Mathematics Essays Examples For College & High School Students in PDF

985 total results

A Discussion About the History of the Pythagorean Theory (490 words, 1 pages)

The Pythagorean theory is probably more widely known than any other complex mathematical idea. The theorem was first used by the Eygptians , butthey had no mathematical proof that the idea was correct. Pythagoras is credited with being the first to prove the theorem. The Pythagorean theorem, which is important ... Read More

The Scientific Contributions of Archimedes, the Greatest Mathematician and Inventor of His Time (749 words, 4 pages)

Archimedes was one of the greatest mathematicians and inventors of histime. He was born in Syracuse, Sicily around the year 287BC. Archimedeswas educated in Alexandria, Egypt, but spent most of his life in Sicily. Whenin Sicily, he stayed in or near Syracuse and did nothing but experiment andresearch.Archimedes made many ... Read More

A Biography of the Life, Achievements and influence of Pythagoras in the Field of Mathematics (1319 words, 2 pages)

Our generation receives an abundance of credit for the technology and innovations we, as creators, invent. We probably receive too much recognition for the sciences that the geniuses of our era bring into existence. Without the help of previous generations, the modern day world would look somewhat like it did ... Read More

How to Solve an Equation Involving an Iteration Formula (208 words, 3 pages)

This is a way of solving equations. An iteration formula might look like the followingxn1 2 1 xn . You are usually given a starting value, which is called x0. If x0 3, substitute 3 into the original equation where it says xn. This will give you x1. (This is ... Read More

Understanding the Concept Behind the Quartiles and its Two Types in Mathematics (434 words, 4 pages)

Quartiles If we divide a cumulative frequency curve into quarters, the value at the lower quarter is referred to as the lower quartile, the value at the middle gives the median and the value at the upper quarter is the upper quartile. A set of numbers may be as follows ... Read More

An Analysis of Probability in Conjunction with Set Theory and Venn Diagrams (314 words, 2 pages)

Probability can be studied in conjunction with set theory, with Venn Diagrams being particularly useful in analysis. The probability of a certain event occurring, for example, can be represented by P(A). The probability of a different event occurring can be written P(B). Clearly, therefore, for two events A and B, ... Read More

Understanding the Calculation of the Median Value in a Group of Numbers (323 words, 3 pages)

The Median Value The median of a group of numbers is the number in the middle, when the numbers are in order of magnitude. For example, if the set of numbers is 4, 1, 6, 2, 6, 7, 8, the median is 6 1, 2, 4, 6, 6, 7, 8 ... Read More

The Significance of the Chain Rule in the Differential Calculus (233 words, 2 pages)

The chain rule is very important in differential calculus and states that dy dy dt dx dt dx This rule allows us to differentiate a vast range of functions. Example If y (1 x) , find dydx . let t 1 x therefore, y t dydt 3t dtdx 2x by ... Read More

The Illustration of the Three Types of Stationary Points on a Graph (516 words, 4 pages)

Stationary points are points on a graph where the gradient is zero and are of three types maximum, minimum or point of inflexion. The three are illustrated here Example Find the coordinates of the stationary points on the graph y x . We know that at stationary points, dydx 0 ... Read More

Showing That Data from a Science Experiment Fits a Rule (223 words, 1 pages)

In order to show that data from a science experiment fits a rule, we have to be able to plot two variables on a graph so that a straight line relationship results (this will be the line of best fit if the data is experimental). In questions, you may be ... Read More

The Comparison Between Algebraic Long Division and Traditional Long Division (240 words, 1 pages)

Algebraic long division is very similar to traditional long division (which you may have come across earlier in your education). Example NB If the quotient (the polynomial that you are dividing) has a term in x missing, add such a term by placing a zero in front of it. For ... Read More

Understanding How the Sigma Notation is Calculated in a Sum Sequence (642 words, 5 pages)

Introduction The series of a sequence is the sum of the sequence to a certain number of terms. It is often written as Sn. So if the sequence is 2, 4, 6, 8, 10, ... , the sum to 3 terms S3 2 4 6 12. The Sigma Notation This ... Read More

Understanding the Pattern of Sequence in Terms of the nth Term (280 words, 2 pages)

Introduction In the sequence 2, 4, 6, 8, 10... there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term 2n. To find the 1st term, put n 1 into the formula, to find the 4th ... Read More

Describing a ‘Set’ in a Sequence of Objects in Mathematics and the Different Types of Sets (241 words, 1 pages)

A set is a group of objects. Each object is known as a member of the set. A set can be represented using curly brackets. So a set containing the numbers 2, 4, 6, 8, 10, ... is 2, 4, 6, 8, 10, ... . Sets are often also represented ... Read More

An Analysis of Simultaneous Equations (372 words, 3 pages)

