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IB Maths AA Topic 3 Notes

This page contains our IB Maths AA notes for topic 3. By reading each one of these notes, you will fully cover the content for IB Maths AA 'Geometry & Trigonometry'.

All Topic 3 Sub-topics 3.1: Fundamentals Of Geometry 3.2: Introduction To Trigonometry 3.3: Applied Trigonometry 3.4: Circles 3.5: Unit Circle 3.6: Trigonometric Identities 3.7: Trigonometric Graphs (HL)3.8: Advanced trigonometry (HL)3.9: Compound angles (HL)3.10: Vectors (HL)3.11: Lines (HL)3.12: Planes

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Chapters

3.1: Fundamentals of geometry

1. Distance in 3D

2. Midpoint in 3D

3. Volume of 3D solids

4. Surface area of 3D solids

5. Angles in 3D shapes

3.2: Introduction to trigonometry

1. Right-angled triangle trigonometry

2. The sine rule

3. The cosine rule

4. Area formula

5. Triangle problem strategy

3.3: Applied trigonometry

2. Angles of elevation & depression

3. Right-angled triangles

4. Non-right-angled applications

5. Constructing diagrams

3.4: Circles

3. Area of a sector

3.5: Unit circle

1. The unit circle

2. Special angles and quadrants

4. Tangent as a gradient

5. Ambiguous case of the sine rule

3.6: Trigonometric identities

1. Core identities

2. Finding unknown ratios

3. Equations with finite intervals

4. Hidden quadratics

5. Graphical methods

3.7: Trigonometric graphs

1. Basic sine, cosine, and tangent graphs

2. Amplitude, period & midline

3. Transformations

4. Sketching trigonometric graphs

5. Real-life contexts

3.8: Advanced trigonometry (HL)

1. Reciprocal trigonometric functions

2. Reciprocal Pythogorean identities

3. Inverse trigonometric functions

3.9: Compound angles (HL)

1. Compound angle formulas

2. Using the identities

3. Proving identities

4. Solving equations

3.10: Vectors (HL)

1. Scalars & Vectors

2. Position vectors

3. Basic vector operations

4. Scaling & parallel vectors

5. Magnitude & unit vectors

6. Vector geometry laws & dividing line segments

7. Scalar (Dot) product

8. Vector (Cross) product

3.11: Lines (HL)

1. Equations of a line

2. Angle between two lines

3. Parallel, coincident, intersecting & skew lines

4. Kinematics interpretation

3.12: Planes (HL)

1. Equations of a plane

2. Finding a normal vector

3. Angles involving planes

4. Meaning of solution sets

5. Intersections

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Distance in 3D

If two points are $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ , then the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Math Topic 3 subTopic 1 notes image 1

This is the three-dimensional version of Pythagoras' theorem.

Find the distance between $A(0,6,0)$ and $D(3,3,6)$ .
Substitute the coordinates into the formula: $d=\sqrt{(3-0)^2+(3-6)^2+(6-0)^2}$ .
$d=\sqrt{3^2+(-3)^2+6^2}$ .
$d=\sqrt{9+9+36}=\sqrt{54}$ .
$d=3\sqrt{6}$ .
So the distance between $A$ and $D$ is $3\sqrt{6}$ .

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