The fifth chapter: intersection and parallel lines.
5. 1 intersection line
Observe and guess the illusion when looking at pictures.
5.2 Parallel lines and their determination
5.3 Properties of parallel lines
Using information technology to explore the positional relationship between two straight lines
5.4 Translation
Mathematical activities
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Review question 5
Chapter VI Real Numbers
6. 1 square root
6.2 cube root
6.3 real numbers
Read and think about why √2 is not a rational number.
Digital activity
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Review question 6
Chapter VII Plane Cartesian Coordinate System
7. 1 plane rectangular coordinate system
Reading and thinking indicate geographical location with latitude and longitude.
7.2 Simple application of coordinate method
Mathematical activities
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Review question 7
Chapter VIII Binary Linear Equations
8. 1 binary linear equations
8.2 Elimination Method-Solving Binary Linear Equation
8.3 Practical Problems and Binary Linear Equations
8.4 Solutions of ternary linear equations
Reading and thinking about the ancient and modern expressions and solutions of linear equations
Mathematical activities
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Review question 8
Chapter 9 Inequality and Unequal Groups
9. 1 inequality
Reading and thinking compare sizes with the difference method.
9.2 One-dimensional linear inequality
9.3 One-dimensional linear inequality system
Mathematical activities
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Review question 9
Chapter 10 Data Collection, Arrangement and Description
10. 1 statistical survey
Experiment and explore how many beans are in the bottle.
10.2 histogram
The application of information technology uses computers to draw statistical charts.
10.3 project learning talking about water saving from data
Mathematical activities
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Review questions 10
The key content of the second volume of the seventh grade mathematics textbook (1) intersecting lines and parallel lines
(1) intersection line
In the same plane, there are two positional relationships between two straight lines: intersecting and parallel. If two straight lines have only one common point, they are said to intersect.
(2) Vertical line
One of the four angles formed by the intersection of two straight lines is a right angle, that is, the two straight lines are perpendicular to each other, one of which is called the perpendicular of the other straight line, and the intersection point is called the vertical foot.
(3) Equilibrium angle
Two straight lines A and B are cut by a third straight line C (or the intersection of C of A and B). On the same side of the cutting line C, cut the corners on the same side of the two straight lines A and B.. We call these two angles congruent angles.
(4) Internal dislocation angle
Two straight lines are cut by a third straight line, and the two corners are on both sides of the cutting line and sandwiched between the two cut straight lines. Diagonal lines with this positional relationship are called inscribed angles.
(5) ipsilateral internal angle
The two angles at which two straight lines intersect with the third line are called inner angles on the same side, which are located on the same side of the cutting line and within the cutting line.
(6) Parallel lines
In geometry, two straight lines that never intersect (and never coincide) on the same plane are called parallel lines.
The nature of parallel lines: ① Two lines are parallel, and the included angle is equal; ② Two straight lines are parallel and the internal dislocation angles are equal; ③ The two straight lines are parallel and complementary.
(7) Translation
Translation means that all points on the map move equidistantly along a straight line in the same plane. This kind of graphic movement is called graphic translation movement, which is called translation for short.
(2) Real numbers
(1) square root
Square root is also called quadratic square root, which is expressed as √ ~ where the non-negative square root is called arithmetic square root. Positive numbers have two real square roots in opposite directions, while negative numbers have no square roots.
(2) Cubic root
If the cube of a number is equal to A, then this number is called the cube root of A, also called the cube root.
Cubic root property
(1) In the range of real numbers, there is only one cube root of any real number.
② Within the range of real numbers, negative numbers cannot be squared, but they can be squared.
The cube root of 0 is 0.
(3) Real numbers
Real number is a general term for rational number and irrational number. Real numbers are closed, ordered, transitive, dense and complete.
(3) Plane rectangular coordinate system
(1) definition
Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short.
(2) Ordered number pairs
In the rectangular coordinate system, for any point on the plane, there is a unique ordered number pair (that is, the coordinate of the point) corresponding to it; Conversely, for any ordered number pair, there is a unique point on the plane corresponding to it.
Binary linear equation
(1) definition
Binary linear equation refers to an equation with two unknowns (such as X and Y), and the degree of the unknowns is 1. Two combined linear equations with two unknowns are called binary linear equations.
(2) The solution method of binary linear equation
① Substitution elimination method
② Method of addition, subtraction and elimination
(5) Unequal and unequal groups
(1) inequality
Using inequality symbols (
(2) the essence of inequality
① symmetry;
② Transitivity;
③ monotonicity of addition, that is, additivity of inequality in the same direction;
④ Monotonicity of multiplication;
⑤ Multiplicity of positive inequality in the same direction;
⑥ Positive inequalities can be multiplied;
⑦ Positive inequalities can be squared;
(3) One-dimensional linear inequality
A formula connected by an inequality symbol contains an unknown number whose degree is 1, whose coefficient is not 0, and whose left and right sides are algebraic expressions is called one-dimensional linear inequality.
(4) One-dimensional linear inequalities
The group of one-dimensional linear inequalities consists of several one-dimensional linear inequalities with the same unknowns.