Univariate vs Bivariate DataUnivariate and Bivariate distribution“If it is proved true that in a large number of instances two variables tend always to fluctuate in the same or in opposite directions, we consider that the fact is established and that a …

Slope and Rate of ChangeThe word slope (gradient, incline, pitch) is used to describe the measurement of the steepness of a straight line. The higher the slope, the steeper the line. The slope of a line is a rate of change.Slope can be expressed in vari…

Trigonometry: Solving Word ProblemsTrigonometry can be used on a daily basis in the workplace. Since trigonometry means “triangle measure”, any profession that deals with measurement deals with trigonometry as well. Carpenters, construction workers and …

Exponential Growth and DecayExponential FunctionsAn exponential function with base b is defined by f (x) = abx where a ≠0, b > 0 , b ≠1, and x is any real number. The base, b, is constant and the exponent, x, is a variable.Notice: The variable x is a…

Solving a Linear Quadratic System GraphicallyThe graphing method of solution:Quadratic equations can also be solved by graphing. Graphing can be done “by hand” or with the use of a graphing calculator. The locations where the graph intersects (crosses) t…

Factoring Trinomials (a = 1)Squaring a binomial creates a perfect square trinomial: What we need to do now, is to “remember” these patterns so that we can be on the look-out for them when factoring. Whether we use the distributive process, use FOIL, or l…

Factoring Difference of Two Perfect Squares  This expression is called a difference of two squares. (Notice the subtraction sign between the terms.)In algebra, a term is a perfect square when the numerical coefficient (the number in front of the variabl…

Solving Fractional EquationsSolving fractional equations is very much like addition and subtraction of fractions, but after the first step, you will GET RID of the denominators! “Getting rid” of the denominators is actually changing them all to the valu…

Monomials, Binomials, and PolynomialsA monomial is the product of non-negative integer powers of variables. Consequently, a monomial has NO variable in its denominator. It has one term. (mono implies one) (notice: no negative exponents, no fractional ex…

Adding and Subtracting FractionsTo ADD and/or SUBTRACT ALGEBRAIC FRACTIONS: In order to add or subtract (or “combine”), algebraic fractions, a common denominator is needed. (This is the same process you use when adding and subtracting “regular number fra…