| Pre-calculus
Contents - A |
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Prerequisites |
The set of real
numbers |
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Rational numbers |
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Irrational numbers |
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The
real number line and relations |
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Interval
definition and notation |
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Distance
and absolute value |
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Properties of the real
numbers |
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Order
of operations |
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Absolute value
equations |
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Linear Inequalities
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Absolute value
inequalities |
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Algebraic expressions |
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Expanding
algebraic expression by removing parentheses |
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The binomial expansion
algorithm |
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Factoring and expanding algebraic expressions, rules for transforming algebraic expressions |
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Factoring
quadratic trinomials |
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Factoring polynomials |
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Rational expressions |
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Solving complex rational expressions
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Imaginary
and Complex Numbers |
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Addition and
subtraction of complex numbers |
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Multiplication and
division of
complex numbers |
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Polar or trigonometric
notation of complex numbers |
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Multiplication
and division of complex numbers in the polar form |
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Exponentiation
and root extraction of complex numbers in the polar form |
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Powers and roots of
complex numbers, use of de Moivre’s formulas |
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Euler’s
formula,
relationship between trigonometric functions and the complex exponential
function |
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Linear
equation
in one variable
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Solving linear equations |
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Linear
equation
in one variable, examples
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Linear Inequalities
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Solving inequalities |
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Properties of
inequalities |
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Examples
of solving single linear inequalities |
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Solving
compound (double) inequalities |
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Equations
with Rational Expressions |
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Solving rational
equations |
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Rational
equations - Linear equations |
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Rational
Inequalities |
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Method of solving
rational inequalities
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The
graph of the translated equilateral (or rectangular) hyperbola
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Quadratic Equations and Quadratic
Function |
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Quadratic equation |
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Solving quadratic equations by completing the
square, the quadratic formula |
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Solving quadratic equations by factoring,
Vieta's formula |
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Quadratic function or
the second-degree polynomial |
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Vertex
(maximum/minimum) - coordinates of translation
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Roots or zeros of the
function, axis of symmetry and y-intercept |
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Transformations
of the quadratic function's expression |
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Graphing a quadratic
function |
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Transformations
of the graph of the quadratic function |
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Quadratic
inequalities
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Solving
quadratic inequalities |
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Graphic solution of
quadratic inequalities |
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Binomial
equations |
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Solving binomial equations |
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Equations
reducible to quadratic - biquadratic equations |
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Solving equations reducible to quadratic |
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Absolute value
equations, quadratic
equations and functions |
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Solving quadratic
equations with absolute value |
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Graphing absolute value
functions or equations, examples |
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Radical
or irrational equations
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Solving
irrational or radical equations |
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Rectangular
(Two-dimensional, Cartesian) Coordinate System |
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Coordinate axes, x-axis
and y-axis,
origin, quadrants
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Points in the
Coordinate plane |
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Midpoint of a line segment
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The distance formula
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Dividing
a line segment in a given ratio |
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The
area
of a triangle |
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The
coordinates of the centroid of a triangle |
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Lines
parallel to the axes, horizontal and vertical lines
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Polar Coordinate System
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Polar
and Cartesian coordinates relations |
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Conversion from polar
to rectangular coordinates |
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Conversion from
rectangular to polar coordinates |
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Polar coordinates of a point |
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Equation
of a line in polar form |
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Lines
parallel to the axes, horizontal and vertical lines |
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Lines
running through the origin or pole (radial lines) |
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Polar
equation
of a line |
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Equation
of a circle in polar form |
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General
equation of a circle in polar coordinates |
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Polar
equation of a circle with a center on the polar axis running
through the pole |
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Polar
equation of a circle with a center at the pole |
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Parametric Equations |
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Parametric
equations definition |
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The
parametric equations of a line |
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The
parametric equations of a line passing through two points |
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The direction of
motion of a parametric curve |
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Evaluation
of
parametric equations for given values of the parameter |
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Sketching parametric
curve |
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Eliminating the
parameter from parametric equations |
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Parametric
and rectangular forms of equations
conversions |
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The
parametric equations of a
quadratic polynomial, parabola |
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The
parametric equations of the parabola, whose axis of symmetry is parallel
to the y-axis
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The parametric equations of the
parabola, whose axis of symmetry is
parallel to the x-axis |
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The parametric equations of a
circle
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The parametric equations of a
circle
centered at the origin with radius
r |
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The parametric equations of a
translated circle with center (x0, y0) and radius r |
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The parametric equations of an
ellipse |
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The parametric equations of an
ellipse
centered at the origin |
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The parametric equations of a
translated ellipse with center at (x0, y0) |
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Parametric equations of a hyperbola
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The
parametric equations of a
hyperbola expressed by trigonometric functions |
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The
parametric equations of a hyperbola expressed by hyperbolic
functions |
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The
definition of the hyperbolic functions |
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Relations
between hyperbolic and trigonometric or circular functions |
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The
parametric equations of the equilateral or rectangular hyperbola |
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The
parametric equations of the general hyperbola |
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Use
of parametric equations, example |
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Trigonometric
Functions Basics |
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Unit of measurement of
angles - a radian (the circular measure) |
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Degrees to radians and radians to degrees conversion examples |
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The unit circle or
the trigonometric circle |
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Definitions of
trigonometric functions |
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Periodicity of
trigonometric functions |
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Signs of trigonometric
functions |
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Trigonometric
functions of arcs from 0
to ±
2p
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Trigonometric
functions of negative arcs or angles |
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Trigonometric
functions of complementary angles |
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Trigonometric
functions of supplementary angles |
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Trigonometric
functions of arcs that differ on p/2 |
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Trigonometric
functions of arcs that differ on p |
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Trigonometric
functions of arcs whose
sum is 2p |
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Trigonometric
functions of angles lying on axes |
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Values of
trigonometric functions of arcs p/6, p/4 and p/3 |
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The values of the trigonometric functions of arcs that are multipliers of
30°
(p/6)
and 45°
(p/4) |
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| Pre-Calculus
contents continue |
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