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