HSC Mathematics Extension 1 - Syllabus & Notes
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Study HSC Mathematics Extension 1 Topics
Absolute value functions
Arrangement of n objects when some are identical
Bernoulli trials
Binomial distribution
Circular and simultaneous inequalities
Combinations
Counting techniques in probability
Definite integrals and substitution
Differentiation of inverse trigonometric functions
Direction fields
Division of polynomials and the remainder theorem
Double angle formulae
Expansion of (1 + x)^n, Pascal’s triangle
Exponential growth and decay
Fundamental counting principle
Graphing polynomials by adding ordinates
Graphing polynomials by multiplying ordinates
Half-angle formulae
Harder exponential growth and decay
Indefinite integrals and substitution
Inequalities involving absolute value and square roots
Integrals involving trigonometric substitution
Integrals of the type ∫f(x)(f(x))^n dx
Integration involving inverse trigonometric functions
Integration of sin^2x and cos^2x
Introduction to differential equations
Introduction to vectors
Inverse functions
Inverse trigonometric functions
Mathematical induction involving series
Mean and variance of the binomial distribution
Modelling with first-order differential equations
More Pascal’s triangle expansions
Multiple roots of a polynomial equation
Normal approximation for the sample proportion
Overview of trigonometric equations
Parametric form of a function or relation
Pascal’s triangle relations and the binomial theorem
Permutations
Pigeonhole principle
Polynomial functions
Polynomials
Problems involving displacement and velocity
Problems involving forces
Projectile motion
Projections of vectors
Proving divisibility by induction
Quadratic inequalities
Rates of change with respect to time
Rational function inequalities
Reciprocal functions
Related rates of change
Relationship between roots and coefficients
Scalar product of vectors
Simple trigonometric equations
Solving differential equations of the form dy/dx = f(x)
Solving differential equations of the form dy/dx = g(y)
Solving differential equations using separation of variables
Solving equations using angle formulae
Solving quadratic trigonometric equations
Solving trigonometric equations using the auxiliary angle method
Square root functions
Sum and difference of two angles
The factor theorem
Trigonometric equations involving angle formulae
Trigonometric products as sums or differences
Using identities to simplify expressions and prove results
Vectors in component form
Vectors in geometric proofs
Vectors in two dimensions
Velocity and acceleration as rates of change
Volumes of solids of revolution
When induction doesn’t work
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