I. Mathematics


Arithmetic


Fractions Properties and operations of fractions. You must understand fractions to master real mathematics.


Scientific notation Representing numbers as powers of ten, like 1.23 × 10-3 – includes some nice videos


The metric system The measurement system of science (and most of the world)


Algebra

Basic algebra Learn the basic "moves" of simple algebra


Pitfalls of algebra Mistakes commonly made and how to avoid them


Solving for x Learn to solve the simplest kinds of algebraic equations.


Geometry


Geometry definitions Learn the language of geometry.


Analytic geometry Also called coordinate geometry, analytic geometry mixes the arithmetic and algebra of coordinates with the shapes and symmetry of geometry.


Distance Distance in the plane is found using the Pythagorean formula.


Lines The algebra of lines or linear functions: slope, intercept; graphing and finding the equations of lines


Midpoint The midpoint of a line segment in n-dimensions is just the average of the coordinates in each direction.


Slope The slope of a line is "rise over run," the steepness of rise or fall from left-to-right.


Parallel lines When a line intersects two parallel lines, all kinds of interesting properties arise.


Triangles The triangle is the most useful of all closed figures in geometry, and the one you should get to know best.


Circles Circles enclose the most area with the least perimeter.


Conic sections Ellipses, circles, hyperbolas and parabolas are all obtained by slicing through a cone in different ways.


The ellipse This section dives into the ellipse in more detail, with animations.


Vectors Vectors are important in math and physics. You must understand them to succeed in a study of mechanics.


Functions


The function concept Crucial for high school students – looking at algebraic equations in a new way


Domain & range Allowed values of x (domain) and y (range) for a function


Factorial function The factorial function,
e.g. 4! = 4·3·2·1 = 24


Quadratic functions VIDEO f(x) = x2 – our first curved function


Polynomial functions VIDEO Functions like f(x)=ax3+bx3+cx2+dx+e


Polynomial long division Dividing one polynomial by another using long-division techniques is a useful skill to know.


Rational functions VIDEO Rational functions are ratios of polynomial functions. They have tricky graphs with features not in polynomial graphs.


Rational & negative exponents VIDEO Using rational and negative exponents well will help you to solve a lot of complicated problems quickly.


Exponential functions VIDEO These rapidly-growing functions have the variable in the exponent.


Logistic growth functions Functions used to model growth with limits.


Compositions of functions Many complex functions are really compositions – one function inside another.


Inverse functions Functions do a job; inverse functions undo that job. They're necessary for solving many real problems.


Logarithmic functions Logarithms are the inverses of exponential functions.


The origin of e From where does the transcendental number e arise?


Parametric functions Functions in which each dimension is a function of a parameter like time.


Trigonometry


Trigonometry basics SOH-CAH-TOA trigonometry


Non-right triangle trig Any right triangle can be redrawn as a sum of two right triangles.


Inverse trig functions Inverse trig. functions undo the action of a trig function


Analytic trigonometry Relationships between trig. functions and how to manipulate them


Trigonometric equations VIDEO Trigonometric equations can have an infinite number of solutions.


Polar coordinates An explanation of polar coodinates and how to manipulate them.


Complex plane Tiptext here


Rock climbing Here's a nice example of how trig is used to solve a real problem.


Conic sections Ellipses, circles, hyperbolas and parabolas are all obtained by slicing through a cone in different ways.


Mathematics of waves The mathematics behind theories of waves like water, sound and light waves.


Calculus — Limits


Calculus start page An overview of what calculus is and how to navigate its many topics


Limits VIDEO The limit is the central concept of calculus.


Trigonometric limits The key trigonometric limits are proved and we'll see how to use them.


L'Hopital's rule L'Hopital's rule makes finding many limits much simpler than evaluating them algebraically, but you have to know derivatives first.


Differential calculus


Calculus start page An overview of what calculus is and how to navigate its many topics


The derivative VIDEO The central concept of differential calculus is derived, and we learn how to use it.


Product rule Derivation of a rule for finding the derivative of a product of functions, f(x)·g(x)


Quotient rule Derivation of a rule for finding the derivative of a ratio of functions, f(x)/g(x)


Chain rule VIDEO Derivation of a rule for finding the derivative of a composition of functions like f(g(x)) or f(g(h(x)))


Newton's method A method for finding the roots of functions numerically using the derivative


Derivatives of trig. functions The derivatives of the trigonometric functions are developed.


Derivatives of log & exp. functions Derivatives of the exponential and logarithmic functions are developed.


Derivatives of inverse functions How to find the derivative of an inverse function, f-1(x)


Linear approximation The derivative is used to find linear approximations of nonlinear functions in a specific neighborhood, a powerful, time-saving technique.


Curve Sketching Calculus enhances our ability, using basic precalculus skills, of sketching the graphs of complicated functions.


Optimization Optimization is finding the minimum or maximum of a meaningful function, such as maximum profit, least time or least cost.


Implicit differentiation VIDEO Implicit differentiation is a powerful technique that allows us to find the derivatives of curves that are not functions, such as the circle x2 + y2 = 1.


Related rates We learn to use the derivative to solve problems in which the rates of two changing things are related.


Parametric functions Finding the derivatives of functions, y(x), in which both y and x are functions of a parameter like time (t).


Ia. Computer coding


 

II. Physics


III. Chemistry


IV. Biology



V. Recipes


 


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