A Level Year 12 / Mathematics / Curriculum
Applied option: Mechanics: structured theory, worked examples, answered practice, and a mastery checklist for A Level Year 12.
Раздел
Ключевые идеи главы в понятной последовательности перед практикой.
Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.
Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.
Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Use a suitable representation, state the rule, and keep every numerical or algebraic step equivalent. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.
Calculate and simplify 5/30 + 6/30.
11/30
Before calculating, explain the key idea from “Forces and equilibrium” and which conditions must be checked.
The answer should show not only which rule is used for “Forces and equilibrium”, but also why it is valid here.
Applied option: Mechanics
Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.
Calculate 3 + 5 × 8 and justify the order of operations.
Multiplication precedes addition.
3 + 5 · 8 = 43.
Find 6/12 of 24.
Multiply by the fraction and simplify first.
6/12 · 24 = 12.
Increase 360 by 45%.
Use multiplier 1 + 45/100.
360 · 1.45 = 522.0.
Divide 132 in the ratio 5:6.
There are 11 ratio parts.
132 : 11 = 12; 60 and 72.
Compare 8/11 and 3/24 using a common denominator or decimals.
Use cross-products.
8 · 24 = 192, 3 · 11 = 33; 8/11 > 3/24.
Write 2000000 in standard form.
The first factor must be at least 1 and less than 10.
2000000 = 2.0 × 10^6.
Estimate 686 ÷ 19.8, then calculate to one decimal place.
Round to compatible numbers before calculating exactly.
Estimate ≈ 700 ÷ 20 = 35.0. Exact ≈ 34.6.
Test the claim 3² + 4² = 7² and explain.
Calculate both sides separately.
9 + 16 = 25, while 7² = 49; false.
Applied option: Mechanics
Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.
Homework 1: Calculate 6 + 6 × 12 and justify the order of operations.
Multiplication precedes addition.
6 + 6 · 12 = 78.
Homework 2: Find 9/27 of 81.
Multiply by the fraction and simplify first.
9/27 · 81 = 27.
Homework 3: Increase 250 by 25%.
Use multiplier 1 + 25/100.
250 · 1.25 = 312.5.
Homework 4: Divide 120 in the ratio 8:2.
There are 10 ratio parts.
120 : 10 = 12; 96 and 24.
Homework 5: Compare 4/8 and 4/16 using a common denominator or decimals.
Use cross-products.
4 · 16 = 64, 4 · 8 = 32; 4/8 > 4/16.
Homework 6: Write 4200000 in standard form.
The first factor must be at least 1 and less than 10.
4200000 = 4.2 × 10^6.
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. Calculate 4 + 6 × 10 and justify the order of operations.
2 баллов4 + 6 · 10 = 64.
2. Find 7/21 of 63.
3 баллов7/21 · 63 = 21.
3. Increase 150 by 15%.
3 баллов150 · 1.15 = 172.5.
4. Divide 96 in the ratio 6:2.
4 баллов96 : 8 = 12; 72 and 24.
5. Compare 9/13 and 4/36 using a common denominator or decimals.
4 баллов9 · 36 = 324, 4 · 13 = 52; 9/13 > 4/36.
6. Write 3000000 in standard form.
4 баллов3000000 = 3.0 × 10^6.
7. Estimate 784 ÷ 29.700000000000003, then calculate to one decimal place.
5 балловEstimate ≈ 800 ÷ 30 = 26.7. Exact ≈ 26.4.
8. Test the claim 4² + 5² = 9² and explain.
5 баллов16 + 25 = 41, while 9² = 81; false.
9. Create and solve a two-step exam-style problem about “Work, energy and power” using 7, 2, and 14.
5 балловA valid response uses the data in two justified steps and includes an independent check; for example 7 × 2 = 14, then 14 + 9 = 23.
10. Write a revision rule for “Momentum”, one example, and one counterexample.
5 балловFull response: an accurate rule for “Momentum”, a numerical example that satisfies it, and an explained counterexample.
Раздел
Источники программы; порядок тем уточняйте в школе и у преподавателя.
Mathematics
A Level Year 12: 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.
