Mathematics knowledge points of eighth grade in Beijing Normal University (1)
real number
Definition: Any finite decimal or infinite cyclic decimal is a rational number. The decimal of infinite cycle is called irrational number.
(Rational numbers can always be expressed by finite decimals or infinite cyclic decimals)
Generally speaking, if the square of a positive number x is equal to a, then this positive number x is called the arithmetic square root of a.
In particular, we stipulate that the arithmetic square root of 0 is 0.
Generally speaking, if the square of a number X is equal to A, then this number X is called the square root of A (also called square root).
Positive numbers have two square roots; 0 has only one square root, which is 0 itself; Negative numbers have no square root.
The operation of finding the square root of a number is called square root, where a is called square root.
Generally speaking, if the cube of a number X is equal to A, then this number X is called the cube root of A (also called cube root).
The cube root of a positive number is a positive number; The cube root of 0 is 0; The cube root of a negative number is a negative number.
The operation of finding the cube root of a number is called square root, where a is called square root.
Rational numbers and irrational numbers are collectively called real numbers, that is, real numbers can be divided into rational numbers and irrational numbers.
Every real number can be represented by a point on the number axis; On the contrary, every point on the number axis represents a real number. That is, there is a one-to-one correspondence between real numbers and points on the number axis.
On the number axis, the point on the right represents a larger number than the point on the left.
Mathematics knowledge points of eighth grade in Beijing Normal University (2)
Square Root, Arithmetic Square Root and Cube Root
1, arithmetic square root: Generally speaking, if the square of a positive number X is equal to A, that is, x=a, then this positive number X is called the arithmetic square root of A. In particular, the arithmetic square root of 0 is 0. Means: write it down? Answer? , pronounced as the root a.
Property: There is only one arithmetic square root of positive number and zero, and the arithmetic square root of zero is zero.
2. Square root: Generally speaking, if the square of a number X is equal to A, that is, x=a, then this number X is called the square root (or quadratic root) of A..
Representation: The square root of a positive number A is recorded as 22oa? , read as? Positive and negative root sign a? .
Property: a positive number has two square roots in opposite directions; The square root of zero is zero; Negative numbers have no square root. Square root: The operation of finding the square root of a number is called square root. Answer? 0
Pay attention to the double nonnegativity of A:
Answer? 0
3. Cubic root
Generally speaking, if the cube of a number X is equal to A, that is, x=a, then this number X is called the cube root (or cube root) of A.
Express: Write it as a.
Property: positive numbers have positive cubic roots; Negative numbers have negative cubic roots; The cube root of zero is zero. Attention:? Aa, this shows that the negative sign in the cube root symbol can be moved outside the root sign.
Mathematics knowledge points of eighth grade in Beijing Normal University (3)
Translation and rotation of graphics
Definition: In a plane, a figure moves a certain distance along a certain direction, and such figure movement is called translation. Translation does not change the shape and size of the graph.
After translation, the line segments connected by the corresponding points are parallel and equal; The corresponding line segments are parallel and equal, and the corresponding angles are equal.
In a plane, turning a figure around a fixed point by an angle in a certain direction is called rotation. This fixed point is called the rotation center and the rotation angle is called the rotation angle. Rotation does not change the size and shape of the graph.