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Prealgebra
Pre-algebra is a common name for a course in middle school mathematics in the United States, usually taught in the 7th grade Seventh grade (or grade seven) is a year or level of education. The seventh grade is the eighth school year, the second or third year of middle school, and the first year of junior high school. Students are around 13-14 years old in this stage of ... or 8th grade#United States, 8th grade. The objective of it is to prepare students for the study of algebra. Usually algebra is taught in the Eighth grade, 8th and Ninth grade, 9th grade. As an intermediate stage after arithmetic, pre-algebra helps students pass certain conceptual barriers. Students are introduced to the idea that an equals sign, rather than just being the answer to a question as in basic arithmetic, means that two sides are Equality (mathematics), equivalent, and can be manipulated together. They also learn how numbers, Variable (mathematics), variables, and words can be used in the same ways. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Course (education)
In higher education a course is a unit of teaching that typically lasts one academic term, is led by one or more instructors (teachers or professors), and has a fixed roster of students. A course usually covers an individual subject. Courses generally have a fixed program of sessions every week during the term, called lessons or classes. Students may receive a grade and academic credit after completion of the course."course" in ''Merriam-Webster Online Dictionary''. Retrieved 15 August 2008. Courses can either be compulsory material or "elective". An elective is usually not a required course, but there are a certain number of non-specific electives that are required for certain majors. The entire collection of courses required to complete an [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the '' radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the '' significand'' or ''mantissa''. The term "mantissa" can be ambiguous where logarithms are involved, because it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4-quadrant Cartesian Coordinate Plane
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (''x''; ''y'') coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise Two-dimensional rotation can occur in two possible directions. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands: from the top to the right, then down and then to the left, and back up to the top. The opposite ... starting from the upper right ("northeast") quadrant. Mnemonic In the above graphic, the words in quotation marks are a mnemonic for remembering which three trigonometric functions (sine, cosine and tangent) are positive in each quadrant. The expression reads "All Science Teachers Cra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parentheses
A bracket is either of two tall fore- or back-facing punctuation marks commonly used to isolate a segment of text or data from its surroundings. Typically deployed in symmetric pairs, an individual bracket may be identified as a 'left' or 'right' bracket or, alternatively, an "opening bracket" or "closing bracket", respectively, depending on the directionality of the context. Specific forms of the mark include parentheses (also called "rounded brackets"), square brackets, curly brackets (also called 'braces'), and angle brackets (also called 'chevrons'), as well as various less common pairs of symbols. As well as signifying the overall class of punctuation, the word "bracket" is commonly used to refer to a specific form of bracket, which varies from region to region. In most English-speaking countries, an unqualified word "bracket" refers to the parenthesis (round bracket); in the United States, the square bracket. Various forms of brackets are used in mathematics, with s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Precedence
In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression is interpreted to have the value , and not . When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus and . These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, forces addition to precede multipl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nth Root
In mathematics, a radicand, also known as an nth root, of a number ''x'' is a number ''r'' which, when raised to the power ''n'', yields ''x'': :r^n = x, where ''n'' is a positive integer, sometimes called the ''degree'' of the root. A root of degree 2 is called a ''square root'' and a root of degree 3, a '' cube root''. Roots of higher degree are referred by using ordinal numbers, as in ''fourth root'', ''twentieth root'', etc. The computation of an th root is a root extraction. For example, 3 is a square root of 9, since 3 = 9, and −3 is also a square root of 9, since (−3) = 9. Any non-zero number considered as a complex number has different complex th roots, including the real ones (at most two). The th root of 0 is zero for all positive integers , since . In particular, if is even and is a positive real number, one of its th roots is real and positive, one is negative, and the others (when ) are non-real complex numbers; if is even and is a negative real numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributivity
In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality x \cdot (y + z) = x \cdot y + x \cdot z is always true in elementary algebra. For example, in elementary arithmetic, one has 2 \cdot (1 + 3) = (2 \cdot 1) + (2 \cdot 3). One says that multiplication ''distributes'' over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted \,\land\,) and the logical or (denoted \,\lor\,) distributes over the other. Definition Given a set S and two binary operators \,*\, and \,+\, on S, *the operation \,*\, is over (or with respect to) \,+\, if, given any elements x, y, \text z of S, x * (y + z) = (x * y) + (x * z); *the operation \,*\, is over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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