Simultaneous equations are two or more equations which are true for two or more unknowns. For example, x y 4 and x - 2y 1 are simultaneous equations which are true for x 3 and y 1. When there are two unknowns, as there are here (x and y), then ... Read More

Describing the Concept of the Hypotenuse in Any Right Angled Triangle (207 words, 2 pages)

In any right angled triangle, for any angle The sine of the angle the length of the opposite side the length of the hypotenuse The cosine of the angle the length of the adjacent side the length of the hypotenuse The tangent of the angle the length of the opposite ... Read More

Describing a Function Rule in a Mathematical Operation (309 words, 2 pages)

Functions A function is a rule which indicates an operation to perform. e.g. if f(x) x 3 f(2) 2 3 7 (i.e. replace x with 2) Functions can be graphed. For example, the graph of f(x) 1x is as follows This is the same graph as y 1x, although the ... Read More

An Overview of the Concept Behind Simultaneous Equations in Mathematics (300 words, 3 pages)

Simultaneous Equations Simultaneous equations are a set of equations which have more than one value which has to be found. At GCSE, it is unlikely that you will have more than two equations with 2 values (x and y) which need to be found. Example A man buys 3 fish ... Read More

How to Solve an Equation by Trial and Improvement (/Error) Method (324 words, 3 pages)

Trial and Improvement Any equation can be solved by trial and improvement (error). However, this is a tedious procedure. Example Solve t t 17 by trial and improvement. Firstly, select a value of t to try in the equation. I have selected t 2. Put this value into the equation. ... Read More

Understanding the Idea Behind the Selected Segment Random Sample (276 words, 1 pages)

Sample Selected segment Random Sample Every member of the population has an equal chance of being included in the sample. Representative sample A sample in which people known to possess certain characteristics are included in proportion to their numbers in the populations being studied. Experimental Group Control Group Correlation Indication ... Read More

A Look at Probability and How It Is Determined Mathematically (644 words, 4 pages)

Introduction Probability is the likelihood or chance of an event occurring. Probability the number of ways of achieving success the total number of possible outcomes For example, the probability of flipping a coin and it being heads is , because there is 1 way of getting a head and the ... Read More

The Different Ways of Representing Data Diagrammatically (247 words, 2 pages)

There are a number of ways of representing data diagrammatically. (See also Histograms). Scatter Graphs These are used to compare two sets of data. A line of best fit is drawn, which should pass through as many points as possible. It should have roughly the same number of points above ... Read More

An Overview of the Determination of the Standard Deviation (337 words, 3 pages)

Standard Deviation Lower case sigma means 'standard deviation'. Capital sigma means 'the sum of'. x bar means 'the mean' The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. ... Read More

An Analysis of the Cumulative Frequency Polygon (374 words, 3 pages)

Cumulative Frequency This is the running total of the frequencies. On a graph, it can be represented by a cumulative frequency polygon, where straight lines join up the points, or a cumulative frequency curve. Example Frequency Cumulative frequency 4 4 6 10 (4 6) 3 13 (4 6 3) 2 ... Read More

How to Determine the Mean from a Group of Items (260 words, 3 pages)

Mean There are four types of average mean, mode, median and range. The mean is what most people mean when they say 'average'. It is found by adding up all of the numbers you have to find the mean of, and dividing by the number of numbers. So the mean ... Read More

The Difference Between Related Angles, Vertically Opposite Angles and Alternate Angles (212 words, 2 pages)

Related Angles Lines AB and CD are parallel to one another (hence the on the lines). a and d are vertically opposite angles. Vertically opposite angles are equal. (b and c, e and h, f and g are also vertically opposite). g and c are corresponding angles. Corresponding angles are ... Read More

Understanding the Idea Behind the Percentage and Its Calculation (416 words, 3 pages)

Percentages A percentage is a fraction whose denominator is 100 (the numerator of a fraction is the top term, the denominator is the bottom term). So 30 30100 310 0.3 To change a decimal into a percentage, multiply by 100. So 0.3 0.3 100 30 . Example Find 25 of ... Read More

How to Determine and Carry Out the Basic Surd Manipulation (221 words, 2 pages)

Basic surd manipulation Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them. Leaving ... Read More

An Overview of the Different Types of Number Integers (637 words, 3 pages)

Types of numbers Integers are whole numbers (both positive and negative). Zero is usually classed as an integer. Natural numbers are positive integers. A rational number is a number which can be written as a fraction where numerator and denominator are integers (where the top and bottom of the fraction ... Read More

An Introduction to the Standards of Measurement: Sine and Cosine Rules (577 words, 3 pages)

8.1 Standards of measurement 8.1.1 Sine and Cosine rules...(both of which are in the data book) The sine rule is Asin a Bsin b Csin c. Where the lower case letters are lengths of the sides of a triangle, and the upper case are the angles opposite these sides...this lets ... Read More

Mathematics Essay Examples