is valid here.
Geometry and measure
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
A 6 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 16 cm, A = 12 cm².
A triangle has base 36 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 36 · 4 = 72 cm².
Two angles in a triangle are 50° and 60°. Find the third.
Triangle angles sum to 180°.
70°.
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 1:700. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 700 = 1400 cm = 14 m.
A cuboid is 3 cm × 4 cm × 7 cm. Find its volume.
V = lwh.
V = 84 cm³.
Points A(0,0) and B(6,6). Find AB.
AB = √(Δx²+Δy²).
AB = √72.
Geometry and measure
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Homework 1: A 9 cm by 3 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 24 cm, A = 27 cm².
Homework 2: A triangle has base 25 cm and height 5 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 25 · 5 = 62.5 cm².
Homework 3: Two angles in a triangle are 80° and 20°. Find the third.
Triangle angles sum to 180°.
80°.
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 1:300. What real length in metres does 3 cm represent?
Multiply in cm, then convert to metres.
3 · 300 = 900 cm = 9 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 7 cm by 3 cm rectangle: find perimeter and area.
2 балівP = 20 cm, A = 21 cm².
2. A triangle has base 15 cm and height 5 cm. Find its area.
3 балівA = 1/2 · 15 · 5 = 37.5 cm².
3. Two angles in a triangle are 60° and 20°. Find the third.
3 балів100°.
4. A right triangle has legs 12 cm and 16 cm. Find the hypotenuse.
4 балів20 cm.
5. A circle has radius 6 cm. Find circumference and area in terms of π.
4 балівC = 12π cm, A = 36π cm².
6. Scale 1:800. What real length in metres does 3 cm represent?
4 балів3 · 800 = 2400 cm = 24 m.
7. A cuboid is 4 cm × 5 cm × 9 cm. Find its volume.
5 балівV = 180 cm³.
8. Points A(0,0) and B(7,2). Find AB.
5 балівAB = √53.
9. Similar shapes have length scale factor 1:4. If the small area is 3 cm², find the large area.
5 балів3 · 4² = 48 cm².
10. Explain which givens and theorem are needed for a complete argument about “Surface area and volume”.
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
KS3 Year 9: 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.
