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IGCSE Year 11 / Mathematics / Curriculum

Exam preparation

Exam preparation: structured theory, worked examples, answered practice, and a mastery checklist for IGCSE Year 11.

学习目标

Recognise, explain, and apply “Core/Extended route”.
Recognise, explain, and apply “Paper 2/4 or route-specific papers”.
Recognise, explain, and apply “Command words”.
Recognise, explain, and apply “Mark-scheme patterns”.
Recognise, explain, and apply “Time management”.

核心概念与检查

I can convert safely between number forms.
I can explain why the chosen operation is appropriate.
Every solution or explanation for “Exam preparation” should include a method, justification, and final check.

单元

核心理论

练习前按清晰顺序掌握本章核心概念。

01

Represent before calculating

Write the number in a useful form, check sign and place value, and only then choose the operation. A clear representation reduces mechanical errors.

02

Equivalent forms

Fractions, decimals, percentages, ratios, and powers can describe the same quantity. Changing form is a solving tool, not a separate trick.

03

Reasonableness check

Estimate before and after the exact calculation. The sign, order of magnitude, and unit must agree with the problem context.

04

Core/Extended route

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.

05

Paper 2/4 or route-specific papers

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.

06

Command words

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.

07

Mark-scheme patterns

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.

08

Time management

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

例题讲解

逐步查看方法，并理解每一步为何成立。

Worked number example

Calculate and simplify 5/35 + 7/35.

1The denominators are equal, so add the numerators.
2Write (5 + 7)/35.
3Simplify by a common factor and check that the value is reasonable.

12/35

Reasoning example

Before calculating, explain the key idea from “Core/Extended route” and which conditions must be checked.

1Define the idea in one clear sentence.
2Connect it to a representation, law, or formula.
3State a restriction, unit, or final check that makes the solution valid.

The answer should show not only which rule is used for “Core/Extended route”, but also why it is valid here.

Exam preparation

含答案练习

八道分层练习，从基础熟练到考试应用。请先独立完成，再查看提示或答案。

基础熟练4 分钟

Calculate 9 + 6 × 15 and justify the order of operations.

提示

Multiplication precedes addition.

答案指南

9 + 6 · 15 = 99.

基础熟练5 分钟

Find 5/15 of 45.

提示

Multiply by the fraction and simplify first.

答案指南

5/15 · 45 = 15.

应用6 分钟

Increase 400 by 40%.

提示

Use multiplier 1 + 40/100.

答案指南

400 · 1.40 = 560.0.

应用7 分钟

Divide 72 in the ratio 4:2.

提示

There are 6 ratio parts.

答案指南

72 : 6 = 12; 48 and 24.

推理8 分钟

Compare 7/11 and 4/28 using a common denominator or decimals.

提示

Use cross-products.

答案指南

7 · 28 = 196, 4 · 11 = 44; 7/11 > 4/28.

推理9 分钟

Write 1800000 in standard form.

提示

The first factor must be at least 1 and less than 10.

答案指南

1800000 = 1.8 × 10^6.

考试题型10 分钟

Estimate 588 ÷ 29.700000000000003, then calculate to one decimal place.

提示

Round to compatible numbers before calculating exactly.

答案指南

Estimate ≈ 600 ÷ 30 = 20.0. Exact ≈ 19.8.

考试题型12 分钟

Test the claim 9² + 5² = 14² and explain.

提示

Calculate both sides separately.

答案指南

81 + 25 = 106, while 14² = 196; false.

常见错误

Dropping brackets or using the wrong order of operations.
Converting a fraction or percentage without checking equivalence.
Answering without an estimate, unit, or sign check.

掌握度检查

I can convert safely between number forms.
I can explain why the chosen operation is appropriate.
I check the result with estimation or an inverse operation.

Exam preparation

章节作业

六道不同作业，从基础到挑战，包含预计用时、提示和答案指南。

基础8 分钟

Homework 1: Calculate 5 + 2 × 7 and justify the order of operations.

提示

Multiplication precedes addition.

答案指南

5 + 2 · 7 = 19.

