VCE Maths Methods Podcast: Recent Episodes
Maths Methods
A summary of the topics covered in VCE Maths Methods Units 1 to 4.
Created by Justin Vincent at Warrnambool College.
Check out more: https://vcemathsmethods.com
Sample proportions, Sampling distribution - small populations, Sampling distribution - large populations, Sampling distribution - normal distribution approximation, Mean & variance of a sample proportion, Sampling distribution - comparing approximations, Mean & variance of the sample proportion, Confidence intervals, Margin of error
Probability density functions, Calculating probabilities, Median value, Mean value, Variance, Cumulative probability distributions
Area under curves,
Left end-point approximation,
Right end-point approximation,
Improvements to rectangle approximations,
Find the total from a rate
Translations, Dilations (from the x axis), Dilations (from the y axis), Reflections (in the x axis), Reflections (in the y axis), Summary, Applying transformations, Finding equations from transformation (graphs), Finding equations from transformations (from points)
Intersection of lines - from a graph, Intersection of lines - substitution of equations, Simultaneous equations - elimination method, Simultaneous equations - matrix method, Families of parallel lines - no solutions, Infinite solutions, Example question
Inverse functions - graphs
Inverse functions - rules
Inverse functions - from equations
Finding inverse functions - one to one.
Values of sin x , cos x & tan x,
Graphs of sin x & cos x,
Transformations of sin graphs,
Solving circular function equations,
Graphs of tan x
The coin toss - three coins
The coin toss - four coins
The binomial probability distribution
Rolling dice
How many trials?
Using the TI nSpire
Graph of binomial distribution
Mean & standard deviation
Continuous probability density functions
The normal distribution
Calculating probabilities
Z tables
Finding values from a probability
Probability distributions
Discrete random variables
Expected values (mean)
Variance
Linear functions - mean & standard deviation
Standard deviation
Area under a curve - integration
Circular functions
Exponential functions
Hyperbolic functions
Area between two curves
Average value of a function
Anti-differentiation of powers of x
Anti-differentiation of circular functions
Anti-differentiation of exponential functions
Anti-differentiation of 1/x
Expanding polynomials with repeated factors using the binomial expansion. Includes a quick introduction to combinations.
Finding the equation of an exponential or logarithmic equation based on the points and asymptotes.
Find the total from a rate, Anti-differentiation, Rules for anti-differentiation, Examples of anti-derivative functions, Finding the original function, Area under a curve - integration, Signed area
Relations, Set rules & symbols, Sets of numbers, Sets & intervals, Functions, Relations, Function notation, Hybrid functions, Hyperbola, Truncus, Square root, Circles, Inverse functions
Probability, Tree diagrams, Lattice diagrams, Venn diagrams, Karnough maps, Probability tables, Union & intersection rules, Conditional probability, Markov chains
Introduction to matrices , Addition & subtraction, Scalar multiplication, Matrix multiplication, The unit matrix, Matrix division - the inverse matrix, Using matrices.
Differentiation by first principles, Differentiation of polynomials, Examples of derivative functions & gradients, Graphs of derivative functions, Tangents, Normal lines, Finding stationary points
Rates of change, Average rate of change, Instantaneous rates of change, Rates of change from graphs, Graphs of motion
Exponents & power rules, Using power rules, Solving exponential equations, Graphs of exponential functions
Expanding cubic expressions, Factorisation by long division, The factor theorem, Graphs of cubic functions
Gradient of lines, Graphing linear equations, Finding the equation of a line, Perpendicular lines, Distance between points, Midpoint of a line
Expanding quadratic expressions,
Factorising quadratic expressions,
Completing the square,
Solving quadratic equations,
The quadratic formula,
The discriminant