Introduction to differential equations Revision Notes, Past Papers & Questions for SSCE HSC Mathematics Extension 1

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SSCE HSC Mathematics Extension 1 Introduction to differential equations Revision Notes

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Other SSCE HSC Mathematics Extension 1 topics to explore

Mathematics Extension 1 HSC

Absolute value functions

Mathematics Extension 1 HSC

Arrangement of n objects when some are identical

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Bernoulli trials

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Binomial distribution

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Circular and simultaneous inequalities

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Combinations

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Counting techniques in probability

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Definite integrals and substitution

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Differentiation of inverse trigonometric functions

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Direction fields

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Division of polynomials and the remainder theorem

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Double angle formulae

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Expansion of (1 + x)^n, Pascal’s triangle

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Exponential growth and decay

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Fundamental counting principle

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Graphing polynomials by adding ordinates

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Graphing polynomials by multiplying ordinates

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Half-angle formulae

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Harder exponential growth and decay

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Indefinite integrals and substitution

Mathematics Extension 1 HSC

Inequalities involving absolute value and square roots

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Integrals involving trigonometric substitution

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Integrals of the type ∫f(x)(f(x))^n dx

Mathematics Extension 1 HSC

Integration involving inverse trigonometric functions

Mathematics Extension 1 HSC

Integration of sin^2x and cos^2x

Mathematics Extension 1 HSC

Introduction to vectors

Mathematics Extension 1 HSC

Inverse functions

Mathematics Extension 1 HSC

Inverse trigonometric functions

Mathematics Extension 1 HSC

Mathematical induction involving series

Mathematics Extension 1 HSC

Mean and variance of the binomial distribution

Mathematics Extension 1 HSC

Modelling with first-order differential equations

Mathematics Extension 1 HSC

More Pascal’s triangle expansions

Mathematics Extension 1 HSC

Multiple roots of a polynomial equation

Mathematics Extension 1 HSC

Normal approximation for the sample proportion

Mathematics Extension 1 HSC

Overview of trigonometric equations

Mathematics Extension 1 HSC

Parametric form of a function or relation

Mathematics Extension 1 HSC

Pascal’s triangle relations and the binomial theorem

Mathematics Extension 1 HSC

Permutations

Mathematics Extension 1 HSC

Pigeonhole principle

Mathematics Extension 1 HSC

Polynomial functions

Mathematics Extension 1 HSC

Polynomials

Mathematics Extension 1 HSC

Problems involving displacement and velocity

Mathematics Extension 1 HSC

Problems involving forces

Mathematics Extension 1 HSC

Projectile motion

Mathematics Extension 1 HSC

Projections of vectors

Mathematics Extension 1 HSC

Proving divisibility by induction

Mathematics Extension 1 HSC

Quadratic inequalities

Mathematics Extension 1 HSC

Rates of change with respect to time

Mathematics Extension 1 HSC

Rational function inequalities

Mathematics Extension 1 HSC

Reciprocal functions

Mathematics Extension 1 HSC

Related rates of change

Mathematics Extension 1 HSC

Relationship between roots and coefficients

Mathematics Extension 1 HSC

Scalar product of vectors

Mathematics Extension 1 HSC

Simple trigonometric equations

Mathematics Extension 1 HSC

Solving differential equations of the form dy/dx = f(x)

Mathematics Extension 1 HSC

Solving differential equations of the form dy/dx = g(y)

Mathematics Extension 1 HSC

Solving differential equations using separation of variables

Mathematics Extension 1 HSC

Solving equations using angle formulae

Mathematics Extension 1 HSC

Solving quadratic trigonometric equations

Mathematics Extension 1 HSC

Solving trigonometric equations using the auxiliary angle method

Mathematics Extension 1 HSC

Square root functions

Mathematics Extension 1 HSC

Sum and difference of two angles

Mathematics Extension 1 HSC

The factor theorem

Mathematics Extension 1 HSC

Trigonometric equations involving angle formulae

Mathematics Extension 1 HSC

Trigonometric products as sums or differences

Mathematics Extension 1 HSC

Using identities to simplify expressions and prove results

Mathematics Extension 1 HSC

Vectors in component form

Mathematics Extension 1 HSC

Vectors in geometric proofs

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Vectors in two dimensions

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Velocity and acceleration as rates of change

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Volumes of solids of revolution

Mathematics Extension 1 HSC

When induction doesn’t work

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