VCE Methods 3/4 notes

Summary:

These VCE Methods 3/4 notes contain comprehensive summary notes on various mathematical topics covered in a CAS Tinspire course in 2022. The topics covered encompass functions and relations, coordinate geometry and matrices, transformations, polynomial functions, exponential and logarithmic functions, circular functions, calculus, and probability.

The section on functions and relations introduces set and interval notation, function notation, and tests to determine if a function is odd, even, or a hybrid function. It also covers composite functions, inverse functions, and the properties of power functions.

The coordinate geometry and matrices section explores linear geometry, including the distance formula, gradient, midpoint, and angle with the x-axis. It also covers various forms of linear equations and simultaneous equations with both two and multiple variables. Matrices are introduced as well.

Transformation topics include translation, dilation, and reflection, while the polynomial functions section delves into quadratics, quadratic equations, factorization, and inequalities. Polynomial division, factorization, and cubic identities are also discussed.

Exponential and logarithmic functions cover index and logarithmic laws, as well as graphs of these functions. Circular functions introduce radians and degrees, reference angles, symmetrical properties, and graphs.

Calculus topics include differentiation using the first principle, properties and rules of derivatives, continuity, and differentiability. Application of differentiation covers rates of change, tangents and normals, stationary points, and maximum and minimum values. Antidifferentiation and integration techniques for estimating area are also included.

Lastly, the probability section addresses discrete and continuous probability, binomial and standard normal distributions, sample proportion distributions, and confidence intervals for population proportions.

These summarized notes provide a comprehensive overview of each topic, making them a valuable resource for students studying these mathematical concepts.

Excerpt:

VCE Methods 3/4 notes

FUNCTIONS AND RELATIONS ……………………………………………………………………………………. 3
Set and interval notation —————————————————————————————————– 3
Functions————————————————————————————————————————– 3
Function notation………………………………………………………………………………………………………..3
Vertical line test ………………………………………………………………………………………………………….4
Horizontal line test………………………………………………………………………………………………………4
Odd and even functions……………………………………………………………………………………………….4
Special functions —————————————————————————————————————- 5
Sum and production of functions ………………………………………………………………………………….5
Piece-wise (Hybrid) functions ……………………………………………………………………………………….6
Composite functions ? ∘ ?(?) ………………………………………………………………………………………6
Inverse functions ? − 1(?) …………………………………………………………………………………………..7
Shapes of power functions ??? …………………………………………………………………………………….8
COORDINATE GEOMETRY AND MATRICES ………………………………………………………………….. 9
Linear geometry—————————————————————————————————————– 9
Distance formula…………………………………………………………………………………………………………9
Gradient …………………………………………………………………………………………………………………….9
Midpoint ……………………………………………………………………………………………………………………9
Angle with x-axis …………………………………………………………………………………………………………9
Perpendicularity………………………………………………………………………………………………………….9
Forms of linear equation —————————————————————————————————– 9
Simultaneous equations—————————————————————————————————- 10
With two variables…………………………………………………………………………………………………….10
With multiple variables………………………………………………………………………………………………11
Matrices ————————————————————————————————————————- 12