IB Diploma DP1 / Mathematics / Curriculum
Geometry and trigonometry: 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.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. 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.
A right triangle has perpendicular sides 9 cm and 12 cm. Find its hypotenuse and area.
Hypotenuse 15 cm, area 54 cm².
Before calculating, explain the key idea from “Trigonometric functions” and which conditions must be checked.
The answer should show not only which rule is used for “Trigonometric functions”, but also why it is valid here.
Geometry and trigonometry
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
A 8 cm by 6 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 28 cm, A = 48 cm².
A triangle has base 12 cm and height 3 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 12 · 3 = 18 cm².
Two angles in a triangle are 70° and 50°. Find the third.
Triangle angles sum to 180°.
60°.
A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
Use a²+b²=c².
10 cm.
A circle has radius 4 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 8π cm, A = 16π cm².
Scale 1:900. What real length in metres does 6 cm represent?
Multiply in cm, then convert to metres.
6 · 900 = 5400 cm = 54 m.
A cuboid is 5 cm × 3 cm × 8 cm. Find its volume.
V = lwh.
V = 120 cm³.
Points A(0,0) and B(8,5). Find AB.
AB = √(Δx²+Δy²).
AB = √89.
Geometry and trigonometry
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: A 4 cm by 2 cm rectangle: find perimeter and area.
P = 2(l+w), A = lw.
P = 12 cm, A = 8 cm².
Homework 2: A triangle has base 28 cm and height 4 cm. Find its area.
A = 1/2 bh.
A = 1/2 · 28 · 4 = 56 cm².
Homework 3: Two angles in a triangle are 30° and 60°. Find the third.
Triangle angles sum to 180°.
90°.
Homework 4: A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
Use a²+b²=c².
15 cm.
Homework 5: A circle has radius 5 cm. Find circumference and area in terms of π.
C = 2πr, A = πr².
C = 10π cm, A = 25π cm².
Homework 6: Scale 1:500. What real length in metres does 2 cm represent?
Multiply in cm, then convert to metres.
2 · 500 = 1000 cm = 10 m.
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. A 9 cm by 2 cm rectangle: find perimeter and area.
2 marksP = 22 cm, A = 18 cm².
2. A triangle has base 20 cm and height 4 cm. Find its area.
3 marksA = 1/2 · 20 · 4 = 40 cm².
3. Two angles in a triangle are 80° and 60°. Find the third.
3 marks40°.
4. A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
4 marks15 cm.
5. A circle has radius 5 cm. Find circumference and area in terms of π.
4 marksC = 10π cm, A = 25π cm².
6. Scale 1:300. What real length in metres does 2 cm represent?
4 marks2 · 300 = 600 cm = 6 m.
7. A cuboid is 6 cm × 4 cm × 10 cm. Find its volume.
5 marksV = 240 cm³.
8. Points A(0,0) and B(9,6). Find AB.
5 marksAB = √117.
9. Similar shapes have length scale factor 1:3. If the small area is 5 cm², find the large area.
5 marks5 · 3² = 45 cm².
10. Explain which givens and theorem are needed for a complete argument about “Vectors introduction where applicable”.
5 marksFull response: a labelled diagram, givens, an applicable theorem with its conditions, and a logically derived conclusion.
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.
