Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵...

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Mock Mash Up.notebook April 09, 2017 Session 2 Mock Mash Up

Transcript of Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵...

Page 1: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Session 2Mock Mash Up

Page 2: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

ExtraRemixWorked example

Exam question methods..

Algebraic Proof

Geometric Proof

Circles and lines

Vectors

3D Trigonometry

Segments

Page 3: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 4: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

∴ Statement is true

∴ is a multiple of 3

Page 5: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 6: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

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Remix

∴ one less than a multiple of 3

∴ is a multiple of 4

Page 7: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 8: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

∴ Statement is true

either (n+1) or (n+2) must be even

2 x even is a multiple of 4

∴ statement is true

Page 9: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 10: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

∵ tangent and radius are perpendicular∵ tangent and radius are perpendicular∵ isosceles triangle ∵ isosceles triangle 

∵ angle at centre double angle at circumference

∵ angles in quadrilateral sum to 180

Page 11: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 12: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

∵ radii equal

∵ BOC is isosceles

∵ SASOAC and OBC are congruent

Page 13: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 14: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

∵ opposite angles in parallelogram are equal

∵ angles around a point sum to 360

∵ base angles in isosceles triangle are equal

∵ angles in triangle sum to 180

Page 15: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 16: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 17: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 18: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 19: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 20: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

1

2

3

Page 21: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 22: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

PC is a scalar multiple of PM and both pass through P so form a straight line.

Page 23: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 24: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

WX is a scalar multiple of WY and both pass through W so form a straight line.

Page 25: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 26: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

WX is a scalar multiple of WY and both pass through W so form a straight line.

Page 27: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 28: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

H

BD

3416

D

BA

1830

H

BD

3416

θ

Page 29: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 30: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

A

B C A

E

C

8

14

7

θ

Page 31: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 32: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

B

CN

4.5

6

M

N B

3

7.5

B

CN

4.5

6

θ

α

Page 33: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 34: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Worked example

Page 35: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 36: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Remix

Page 37: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra

Page 38: Mock Mash Up.notebook - MathedUp! · Mock Mash Up.notebook April 09, 2017 Worked example ∵ tangent and radius are perpendicular ∵ tangent and radius are perpendicular ∵ isosceles

Mock Mash Up.notebook April 09, 2017

Extra