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IB Diploma DP1 / Mathematics / Curriculum

Number and algebra

Number and algebra: structured theory, worked examples, answered practice, and a mastery checklist for IB Diploma DP1.

Цели обучения

Recognise, explain, and apply “Sequences and series”.
Recognise, explain, and apply “Exponents and logarithms”.
Recognise, explain, and apply “Binomial theorem where applicable”.
Recognise, explain, and apply “Algebraic manipulation”.
Recognise, explain, and apply “Financial mathematics mainly for AI route”.

Ключевые идеи и проверки

I can expand and factor with a check.
I solve equations using equivalent steps.
Every solution or explanation for “Number and algebra” should include a method, justification, and final check.

Раздел

Основная теория

Ключевые идеи главы в понятной последовательности перед практикой.

01

Variables and equivalence

A variable represents a number or quantity. Every algebraic transformation must preserve the equivalence of the original expression or equation.

02

One valid step at a time

Write each transformation on a new line and apply the same valid operation to both sides. This keeps the solution easy to audit.

03

Substitute and verify

A final value is not a complete solution until it is substituted into the original relation. Verification catches sign and expansion errors.

04

Sequences and series

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

Exponents and logarithms

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

Binomial theorem where applicable

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

Algebraic manipulation

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

Financial mathematics mainly for AI 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.

Mathematics

Разобранные примеры

Следуйте методу шаг за шагом и проверяйте обоснование каждого шага.

Worked equation example

Solve 3(x - 2) + 3 = 2x + 6.

1Expand the bracket.
2Collect x-terms on one side and constants on the other.
3Divide by the coefficient of x and verify in the original equation.

x = 9

Reasoning example

Before calculating, explain the key idea from “Sequences and series” 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 “Sequences and series”, but also why it is valid here.

Number and algebra

Практика с ответами

Восемь заданий от базовых навыков до экзаменационного уровня. Сначала решите самостоятельно.

Базовый навык4 минут

Solve 7x + 2 = 16.

Подсказка

Subtract 2 from both sides, then divide by 7.

Ответ

x = 2.

Базовый навык5 минут

Expand and simplify 3(x + 4) - 4x.

Подсказка

Multiply every term inside the bracket.

Ответ

3x + 12 - 4x = -1x + 12.

Применение6 минут

Factorise 6x + 36.

Подсказка

Take out the common factor 6.

Ответ

6(x + 6).

Применение7 минут

For f(x) = 9x + 3, find f(12) and solve f(x) = 30.

Подсказка

Substitute, then solve the equation.

Ответ

f(12) = 111; x = 3.

Обоснование8 минут

A sequence starts 5, 10, 15. Find its nth term and 10th term.

Подсказка

The common difference is 5.

Ответ

5n + 0; term 10 = 50.

Обоснование9 минут

Solve 8x + 2 > 18.

Подсказка

Use equation steps; the coefficient of x is positive.

Ответ

x > 2.

Экзаменационный10 минут

Solve x + y = 8, x - y = 0.

Подсказка

Add the two equations.

Ответ

x = 4, y = 4.

Экзаменационный12 минут

A learner writes 7(x + 6) = 7x + 6. Identify and correct the error.

Подсказка

The outside factor multiplies every term.

Ответ

7(x + 6) = 7x + 42.

Частые ошибки

Changing a sign without applying it to every term.
Combining terms that are not like terms.
Dividing by an expression that may be zero without stating a restriction.

Проверка понимания

I can expand and factor with a check.
I solve equations using equivalent steps.
I verify the solution in the original relation.

Number and algebra

Домашняя работа по главе

Шесть разных заданий от базового уровня до сложного с временем, подсказками и ответами.

Базовый8 минут

Homework 1: Solve 3x + 3 = 12.

Подсказка

Subtract 3 from both sides, then divide by 3.

Ответ

x = 3.

Базовый10 минут

Homework 2: Expand and simplify 6(x + 5) - 5x.

Подсказка

Multiply every term inside the bracket.

Ответ

6x + 30 - 5x = 1x + 30.

