Algorithm: An organized program that performs a specific form of calculation or solves a certain kind of problem. For example: long division.
Arithmetic progression: contains elements A 1, A2, A3, ... and the difference of successive terms is a constant, that is, for each I,; For example, the sequence {2, 5, 8, 1 1, 14, ...} has a tolerance of 3.
Asymptote: when the variable increases from the origin to infinity, the curve of the function will be very close to some straight lines; For example, the x axis is the only asymptote of the graph of the function sin (x)/x)/x.
Axiom: the basic assumption of a mathematical system, from which theorems can be derived; For example, this system can be a point and a straight line on the plane, and the axiom can be "any two different points on the plane have a unique straight line passing through these two points".
Binomial: An algebraic expression consisting of the sum or difference of two monomials (please refer to the definition of monomials). For example: 4a-8b.
Binomial coefficient: when n is any positive integer, k is any integer between 0 and n (either 0 or n), and binomial coefficient B(n, k) is. The common symbol of B(n, k) is nCk or. Except 0! Besides, the symbol n! (n factorial) means the product of all integers from 1 to n (for example: 5! =5×4×3×2× 1= 120); 0! Is a special case defined as 1 (that is, 0! = 1)。
Binomial distribution: a probabilistic term. In n independent experiments with two results, the probability of k results is a (or the probability of n-k results is b), and the possible results are recorded as a and B.
Binomial Theorem: For every positive integer n, it is a polynomial, and the binomial coefficient nCk is a monomial coefficient.
Box diagram: display the median, quartile and extreme value of data by drawing. A block diagram shows the distribution and concentration of data.
Complex number: complex number can be expressed as a+bi, a and b are real numbers, and I satisfies the equation. The definition of multiplication is: (a+bi) (c+di) = (AC-BD)+(AD+BC) i; The definition of complex addition is: (a+bi)+(c+di) = (a+c)+(b+d) i.
Congruence: Two figures in a plane or space, if one figure and the other figure are integrated by rigid body motion (see the definition of rigid body motion).
Guess: an educated guess.
Coordinate system: a corresponding rule, which clearly marks two or more quantities at some points. The corresponding rule must meet certain characteristics, and these points can clearly determine the quantities; For example, the common cartesian coordinate system x and y on the plane.
Inference: the result directly derived from the theorem.
Cosine: Cosine cos(θ) is the X coordinate of a point on the unit circle, so that the rays of the connection point and the origin make an angle θ with the positive direction of the X axis. When θ is an angle of a right triangle, then cos(θ) is the ratio of the hypotenuse to the adjacent side of the right triangle.
Expansion: a geometric term is transformation d in plane or space. If the graph is transformed, point P is transformed into itself, the angles of other points with point P are unchanged, and the distance from point P is R times, and all rays passing through point P will be transformed into themselves, then this is the expansion (or expansion) of point P; If point P is the origin of Cartesian coordinate system on the plane, then expansion transformation D corresponds point (x, y) to point (rx, ry).
Dimensional analysis: an algebraic algorithm for calculating unit measurement, which uses algebraic method to find the correct unit of quantity; For example, the unit of speed is length divided by time (such as how many meters per second), and the unit of acceleration is speed divided by time; So the unit of acceleration is (m/s)/s = m/(s squared).
Expansion: the expansion of algebraic expression is equivalent expression); Without brackets; For example, equals.
Exponent: The number of times a number or variable is raised.
Exponential function: a function usually used to study growth and decline. Its form is that a is a positive number.
Factor: Two or more numbers are multiplied, and any number is called a factor. In the formula of 3.172×11.315, the factors are 3.7 12 and 1 1.365438.
Field: refers to "number system", similar to "rational number system". Elements in the system can be added and multiplied. There is a 0 and a multiplication unit in the system (called 1), and the rules of arithmetic combination are similar. For example: for any a, b, c: ab = ba; 1 . a = a； 0+a = a； a+b = b+ a； a(b+ c)= a . b+ a . c； Equations a.x = b (unless a=0) and a+x = b have unique solutions. Complex numbers, real numbers and rational numbers all form domains, and there are other domains (such as all types of real numbers).
