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Specialist Maths - Units 3 & 4 (2016-22)

Units 3 & 4 Specialist Maths
These lessons are for the 2016 - 2022 Study Design

Topics

 Functions & Graphs
Differential Calculus
Differential Equations
Vectors & Vector Calculus
Probability & Statistics
 Algebra (Complex Numbers)
Integral Calculus
Kinematics
Dynamics (Mechanics)

Exam Resources

Access the Exam Resource Page HERE
 
Functions & Graphs
Circular Functions
Circles, Ellipses, Hyperbolae
Reciprocal Circular Functions
Note: There are a couple of arithmetic errors in an example. The process is correct.
Inverse Circular Functions
Graphing Rational Functions
Modulus Function
Parametric Equations
Compound and Double Angle Formulae
Note: There is a domain error in the last part of the last example. The process is correct.
Solving Equations with Sec, Cosec, Cot
 
Algebra and Complex Numbers
Definitions and Properties
Polar Form (modulus-argument)
Solving quadratic equations over the Complex Field
Solving Equations using De Moivre’s theorem
Modulus, Conjugate & Division
Operations in Polar form (modulus–argument)
Solving polynomial equations over the Complex Field
Sketching subsets of the complex plane
Finding Complex Roots
Information on how this can be done on the Casio Classpad using a program can be found HERE
 
Differential Calculus
Chain, Product & Quotient Rules
Derivative of Inverse Circular Functions
Points of Inflection
Rational Functions
Derivative of x = f(y)
Second Derivatives
Related Rates
Implicit Differentiation
 
Integral Calculus
Antidifferentiation
Integration by Substitution
Integration using Trigonometric Identities
Integration Review
Area Between Curves
There is an error in the third example for the integration of sin(2x).   It should be -1/2cos(2x).   It gets fixed in the end.
Volume of Revolution
Antiderivatives of Inverse Circular Functions
Definite Integrals by Substitution
Integration using Partial Fractions
Polynomial Division with the Classpad
File Size: 368 kb
File Type: pdf
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Partial Fractions with the Classpad
File Size: 468 kb
File Type: pdf
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 Fundamental Theorem of Calculus (area)
Integration with CAS
The TV in the other video does not come out well.
This video shows the calculator

Lengths of Curves
 
Differential Equations
Verifying Solutions
Function of the Dependent Variable
Separation of Variables
Using a Definite Integral
Slope (direction) field for a differential equation
Function of the Independent Variable
Applications
Differential Equations with related rates
Euler's Method
 
Kinematics
Position, Velocity & Acceleration
Velocity-time graphs
Expressions for acceleration
Constant Acceleration Formula
 D.E.'s of the form v = f(x) and a = f(v)
 
Vectors & Vector Calculus
Vector Operations & Resolution of Vectors
The notes referred to in the above video are below
Vectors - Definitions - handout
File Size: 591 kb
File Type: pdf
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Vector Components - handout
File Size: 327 kb
File Type: pdf
Download File

Vector Projections (components, resolutes)
Geometric Proofs using Vectors
Vector calculus
Velocity and acceleration for motion along a curve
Scalar (dot) Product of Vectors
Collinearity
Vector functions - Position vectors as function of time
 
 Dynamics (Mechanics)
Force
Resolution of Forces, Inclined Plane
Variable Force
Vector Functions
Newton's Second Law
Connected Particles
Equilibrium
 
Probability and Statistics
Linear Combinations of Random Variables and Independent Normal Random Variables
The Central Limit Theorem
Hypothesis Testing for the Mean
Errors in Hypothesis Testing
The Distribution of the Sample Mean of a normally distributed random variable
Confidence Intervals for the Population Mean
One-Tail and Two-Tail tests
binomial pdf and pascals triangle
File Size: 222 kb
File Type: pdf
Download File

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  • Home
  • Units 1 & 2 Physics
    • Thermal
    • Elect U1
    • Matter
    • Motion-2
    • Radiation-Health
  • Units 3 & 4 Physics
    • Motion 3-4
    • Move without contact
    • Electrical Energy
    • Waves-Light
    • Light-Matter
    • Practical Investigation
    • Physics Exam Resources >
      • 2021 Physics Exam Videos
  • Maths Pages
    • 3-4 Methods >
      • Methods Exam Resources >
        • 2021 MM Exam 1 Videos
        • 2021 MM Exam 2 Videos
    • Units 1 & 2 Methods
    • Specialist Units 3 & 4 (2016-21) >
      • Specialist Maths Exam Resources >
        • 2021 SM Exam 1 Videos
        • 2021 SM Exam 2 Videos
    • Specialist Units 1 & 2 (2016-21)
    • 3-4 Further
  • Credits & Stuff
  • Previous Study Designs
    • Specialist 1-2 (2006-15)