|
Learning Outcomes |
Resources
|
COMPLEX NUMBERS
|
|
| Why do we need complex numbers? | ARTICLE |
| Indices/surds | |
| Expand (x+1)(x-6)(x+2) | Expanding three brackets
|
| Expand (a+b+c+d)^2 | |
| Factorising x^1/2 - x^3/2 | Factorising Difference of Squares |
| Factorising pq+pr-qs-rs | |
| Factorising x^2+7x+12 | |
| Factorising 4x^2-44x+112 | |
| Factorising 2x^2+11x+12 | Factorising Quadratics with a not 1 |
| Factorising x^16 - x^8 | Factorising Difference |
| Factorising mixed | |
| Factorising x^3+8 |
|
| Solving quadratics 4x^2=9 | |
| Solving quadratics x^2+7x-3=0 |
|
| Solving ineq's 2(1-4x)/5 +6 less than (1-x)/2 | |
| Change the subject y=4/3x | |
| Algebraic fractions (7x-14)/(5x-10) | |
| Algebraic fractions add/ subtract | Add and Subtract Algebraic Fractions
|
EXTENSION |
Changing Subject Rational Functions
Partial Fraction Decomposition |
| REVISION (2 LESSONS):MANIPULATE FUNCTIONS | |
| Domain/range | |
| Function or not? | |
| Transformation of functions | |
| Even/odd or periodic? | |
| Composite functions | Composition Functions |
| Inverse functions | |
| Rational functions (ax+b)/(cx+d) | |
| Domain/range of rational functions | |
| Sketch rational functions | |
| EXTENSION |
|
| REVISION (2 LESSONS):EXP AND LOG FUNCTIONS | |
| Sketch e^(-x) or e^(2x)+1 | |
| Solve log base 3 of(x)=4 | |
| Simplify 3log(4)+2log(2) | |
| Solve exp eq's 6^(x)+18=40 | |
| Sketch ln(x)-2 | |
| Applications of log's | MODELLING LOGS ACTIVITY |
EXTENSION |
|
TOPIC 4 FALLS INTO THE CATEGORY OF CONICS
TEACH ONLY POLAR COORDINATES |
|
| REMAINDER AND FACTOR TH (3 LESSONS) | |
| Long division | Long Division Algorithm
|
| Remainder theorem | Substitution technique
Dividing polynomials and the remainder theorem
Remainder theorem |
| Factor theorem | |
EXTENSION |
|
| BINOMIAL TH (5 LESSONS) (NOT IN THE SYLLABUS) | |
| -Evaluate factorials | |
| -Combinations | |
| -Binomial coefficients |
|
-Expand (y+1/y)^6
| |
| -Approximation (10.1)^5 | |
| -General term | |
EXTENSION | |
| SURDS (4 lessons) | |
| Rational or irrational? | Rational or Irrational |
| Simplify surds sqrt(72) | |
| Add/subtract surds 3sqrt(64) -2sqrt(32) | |
| Multiply 2sqrt(32) x sqrt(27) | |
| Rationalise 3/2sqrt(5) | Rationalise Denominators
|
| Rationalise 4/(sqrt6+sqrt3) |
|
EXTENSION | |
| QUADRATICS (3 LESSONS) | |
| Discriminant | |
| Complete square | |
| Applications of quadratic | |
| Inequations | |
| Prove inequalities | |
EXTENSION | |
|
COMPLEX INTRODUCTION (6 LESSONS) | Why do we need them?
|
| Equating imaginary numbers | |
| Add/subtract | |
| Multiply |
|
| Powers of i | Imaginary Units and Its Powers
IMAGING SONG |
| Conjugates | |
| Division | |
| Modulus | |
| Mixed | APPLICATIONS OF COMPLEX NUMBERS |
EXTENSION |
CLASSROOM ACTIVITIES!
z^5+243=0 and z^5-243=0
|
COMPLEX & POLYNOMIALS (5 LESSONS) |
INTERPRETATION OF COMPLEX |
| Fundamental theorem of Algebra | FACTORISING USING CALCULATOR |
| Solving quadratics by completing square | |
| Solving quadratics by using formula | |
| Polynomials given roots | |
Using factor theorem |
|
| Using conjugate root theorem | |
EXTENSION | PHANTON GRAPHS (BRILLIANT!)
QUARTIC EQUATIONS |
| DE MOIVRE'S & COMPLEX ROOTS (4 LESSONS) | De moivre |
| Rectangular to polar and vice versa | Polar Coordinates (r,arg)
|
| Multiply polar numbers |
Euler's Identity using Taylor Series
Multiplying Polar Form
Polar numbers and trig applications
Why polar form?
Polar form
Multiplying in Polar Form |
| De Moivre's (3+i)^6 | DE MOIVRE'S
De Moivre's Backwards
SQUARE ROOT OF -1 |
| Symmetry property | ROOTS OF A POLYNOMIAL APP!
|
| EXTENSION | Solving Quartics with Real Solutions
|
