IGCSE Year 11 / Mathematics / Curriculum
Exam preparation: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 11.
Розділ
Ключові ідеї глави у зрозумілій послідовності перед практикою.
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
Дотримуйтесь методу крок за кроком і перевіряйте обґрунтування.
Calculate and simplify 5/35 + 7/35.
12/35
Before calculating, explain the key idea from “Core/Extended route” and which conditions must be checked.
The answer should show not only which rule is used for “Core/Extended route”, but also why it is valid here.
Exam preparation
Вісім завдань від базових навичок до екзаменаційного рівня. Спочатку виконайте самостійно.
Calculate 9 + 6 × 15 and justify the order of operations.
Multiplication precedes addition.
9 + 6 · 15 = 99.
Find 5/15 of 45.
Multiply by the fraction and simplify first.
5/15 · 45 = 15.
Increase 400 by 40%.
Use multiplier 1 + 40/100.
400 · 1.40 = 560.0.
Divide 72 in the ratio 4:2.
There are 6 ratio parts.
72 : 6 = 12; 48 and 24.
Compare 7/11 and 4/28 using a common denominator or decimals.
Use cross-products.
7 · 28 = 196, 4 · 11 = 44; 7/11 > 4/28.
Write 1800000 in standard form.
The first factor must be at least 1 and less than 10.
1800000 = 1.8 × 10^6.
Estimate 588 ÷ 29.700000000000003, then calculate to one decimal place.
Round to compatible numbers before calculating exactly.
Estimate ≈ 600 ÷ 30 = 20.0. Exact ≈ 19.8.
Test the claim 9² + 5² = 14² and explain.
Calculate both sides separately.
81 + 25 = 106, while 14² = 196; false.
Exam preparation
Шість різних завдань від базового рівня до складного з часом, підказками та відповідями.
Homework 1: Calculate 5 + 2 × 7 and justify the order of operations.
Multiplication precedes addition.
5 + 2 · 7 = 19.
Homework 2: Find 8/32 of 128.
Multiply by the fraction and simplify first.
8/32 · 128 = 32.
Homework 3: Increase 240 by 20%.
Use multiplier 1 + 20/100.
240 · 1.20 = 288.0.
Homework 4: Divide 120 in the ratio 7:3.
There are 10 ratio parts.
120 : 10 = 12; 84 and 36.
Homework 5: Compare 3/8 and 5/15 using a common denominator or decimals.
Use cross-products.
3 · 15 = 45, 5 · 8 = 40; 3/8 > 5/15.
Homework 6: Write 1200000 in standard form.
The first factor must be at least 1 and less than 10.
1200000 = 1.2 × 10^6.
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. Calculate 3 + 2 × 5 and justify the order of operations.
2 балів3 + 2 · 5 = 13.
2. Find 6/24 of 96.
3 балів6/24 · 96 = 24.
3. Increase 540 by 45%.
3 балів540 · 1.45 = 783.0.
4. Divide 96 in the ratio 5:3.
4 балів96 : 8 = 12; 60 and 36.
5. Compare 8/13 and 5/40 using a common denominator or decimals.
4 балів8 · 40 = 320, 5 · 13 = 65; 8/13 > 5/40.
6. Write 800000 in standard form.
4 балів800000 = 0.8 × 10^6.
7. Estimate 686 ÷ 39.6, then calculate to one decimal place.
5 балівEstimate ≈ 700 ÷ 40 = 17.5. Exact ≈ 17.3.
8. Test the claim 3² + 6² = 9² and explain.
5 балів9 + 36 = 45, while 9² = 81; false.
9. Create and solve a two-step exam-style problem about “Mark-scheme patterns” using 6, 3, and 18.
5 балівA valid response uses the data in two justified steps and includes an independent check; for example 6 × 3 = 18, then 18 + 9 = 27.
10. Write a revision rule for “Time management”, one example, and one counterexample.
5 балівFull response: an accurate rule for “Time management”, a numerical example that satisfies it, and an explained counterexample.
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.