Углубленный12 минут

Homework 3: Factorise 9x + 18.

Подсказка

Take out the common factor 9.

Ответ

9(x + 2).

Углубленный15 минут

Homework 4: For f(x) = 5x + 4, find f(9) and solve f(x) = 24.

Подсказка

Substitute, then solve the equation.

Ответ

f(9) = 49; x = 4.

Сложный18 минут

Homework 5: A sequence starts 6, 14, 22. Find its nth term and 10th term.

Подсказка

The common difference is 8.

Ответ

8n + -2; term 10 = 78.

Сложный20 минут

Homework 6: Solve 4x + 3 > 15.

Подсказка

Use equation steps; the coefficient of x is positive.

Ответ

x > 3.

50 минут / 40 баллов

Полный тест по главе

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. Solve 8x + 3 = 27.

2 баллов

Ответ

x = 3.

2. Expand and simplify 4(x + 5) - 5x.

3 баллов

Ответ

4x + 20 - 5x = -1x + 20.

3. Factorise 7x + 14.

3 баллов

Ответ

7(x + 2).

4. For f(x) = 3x + 4, find f(7) and solve f(x) = 16.

4 баллов

Ответ

f(7) = 25; x = 4.

5. A sequence starts 6, 12, 18. Find its nth term and 10th term.

4 баллов

Ответ

6n + 0; term 10 = 60.

6. Solve 9x + 3 > 30.

4 баллов

Ответ

x > 3.

7. Solve x + y = 10, x - y = 0.

5 баллов

Ответ

x = 5, y = 5.

8. A learner writes 8(x + 2) = 8x + 2. Identify and correct the error.

5 баллов

Ответ

8(x + 2) = 8x + 16.

9. Model this: 4 tickets cost x euros each plus a fixed 4 euros. Write the cost and find it for x = 8.

5 баллов

Ответ

C = 4x + 4; C(8) = 36.

10. Represent “Financial mathematics mainly for AI route” as an equation, a graph, and a verbal description of the same model.

5 баллов

Ответ

Example y = 7x + 6: a line with gradient 7, intercept 6, meaning “starts at 6 and rises by 7 per unit”.

Раздел

Официальные источники

Источники программы; порядок тем уточняйте в школе и у преподавателя.

UK Department for Education - MathematicsOfficial national curriculum progression and attainment guidance.International Baccalaureate - DP curriculumOfficial DP subject structure and current subject briefs.

Mathematics

IB Diploma DP1: структурированный маршрут по математике и физике с главами, практикой и следующими шагами.

Назад к предмету

Что покрывает глава

Структура следует учебнику и помогает организовать изучение темы.

Sequences and series

Exponents and logarithms

Binomial theorem where applicable

Algebraic manipulation

Financial mathematics mainly for AI route

Где сфокусироваться

Темы, где чаще возникают ошибки или нужна дополнительная практика.

I can expand and factor with a check.

I solve equations using equivalent steps.

I verify the solution in the original relation.

Источники, ежедневные материалы и ресурсы

С чего начать: учебник, daily material, PDFs, videos и worked examples.

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.

Практика по подтемам

Целевая практика перед full tests, чтобы coverage было понятным.

Solve 7x + 2 = 16.

Expand and simplify 3(x + 4) - 4x.

Factorise 6x + 36.

For f(x) = 9x + 3, find f(12) and solve f(x) = 30.

A sequence starts 5, 10, 15. Find its nth term and 10th term.

Solve 8x + 2 > 18.

Solve x + y = 8, x - y = 0.

A learner writes 7(x + 6) = 7x + 6. Identify and correct the error.

Mocks и проверка прогресса

Как измерять прогресс по главе и когда включать ее в общий 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.

Следующий шаг

Что делать после главы и как она связана со следующим разделом.

Complete the practice without support.

Explain the core method aloud in under two minutes.

Continue to the next chapter or request targeted tutor support.

Примечание: официальную экзаменационную программу каждого года всегда уточняйте в школе, у преподавателя и по текущим официальным источникам.