Function: How one variable determines the correspondence of another value.
Geometric series: there is a common ratio between several consecutive terms in a series, and the solution of each consecutive term in the series is to multiply the previous term by the common ratio. For example, in the sequence {1, 3, 9, 27, 8 1...}, the common ratio is 3.
Heuristic demonstration: This explanation method is generally used in mathematics. This explanation is used to imply the truth of a mathematical statement, but it is not necessarily completely logically correct or complete.
Histogram: a statistical chart with vertical squares, with no gaps between them, which is usually used to represent statistical frequency data.
Hypothesis: Similar hypothesis.
Inequality: the relationship between two quantities, which can indicate that one quantity is less than or equal to the other.
Integer: a set containing positive numbers, negative numbers and 0; For example: {…-2,-1, 0, 1, 2…}.
Irrational number: real number, which cannot be expressed as the ratio of two integers; Such as the square root of 2 or pi.
Lemma: a slightly less formal true statement than theorem. In a long continuous reasoning process, it is usually a transitional narrative. Lemmas are usually independent.
Linear equation: an equation in which a straight line equals zero.
Linear expression: a formula is written as ax+b, x is a variable, and a and b are constants; Or more variables, expressed as ax+by+c, ax+by+cz+d, ......
Logarithm: Logarithm is the reciprocal of the exponent. The equation can be written as a logarithm with base A and X as Y. Any positive number except 1 can be regarded as the base of logarithmic function (the base is the logarithm of 10, which is called ordinary logarithm; Logarithm based on e is called natural logarithm).
Mean value: a statistical term. Two or more quantities are added and divided by the number of times of these quantities to get the average value.
Median: a statistical term that arranges a group of numbers in order of size, with the numbers in the middle.
Mode: statistical term, which is the most common number in a series of numbers.
Monomial: For variables x, y, z, the monomial is a formal formula, where m, n, k are nonnegative integers and a is a constant (for example,, or).
Non-standard unit: a unit used for measurement, expressed in the form of objects (such as paper clips, branches, shoes, etc.).
Parallelism: In Euclidean geometry, two different straight lines are defined as parallel if they do not intersect. In the coordinate plane, two different straight lines are parallel if and only if they have the same slope.
Replacement: the set {1, 2, ..., n} refers to the recombination of these numbers.
Polar coordinates: a plane coordinate system based on R (distance from the origin) and θ (angle between the positive direction of the X axis and the straight line from the point to the origin).
Polar coordinates: A formula that uses polar coordinates (r, θ) to express the set relation of points on a plane. (For example, r=2cosθ is the polar coordinate equation of a circle).
Polynomial: the sum of algebraic nouns and monomials; For example:
Axiom: A statement similar to an axiom.
Prime number: the natural number P greater than 1 is a prime number, and the positive integer factors of if and if P are only 1 and P. The first seven prime numbers are 2, 3, 5, 7,1,13, 17.
Probability space: the collection of all events, and each event will be given a quantity, which is called its probability. For example, if you roll a pair of dice five times, the possible sum 12 is called an event, and the probability of this event is.
Quadratic function: suppose a function f can be written, where a, b and c are the sum of real numbers. Note that quadratic functions are second-order polynomials.
Random variable: a function that assigns a numerical value to each event in the probability space.
Range: statistical term, the difference between the maximum and minimum values in a data set; The image of mathematical nouns and functions.
Ratio: Comparison of two numbers, usually indicating the number of components. For example, if there are two girls in the classroom, there will be three boys, and the ratio of boys to girls is 3: 2 or 3/2 (pronounced three to two).
Rational number: any number can be expressed as the quotient of two integers; For example: 7/3,5/11,-5/13,7 = 7/1.
Real number: the set of all decimals, whether finite or infinite.
