Pre-requisites for Pre-Calculus Archives

Mid-Point Formula

Midpoint The point halfway between two points on the coordinate plane is found by calculating the average values of the x and y coordinates. The mid-point formula is:    Examples: Use the distance formula and find the distance between two points and use the mid-point formula to find the point halfway between the same two points. 1. …

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Distance Formula

 What is the Distance Formula? The distance between two points on a coordinate plane can found by using the distance formula. To understand and discover the distance formula you must use the Pythagorean Theorem.  If you have a right triangle, then the square on the hypotenuse is equal to the sum of the squares of the other…

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Cartesian Plane

Cartesian Plane The Cartesian Plane is used to plot points.  A rectangular coordinate system consists of points called ordered pairs.  (x,y)  The coordinates of the points and listed in alphabetical order so x comes first in an ordered pair (x,y). x-axis –> horizontal number line y-axis –> vertical number line origin –> point of intersection…

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Solving Inequalities

Solving Inequalities Simple Inequalities contain one of the following signs . When solving an inequality, one is trying to find all the valid solutions. Example:                                                                 all real nos. less than 3  An inequality can be bounded or unbounded / open or closed.  We use rounded brackets to indicate an open ended inequality…

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Solving All Kinds of Polynomial Equations

Solving Equations of a Higher Degree The number of roots or solutions [values for x] is dependent on the degree of the polynomial in an equation.  If the degree is 2, as in a quadratic equation, there is the possibility of two roots.  If the degree is six, there can be up to six roots. …

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Quadratic Equations

Quadratic Equations A quadratic equation in x is an equation that can be written in the general form     where a, b and c are real numbers, with a  0. A quadratic equation in x is also known as a second-degree polynomial equation in x. There are four ways to solve a quadratic equation. 1. …

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Linear Equations

Linear Equations Vocabulary: An equation in x is a statement that two algebraic expressions are equal. To solve –> finding all the values of x for which the equation is true. The values of x are called solutions. identity –> true for every real number in the domain conditional equation –> is true for just…

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Rational Expressions

Rational Expressions Domain — what values of x make the statement valid?  Usually the domain is all real numbers but …. or all real #’s such that x does not equal …. Examples:                                            Domain:                                        all reals                                                all reals such that     [cannot be a negative                                                                                                            #  under a   sign]                                                   all reals such…

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Factoring Polynomials

Factoring Polynomials Definition:  Factoring is the process of writing a polynomial as a product of factors. Types of Factoring: 1.  The first step in factoring is to find the CF [common factor]. Examples:                                                                                                                                             in example d) above, one is trying to find the common factor so the remaining factors have integer coefficients….

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Polynomials

Polynomials The following is a polynomial in x: The polynomial is of degree n*,  is the leading coefficient, and  is the constant term. * the exponent must be a positive integer. Important Vocabulary: 1.  polynomial – an algebraic expression a number of terms 2.  coefficient – the number in front of the variable 3.  degree…

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