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Pythagorean Theorem (with problems)

Pythagoras' Theorem: Given a right triangle with sides a and b and a hypotenuse h (the side opposite the right angle). Then,

Remember that:

A right triangle (right-angled triangle in B ...

Integration by parts

When the integrand is formed by a product (or a division, which we can treat like a product) it's recommended the use of the method known as integration by parts, that consists in applying the fol ...

Logarithmic Equations and Systems

A logarithmic equation is an equation that has an unknown factor in the argument of a logarithm. In reality, the resolution is reduced to the resolution of equations of the same type as the expression ...

U-Substitution

When the integrand is formed by a product (or a division, which we can treat like a product) it's recommended the use of the method known as integration by u-substitution, that consists in applyin ...

Solving a Linear Equation System

Solving this type of problems (a system) consists in finding a value for each unknown factor in a way that it applies to all the equations in the system.

In this section we'll resolve systems (lin ...

Resolved Exercises of Powers (Exponents)

Simplifying Expressions with Exponents

The activities are in order of increasing difficulty: we use the properties of exponentials (power of products, power of quotient, power of a power,..) and, after ...

Resolved Problems of Linear Equation Systems

In this section we have exercises that require to be considered as a system of equations of second dimension (two equations and two unknown factors). If we don't remember how to resolve systems (e ...

Solving a Linear Equation

In this section we resolve linear equations with an increasing difficulty: simple equations, with fractions (where we'll use the least common multiple of the denominators), with parenthesis and wi ...

Resolved Problems of Linear Equations

In this section we are going to resolve problems with linear equations, the typical type of problems we'll encounter in out day to day life. The solution requires a lay out and a resolution of the ...

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