Reflection: the reflection of a straight line on a plane or a plane in space is a transformation, and every point on the plane is mirrored by that straight line; Or a point in space is mirrored by a plane, and any geometric figure will be mirrored after reflection.
Rigid body motion: a transformation that keeps the distance and angle constant in plane or space.
Finding the root: find the factors of the known number, and multiply the factors to get the given original number; For example, the fifth root of 32 is 2, because 2 × 2 × 2 × 2 = 32.
Rotation: the plane rotation through the rotation angle of point P means that point P is fixed to do rigid body motion T, so that if Q is a point different from point P on the plane, the included angle between straight line PQ and straight line PT(Q) is; Spatial rotation angle refers to the rigid body motion t fixed on the straight line L, so that the plane perpendicular to L rotates at the intersection of L and the plane.
Scalar matrix: all diagonal elements of the matrix are equal, and all off-diagonal elements are zero. Identity matrix is an example.
Scatter chart: statistical chart consists of points, which can present a collection of data.
Scientific symbol: a simplified representation of a very large or very small number. Using scientific notation to represent a number is to multiply a decimal from 1 to 10 by an index with 10 as the base. (For example: 7000= or 0.00000 19= 1.9×)
Eratosthenes's Sieve: One solution can get all the prime numbers in a certain range. Suppose this range is 2 to 300, and the practice is to start from 2 and drop all numbers between 2 and 300 that are multiples of 2 but not equal to 2; Then cross out the next one, that is, 3, and cross out numbers that are multiples of 3 but not equal to 3 between all 2 and 300; Then cross out the next number, which is 5, and cross out all numbers between 2 and 300 that are multiples of 5 but not equal to 5. And so on. At each stage, the next number must be a prime number. At the end of these steps, when all the numbers below 300 are not deleted, every remaining number is a prime number. (Take prime numbers within 300 as an example. Once the multiple of 17 (not 17 itself) is crossed out, this step stops. Because the product of any two prime numbers greater than 17 must be greater than 300. )。
Similarity: a geometric term. If there is an expansion (see the definition of expansion transformation) that makes shape S and shape R congruent, then shape R is similar to shape S. If they are congruent with any expanded or contracted figure, then R and S are similar.
Sine: Sine (θ) is the Y coordinate of all points on the unit circle, so that the ray connecting the point with the origin makes an angle θ with the positive direction of the X axis. When θ is an angle of a right triangle, then sin(θ) is the ratio of the opposite side to the hypotenuse.
Square root: the square root of n refers to all the m values that can make it true; For example, the square roots of 16 are 4 and -4. The square roots of-16 are 4i and -4i.
Standard deviation: a statistical term indicating the deviation of a sample.
Symmetry: The symmetry of shape S in plane or space is a rigid body motion T, which is to map the whole S onto itself (T(S)=S). For example, the reflection of diagonal and right angle rotating in the center is symmetrical about the square.
Linear equations: A set of linear equations (for example, x+y=7, x-y= 1). Its solution is a set of numbers, and the equation can be established by replacing variables with these numbers. Take this problem as an example, "x=4, y=3" is a solution.
Theorem: A meaningful statement of truth in mathematics. Its expression is "p contains q", where p stands for hypothesis and q stands for conclusion.
Translation: a special rigid body motion, where v is a specific vector of a plane or space, and all x->; x+v .
Transverse: A geometric term in which it is known that there are two or more straight lines on a plane. A cross section is a straight line, and these straight lines are different from the above-mentioned straight lines, and they cross each other through a point.
Unit fraction: the form of fraction is 1∕n, where n is a positive integer.
Variable: a specific position in an algebraic expression; For example: 3x+y=23, and both x and y are variables.
Vector: a physical term that refers to a measurable quantity (such as force) with direction and magnitude, and sometimes refers to the point of action; A mathematical term, vector, is a part of algebraic system. A vector can be added and multiplied with a real number. The addition and multiplication of the whole system follow specific rules, similar to the combination rules of physical vectors.
Zero point of function: At these points, the function value is equal to zero.