KS3 Year 8 / Mathematics / Curriculum
Geometry and measure: structured theory, worked examples, answered practice, and a mastery checklist for KS3 Year 8.
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 12 cm and 16 cm. Find its hypotenuse and area.
Hypotenuse 20 cm, area 96 cm².
Before calculating, explain the key idea from “Parallel line angle facts” and which conditions must be checked.
The answer should show not only which rule is used for “Parallel line angle facts”, but also why it is valid here.
Geometry and measure
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
A 5 cm by 5 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 20 cm, A = 25 cm².
A triangle has base 16 cm and height 2 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 16 · 2 = 16 cm².
Two angles in a triangle are 40° and 40°. Find the third.
Triangle angles sum to 180°.
100°.
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 1:600. What real length in metres does 5 cm represent?
Multiply in cm, then convert to metres.
5 · 600 = 3000 cm = 30 m.
A cuboid is 9 cm × 2 cm × 11 cm. Find its volume.
V = lwh.
V = 198 cm³.
Points A(0,0) and B(5,4). Find AB.
AB = √(Δx²+Δy²).
AB = √41.
Geometry and measure
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: A 8 cm by 6 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 28 cm, A = 48 cm².
Homework 2: A triangle has base 12 cm and height 3 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 12 · 3 = 18 cm².
Homework 3: Two angles in a triangle are 70° and 50°. Find the third.
Triangle angles sum to 180°.
60°.
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 1:900. What real length in metres does 6 cm represent?
Multiply in cm, then convert to metres.
6 · 900 = 5400 cm = 54 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 6 cm by 6 cm rectangle: find perimeter and area.
2 балловP = 24 cm, A = 36 cm².
2. A triangle has base 27 cm and height 3 cm. Find its area.
3 балловA = 1/2 · 27 · 3 = 40.5 cm².
3. Two angles in a triangle are 50° and 50°. Find the third.
3 баллов80°.
4. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
4 баллов10 cm.
5. A circle has radius 4 cm. Find circumference and area in terms of π.
4 балловC = 8π cm, A = 16π cm².
6. Scale 1:700. What real length in metres does 6 cm represent?
4 баллов6 · 700 = 4200 cm = 42 m.
7. A cuboid is 3 cm × 3 cm × 6 cm. Find its volume.
5 балловV = 54 cm³.
8. Points A(0,0) and B(6,5). Find AB.
5 балловAB = √61.
9. Similar shapes have length scale factor 1:2. If the small area is 9 cm², find the large area.
5 баллов9 · 2² = 36 cm².
10. Explain which givens and theorem are needed for a complete argument about “Parallel line angle facts”.
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
KS3 Year 8: 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.
