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
Transformations of parabolas, Graphing quadratics, Finding the equation of quadratics
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
Euler's Rule for Linear Approximations
Related rates of change
Finding derivatives using the product & quotient rules.
Finding the derivatives of circular functions (sin, cos or tan x).
Derivatives of logarithmic functions
Derivatives of exponential functions.
Using the chain rule to find derivatives.
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
Radians & degrees, Sin, cos & tan, The unit circle, Values of sin x , cos x & tan x
Logarithms, Log rules, Solving logarithmic equations, Graph of a logarithmic function
