IGCSE Math RevisionGeometry and trigonometry: Edexcel IGCSE Maths (4MA1) knowledge organiser
Everything to know about geometry and trigonometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.
Key definitions
- Scale Drawings and Bearings
- Bearings are 3-figure angles measured clockwise from North. Back-bearing = original ± 180°.
- Pythagoras' Theorem
- Pythagoras: in a right-angled triangle, a² + b² = c² (c = hypotenuse).
- Sine and Cosine Rules
- For triangles without a right angle: sine rule a/sin A = b/sin B, cosine rule a² = b² + c² − 2bc cos A, area = ½ab sin C.
- Vectors
- A vector has size and direction. Add column vectors component by component; parallel vectors are multiples of each other.
Key formulas
Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.
| Pythagoras | \(a^2+b^2=c^2\) |
| SOHCAHTOA | \(\sin\theta=\frac{\text{opp}}{\text{hyp}},\) \(\cos\theta=\frac{\text{adj}}{\text{hyp}},\) \(\tan\theta=\frac{\text{opp}}{\text{adj}}\) |
| Sine ruleOn the 4MA1 formulae page | \(\frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}\) |
| Cosine ruleOn the 4MA1 formulae page | \(a^2=b^2+c^2-2bc\cos A\) |
| Area of a triangleOn the 4MA1 formulae page | \(\tfrac12ab\sin C\) |
| Exact values | \(\sin30^\circ=\tfrac12,\) \(\cos60^\circ=\tfrac12,\) \(\tan45^\circ=1,\) \(\sin60^\circ=\tfrac{\sqrt3}2,\) \(\sin45^\circ=\tfrac{\sqrt2}2\) |
| Polygons (\(n\) sides) | \(\text{interior sum}=(n-2)\times180^\circ,\) \(\text{exterior angle (regular)}=\tfrac{360^\circ}n\) |
| Areas | \(\text{triangle }\tfrac12bh,\) \(\text{parallelogram }bh\) |
| Area of a trapeziumOn the 4MA1 formulae page | \(\tfrac12(a+b)h\) |
| Circle | \(C=2\pi r=\pi d,\) \(A=\pi r^2\) |
| Arc; sector | \(\text{arc}=\frac{\theta}{360}\times2\pi r,\) \(\text{sector}=\frac{\theta}{360}\times\pi r^2\) |
| Prism; cylinderOn the 4MA1 formulae page | \(V=\text{cross-section}\times\text{length};\) \(V=\pi r^2h,\) \(\text{curved }A=2\pi rh\) |
| Cone (slant \(l\))On the 4MA1 formulae page | \(V=\tfrac13\pi r^2h,\) \(\text{curved }A=\pi rl\) |
| SphereOn the 4MA1 formulae page | \(V=\tfrac43\pi r^3,\) \(A=4\pi r^2\) |
| Pyramid | \(V=\tfrac13\times\text{base area}\times h\) |
| Similar shapes, scale factor \(k\) | \(\text{lengths}\times k,\) \(\text{areas}\times k^2,\) \(\text{volumes}\times k^3\) |
More formulas are on the full Edexcel IGCSE Maths (4MA1) formula sheet.
Worked example
Find the area of a triangle with sides 7 cm and 9 cm and included angle 40°.
- ½ × 7 × 9 × sin 40° = 20.2 cm² (3 s.f.).
Common mistakes
- Similar shapes: length scale factor used for area or volume
- Circle theorems: reasons not in the recognised wording
- Confusing alternate and co-interior angles
- Using 360 ÷ n for the interior angle
More on what examiners see students get wrong: Examiner Insights.
You should be able to…
- Use the relationship between speed, distance and time to solve problems, including converting between units such as km/h and m/s.
- Calculate the perimeter and area of triangles, parallelograms and trapezia, and find missing lengths from a given area.
- Solve problems with angles of elevation and depression and with bearings by drawing right-angled triangles and using trigonometry.
- Use the area scale factor k² for similar shapes to find missing areas or lengths, such as the area of an enlarged photograph.
- Use the cosine rule to find a missing side, or an angle when all three sides are known, in triangles that are not right-angled.
- Write geometric proofs using angle facts, congruence and circle theorems, giving a clear reason for every step of the argument.
The printable sheet
Revise it next
- Geometry and trigonometry: revision notes
- Practise geometry and trigonometry
- Skill Builders
- Edexcel IGCSE Maths (4MA1) formula sheet (PDF)
Other Edexcel IGCSE Maths (4MA1) topics: Number · Algebra · Graphs, sequences and calculus · Statistics and probability · All Edexcel IGCSE Maths (4MA1) organisers