IB Diploma DP1 / Mathematics / Curriculum
Number and algebra: structured theory, worked examples, answered practice, and a mastery checklist for IB Diploma DP1.
CHAPTER PLAN
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Estimated active study time
209 minutes
Objectives, key ideas, and structured theory.
Open →Worked examples that explain every step.
Open →Graded tasks with hints and answer guidance.
Open →Assignments from core work to challenge.
Open →A timed, marked test with solution guidance.
Open →Progress is stored only in this browser and does not require AI credits.
Unit
The essential chapter ideas in a clear sequence before practice.
A variable represents a number or quantity. Every algebraic transformation must preserve the equivalence of the original expression or equation.
Write each transformation on a new line and apply the same valid operation to both sides. This keeps the solution easy to audit.
A final value is not a complete solution until it is substituted into the original relation. Verification catches sign and expansion errors.
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
Follow the method step by step and check why every step is valid.
Solve 3(x - 2) + 3 = 2x + 6.
x = 9
Before calculating, explain the key idea from “Sequences and series” and which conditions must be checked.
The answer should show not only which rule is used for “Sequences and series”, but also why it is valid here.
Number and algebra
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Solve 7x + 2 = 16.
Subtract 2 from both sides, then divide by 7.
x = 2.
Expand and simplify 3(x + 4) - 4x.
Multiply every term inside the bracket.
3x + 12 - 4x = -1x + 12.
Factorise 6x + 36.
Take out the common factor 6.
6(x + 6).
For f(x) = 9x + 3, find f(12) and solve f(x) = 30.
Substitute, then solve the equation.
f(12) = 111; x = 3.
A sequence starts 5, 10, 15. Find its nth term and 10th term.
The common difference is 5.
5n + 0; term 10 = 50.
Solve 8x + 2 > 18.
Use equation steps; the coefficient of x is positive.
x > 2.
Solve x + y = 8, x - y = 0.
Add the two equations.
x = 4, y = 4.
A learner writes 7(x + 6) = 7x + 6. Identify and correct the error.
The outside factor multiplies every term.
7(x + 6) = 7x + 42.
Number and algebra
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Solve 3x + 3 = 12.
Subtract 3 from both sides, then divide by 3.
x = 3.
Homework 2: Expand and simplify 6(x + 5) - 5x.
Multiply every term inside the bracket.
6x + 30 - 5x = 1x + 30.
Homework 3: Factorise 9x + 18.
Take out the common factor 9.
9(x + 2).
Homework 4: For f(x) = 5x + 4, find f(9) and solve f(x) = 24.
Substitute, then solve the equation.
f(9) = 49; x = 4.
Homework 5: A sequence starts 6, 14, 22. Find its nth term and 10th term.
The common difference is 8.
8n + -2; term 10 = 78.
Homework 6: Solve 4x + 3 > 15.
Use equation steps; the coefficient of x is positive.
x > 3.
50 minutes / 40 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Solve 8x + 3 = 27.
2 marksx = 3.
2. Expand and simplify 4(x + 5) - 5x.
3 marks4x + 20 - 5x = -1x + 20.
3. Factorise 7x + 14.
3 marks7(x + 2).
4. For f(x) = 3x + 4, find f(7) and solve f(x) = 16.
4 marksf(7) = 25; x = 4.
5. A sequence starts 6, 12, 18. Find its nth term and 10th term.
4 marks6n + 0; term 10 = 60.
6. Solve 9x + 3 > 30.
4 marksx > 3.
7. Solve x + y = 10, x - y = 0.
5 marksx = 5, y = 5.
8. A learner writes 8(x + 2) = 8x + 2. Identify and correct the error.
5 marks8(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 marksC = 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 marksExample y = 7x + 6: a line with gradient 7, intercept 6, meaning “starts at 6 and rises by 7 per unit”.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Mathematics
Start from the board specification and work topic by topic before full papers.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.
