A Level Year 13 / Mathematics / Curriculum
Pure Mathematics 3: structured theory, worked examples, answered practice, and a mastery checklist for A Level Year 13.
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 12 cm and 16 cm. Find its hypotenuse and area.
Hypotenuse 20 cm, area 96 cm².
Before calculating, explain the key idea from “Advanced functions” and which conditions must be checked.
The answer should show not only which rule is used for “Advanced functions”, but also why it is valid here.
Pure Mathematics 3
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
A 5 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 14 cm, A = 10 cm².
A triangle has base 32 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 32 · 4 = 64 cm².
Two angles in a triangle are 40° and 60°. Find the third.
Triangle angles sum to 180°.
80°.
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 1:600. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 600 = 1200 cm = 12 m.
A cuboid is 9 cm × 4 cm × 13 cm. Find its volume.
V = lwh.
V = 468 cm³.
Points A(0,0) and B(5,6). Find AB.
AB = √(Δx²+Δy²).
AB = √61.
Pure Mathematics 3
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Homework 1: A 8 cm by 3 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 22 cm, A = 24 cm².
Homework 2: A triangle has base 20 cm and height 5 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 20 · 5 = 50 cm².
Homework 3: Two angles in a triangle are 70° and 20°. Find the third.
Triangle angles sum to 180°.
90°.
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 1:900. What real length in metres does 3 cm represent?
Multiply in cm, then convert to metres.
3 · 900 = 2700 cm = 27 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 6 cm by 3 cm rectangle: find perimeter and area.
2 балівP = 18 cm, A = 18 cm².
2. A triangle has base 45 cm and height 5 cm. Find its area.
3 балівA = 1/2 · 45 · 5 = 112.5 cm².
3. Two angles in a triangle are 50° and 20°. Find the third.
3 балів110°.
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 1:700. What real length in metres does 3 cm represent?
4 балів3 · 700 = 2100 cm = 21 m.
7. A cuboid is 3 cm × 5 cm × 8 cm. Find its volume.
5 балівV = 120 cm³.
8. Points A(0,0) and B(6,2). Find AB.
5 балівAB = √40.
9. Similar shapes have length scale factor 1:4. If the small area is 9 cm², find the large area.
5 балів9 · 4² = 144 cm².
10. Explain which givens and theorem are needed for a complete argument about “Parametric equations”.
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
A Level Year 13: 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.