基础10 分钟

Homework 2: Find 8/32 of 128.

提示

Multiply by the fraction and simplify first.

答案指南

8/32 · 128 = 32.

进阶12 分钟

Homework 3: Increase 240 by 20%.

提示

Use multiplier 1 + 20/100.

答案指南

240 · 1.20 = 288.0.

进阶15 分钟

Homework 4: Divide 120 in the ratio 7:3.

提示

There are 10 ratio parts.

答案指南

120 : 10 = 12; 84 and 36.

挑战18 分钟

Homework 5: Compare 3/8 and 5/15 using a common denominator or decimals.

提示

Use cross-products.

答案指南

3 · 15 = 45, 5 · 8 = 40; 3/8 > 5/15.

挑战20 分钟

Homework 6: Write 1200000 in standard form.

提示

The first factor must be at least 1 and less than 10.

答案指南

1200000 = 1.2 × 10^6.

50 分钟 / 40 分

完整章节测试

带计时器、完整分值和参考答案的章节自测。

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 分

答案指南

3 + 2 · 5 = 13.

2. Find 6/24 of 96.

3 分

答案指南

6/24 · 96 = 24.

3. Increase 540 by 45%.

3 分

答案指南

540 · 1.45 = 783.0.

4. Divide 96 in the ratio 5:3.

4 分

答案指南

96 : 8 = 12; 60 and 36.

5. Compare 8/13 and 5/40 using a common denominator or decimals.

4 分

答案指南

8 · 40 = 320, 5 · 13 = 65; 8/13 > 5/40.

6. Write 800000 in standard form.

4 分

答案指南

800000 = 0.8 × 10^6.

7. Estimate 686 ÷ 39.6, then calculate to one decimal place.

5 分

答案指南

Estimate ≈ 700 ÷ 40 = 17.5. Exact ≈ 17.3.

8. Test the claim 3² + 6² = 9² and explain.

5 分

答案指南

9 + 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 分

答案指南

A 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 分

答案指南

Full response: an accurate rule for “Time management”, a numerical example that satisfies it, and an explained counterexample.

单元

官方来源与核验

课程参考来源；教学顺序请始终与学校和老师确认。

UK Department for Education - MathematicsOfficial national curriculum progression and attainment guidance.Cambridge InternationalOfficial programme, syllabus, and qualification information; confirm the current syllabus code.

Mathematics

IGCSE Year 11: 数学与物理的结构化路线，包含章节、练习和下一步。

本章覆盖内容

结构跟随教材，用来帮助组织学习。

Core/Extended route

Paper 2/4 or route-specific papers

Command words

Mark-scheme patterns

Time management

重点关注

通常容易出错或需要更多复习的部分。

I can convert safely between number forms.

I can explain why the chosen operation is appropriate.

I check the result with estimation or an inverse operation.

来源、日常资料与学习资源

从教材、daily material、PDFs、videos 和 worked examples 开始。

Start from the official textbook or specification referenced on the subject page.

Use the notes and examples as support, not as a replacement for the official syllabus.

Check the current syllabus version before exam preparation.

按小主题练习

进入 full tests 前先做 targeted practice，让覆盖情况更清楚。

Calculate 9 + 6 × 15 and justify the order of operations.

Find 5/15 of 45.

Increase 400 by 40%.

Divide 72 in the ratio 4:2.

Compare 7/11 and 4/28 using a common denominator or decimals.

Write 1800000 in standard form.

Estimate 588 ÷ 29.700000000000003, then calculate to one decimal place.

Test the claim 9² + 5² = 14² and explain.

Mocks 与进度检查

如何衡量本章进度，以及何时加入综合 mock。

Start with untimed practice by subtopic.

Move to a short timed checkpoint only after completing the mastery checklist.

Record each error with the correct method and revisit it after 48 hours.

下一步

完成本章后该做什么，以及它如何连接到下一单元。

Complete the practice without support.

Explain the core method aloud in under two minutes.

Continue to the next chapter or request targeted tutor support.

说明：每学年的正式考试范围请始终以学校、老师和当前官方来源为准。