Mathematics Specialist Units 1 & 2
Based on AJ Sadler's Text
Chapter 4 - Vectors in Component Form
Unit Vectors:
https://www.khanacademy.org/math/precalculus/vectors-precalc/magnitude-direction/v/unit-vector-intro
http://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/v/unit-vectors-and-engineering-notation
Ordered set notations:
http://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/v/projectile-motion-with-ordered-set-notation
Vector Dot Product: https://www.khanacademy.org/science/physics/electricity-magnetism/new-topic-2015-04-15T21:11:22.485Z/v/the-dot-product
Unit Vectors:
https://www.khanacademy.org/math/precalculus/vectors-precalc/magnitude-direction/v/unit-vector-intro
http://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/v/unit-vectors-and-engineering-notation
Ordered set notations:
http://www.khanacademy.org/science/physics/two-dimensional-motion/two-dimensional-projectile-mot/v/projectile-motion-with-ordered-set-notation
Vector Dot Product: https://www.khanacademy.org/science/physics/electricity-magnetism/new-topic-2015-04-15T21:11:22.485Z/v/the-dot-product
Chapter 12: Proof
There are a lot of really good proof videos at WooTube. The proof videos are at the following address:
https://www.youtube.com/user/misterwootube/search?query=proof
Mathematical induction set: https://www.youtube.com/playlist?list=PL5KkMZvBpo5Bf6wS0saU1yNvDxBWN5o9j
Induction Inequality Proofs (Eddie Woo): https://www.youtube.com/watch?v=7VLSjyUa2aA
There are a lot of really good proof videos at WooTube. The proof videos are at the following address:
https://www.youtube.com/user/misterwootube/search?query=proof
Mathematical induction set: https://www.youtube.com/playlist?list=PL5KkMZvBpo5Bf6wS0saU1yNvDxBWN5o9j
Induction Inequality Proofs (Eddie Woo): https://www.youtube.com/watch?v=7VLSjyUa2aA
Worked Solution to Unit 2 Ex 12C Q 10 is below:
u2_ex_12c_q_10.pdf |
Chapter 13: Complex Numbers
Introduction to i and imaginary numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/imaginary_unit_i-a2/v/introduction-to-i-and-imaginary-numbers
i as the principal square root of -1: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/imaginary_unit_i-a2/v/i-as-the-principal-root-of-1-a-little-technical
Adding Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/adding-complex-numbers
Subtracting Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/subtracting-complex-numbers
Multiplying Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/multiplying-complex-numbers
Dividing Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/dividing-complex-numbers
Complex Conjugates: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-conjugates-example
Complex Roots of a Quadratic equation: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-roots-from-the-quadratic-formula
Plotting on the Complex Plane: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/plotting-complex-numbers-on-the-complex-plane
Absolute Value of a complex number: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/absolute-value-of-a-complex-number
Introduction to i and imaginary numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/imaginary_unit_i-a2/v/introduction-to-i-and-imaginary-numbers
i as the principal square root of -1: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/imaginary_unit_i-a2/v/i-as-the-principal-root-of-1-a-little-technical
Adding Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/adding-complex-numbers
Subtracting Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/subtracting-complex-numbers
Multiplying Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/multiplying-complex-numbers
Dividing Complex Numbers: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/dividing-complex-numbers
Complex Conjugates: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-conjugates-example
Complex Roots of a Quadratic equation: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-roots-from-the-quadratic-formula
Plotting on the Complex Plane: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/plotting-complex-numbers-on-the-complex-plane
Absolute Value of a complex number: https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/absolute-value-of-a-complex-number