Year 11 Term 1: Pythagoras in 3d, area using sine, bearings

Bearings• Measured from north

• Measured in a clockwise direction• Always have 3 digits

Note: Where you are going FROM is usually written 2nd

e.g, Find the bearing of B from A

Note: 2 North lines can form a supplementary angle (sum to 180⁰)

Pythagoras theorem

a² + b² = c²

c

b

a

Year 11 Term 1: Sine and Cosine rule

Cosine rule2 sides and the angle in between or all 3 sides

𝑥2 = 9.62 + 7.82 − (2 × 9.6 × 7.8 × cos 85)

𝑥 = 11.8

cos 𝜃 =7.22 + 8.12 − 6.62

2 × 7.2 × 8.1

𝜃 = 50.7°

Sine ruleComparable pair

sin 𝜃

1.9=sin 85

2.4

𝑥

sin 85=

5.2

sin 46

𝑥 =5.2 × sin 85

sin 46= 3.75𝑐𝑚

sin 𝜃 =1.9 × sin 85

2.4= 0.789

𝜃 = 𝑠𝑖𝑛−1 0.789 = 52.1°

Year 11 Term 1: manipulating surds

Year 11 Term 1: Completing the square and the quadratic formula

Year 11 Term 1: enlargements with fractional and negative scale factors and direct and inverse proportion

Composite functions

Inverse functions

Year 11 Term 1: Composite and inverse functions

Year 11 Term 1: Vectors