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
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Episode 35: Episode 35 - Sampling & populations
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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…
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Episode 34: Episode 34 - Continuous probability distributions
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13:39
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13:39
Probability density functions, Calculating probabilities, Median value, Mean value, Variance, Cumulative probability distributions
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Episode 33: Episode 33 - Approximating areas under curves
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Area under curves, Left end-point approximation, Right end-point approximation, Improvements to rectangle approximations, Find the total from a rate
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Episode 32: Episode 32 - Quadratic graphs
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Transformations of parabolas, Graphing quadratics, Finding the equation of quadratics
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Episode 31: Episode 31 - Transformation of functions
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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)
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Episode 30: Episode 30 - Simultaneous equations
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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
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Episode 29: Episode 29 - Inverse functions
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Inverse functions - graphs Inverse functions - rules Inverse functions - from equations Finding inverse functions - one to one.
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Episode 28: Episode 28 - Graphs of circular functions
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12:44
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
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Episode 27: Episode 27 - The binomial probability distribution
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18:37
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
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Episode 26: Episode 26 - The normal distribution
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Continuous probability density functions The normal distribution Calculating probabilities Z tables Finding values from a probability
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Episode 25: Episode 25 - Discrete probability distributions
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Probability distributions Discrete random variables Expected values (mean) Variance Linear functions - mean & standard deviation Standard deviation
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Episode 24: Episode 24 - Definite integrals
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Area under a curve - integration Circular functions Exponential functions Hyperbolic functions Area between two curves Average value of a function
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Episode 23: Episode 23 - More Integration
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Anti-differentiation of powers of x Anti-differentiation of circular functions Anti-differentiation of exponential functions Anti-differentiation of 1/x
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Episode 22: Episode 22 - Euler's Rule for Linear Approximations
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Euler's Rule for Linear Approximations
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Episode 21: Episode 21 - Related rates of change
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Related rates of change
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Episode 20: Episode 20 - The product & quotient rules
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Finding derivatives using the product & quotient rules.
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Episode 19: Episode 19 - Derivatives of circular functions
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Finding the derivatives of circular functions (sin, cos or tan x).
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Episode 18: Episode 18 - Derivatives of logarithmic functions
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Derivatives of logarithmic functions
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Episode 17: Episode 17 - Derivatives of exponential functions
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Derivatives of exponential functions.
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Episode 16: Episode 16 - The chain rule
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11:23
Using the chain rule to find derivatives.
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Episode 15: Episode 15 - Binomial expansion
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Expanding polynomials with repeated factors using the binomial expansion. Includes a quick introduction to combinations.
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Episode 14: Episode 14 - Modelling with exponential and logarithmic functions
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12:32
Finding the equation of an exponential or logarithmic equation based on the points and asymptotes.
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Episode 13: Episode 13 - Integration
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18:42
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
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Episode 12: Episode 12 - Functions & Relations
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Relations, Set rules & symbols, Sets of numbers, Sets & intervals, Functions, Relations, Function notation, Hybrid functions, Hyperbola, Truncus, Square root, Circles, Inverse functions
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Episode 11: Episode 11 - Probability
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Probability, Tree diagrams, Lattice diagrams, Venn diagrams, Karnough maps, Probability tables, Union & intersection rules, Conditional probability, Markov chains
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Episode 10: Episode 10 - Matrix Operations
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19:39
Introduction to matrices , Addition & subtraction, Scalar multiplication, Matrix multiplication, The unit matrix, Matrix division - the inverse matrix, Using matrices.
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Episode 9: Episode 9 - Differentiation
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Differentiation by first principles, Differentiation of polynomials, Examples of derivative functions & gradients, Graphs of derivative functions, Tangents, Normal lines, Finding stationary points
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Episode 8: Episode 8 - Rates of change
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10:30
Rates of change, Average rate of change, Instantaneous rates of change, Rates of change from graphs, Graphs of motion
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Episode 7: Episode 7 - Circular functions & angles
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Radians & degrees, Sin, cos & tan, The unit circle, Values of sin x , cos x & tan x
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Episode 6: Episode 6 - Logarithmic functions
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Logarithms, Log rules, Solving logarithmic equations, Graph of a logarithmic function
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Episode 5: Episode 5 - Exponential functions
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16:35
Exponents & power rules, Using power rules, Solving exponential equations, Graphs of exponential functions
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Episode 4: Episode 4 - CAS calculator skills - Cubic functions
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Some tips on graphing and solving cubic functions using the TI-Nspire CAS calculator.
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Episode 3: Episode 3 - Cubic Functions
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Expanding cubic expressions, Factorisation by long division, The factor theorem, Graphs of cubic functions
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Episode 1: Episode 1 - Linear Functions
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17:10
Gradient of lines, Graphing linear equations, Finding the equation of a line, Perpendicular lines, Distance between points, Midpoint of a line
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Episode 2: Episode 2 - Factorising & solving quadratic equations
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Expanding quadratic expressions, Factorising quadratic expressions, Completing the square, Solving quadratic equations, The quadratic formula, The discriminant
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