Tree DiagramsWhen attempting to determine a sample space (the possible outcomes from an experiment), it is often helpful to draw a diagram which illustrates how to arrive at the answer. One such diagram is a tree diagram.In addition to helping determine…

Statistical StudiesStatistics is concerned with the collection and analysis of data. There are several different types of statistical studies that are used to collect data. Let’s take a look at surveys, experimental studies and observational studies.1. S…

Binomial Probability “Exactly”In a binomial experiment there are two mutually exclusive outcomes, often referred to as “success” and “failure”. If the probability of success is p, the probability of failure is 1 – p.Such an experiment whose outcome is ra…

Conversion Of Decimal Numbers Into Rational Numbers Of The Form m/nCase I: When the decimal number is of terminating nature. Algorithm:Step-1: Obtain the rational number.Step-2: Determine the number of digits in its decimal part.Step-3: Remove decimal p…

Inverse Variation(The Opposite of Direct Variation)In an inverse variation, the values of the two variables change in an opposite manner – as one value increases, the other decreases. For instance, a biker traveling at 8 mph can cover 8 miles in 1 hour.…

Functional Notation and EvaluatingFunctional Notation:Traditionally, functions are referred to by the letter name f, but f need not be the only letter used in function names. The following are but a few of the notations that may be used to name a functi…

Solving Rational EquationsA rational equation is an equation in which one or more of the terms is a fractional one. When solving these rational equations, we utilize one of two methods that will eliminate the denominator of each of the terms. Method 1 :…

What Is Surd Or RadicalReal Number Line: Irrational numbers like √2, √3, √5 etc. can be represented by points on the number line. Since all rational numbers and irrational numbers can be represented on the number line, we call the number line as real nu…

Factoring TrinomialsIn the Algebra lesson on factoring trinomials where a = 1, we learned that factoring may require that we put our investigative skills to work. Those skills will really be put to the test when our trinomial starts with an a-value othe…

Factor TheoremTheorem: If p(x) is a polynomial of degree n ≥ 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). Proof: By the Remainder Theorem, p(x) = (x – a) q(x) + p(a). (i) I…