First unit
A, axisymmetric graphics
Only the figure of 1 symmetry axis is (isosceles triangle, isosceles trapezoid, semicircle).
A figure with two axes of symmetry is (rectangle)
A figure with three axes of symmetry is an equilateral triangle.
A figure with four axes of symmetry is (a square).
A figure with countless axes of symmetry is (circle, ring)
2. The figure of the circular symmetry axis is (the straight line where the diameter is located).
The symmetry axis is a straight line.
4. The circle is a (plane figure, curve, axis symmetry) figure.
Second, in the same circle or equal circle (an essential premise), the diameter is twice the radius, and the radius is half the diameter.
d=2r r=d÷2
Third, in the same circle or equal circle (a necessary prerequisite), the diameters are all equal and the radii are all equal.
Fourth, the center of the circle determines the position of the circle, and the radius determines the size of the circle. The distance between two feet of a compass is the radius of a circle.
Five, the circumference of the circle
1, the length of the curve around the circle is called the circumference of the circle.
2. The quotient of the circumference of a circle divided by the diameter (the ratio of circumference to diameter) is called pi, which is a fixed number and has nothing to do with the size of the circle. π>3. 14。 The circumference of a circle is about 3. 14 times the diameter.
3.c circle =πd c circle =2πr
4. The circumference of a rectangle = (length+width) × 2 = (a+b) × 2.
Circumference of a square = side length × 4 = 4a
5. The unit of length and circumference is: km m DM cm mm
6. Find the diameter d = c÷πfrom the known circumference.
Find the radius r = c ÷ π ÷ 2 from the known perimeter.
7、3. 14×( 1――9)
Six, the circumference of a semicircle
C semicircle = d+π d ÷ 2c semicircle = 2r+π r
Seven, circle area
1. Divide the circle into several parts evenly, and you can make a parallelogram or rectangle.
2.s circle = π R2 = π (d÷2) 2
3.s rectangle = length× width = ab
S square = side length × side length = A2
S parallelogram = base × height = ah
S triangle = base × height ÷ 2 = ah ÷ 2
S trapezoid = (upper bottom+lower bottom) × height ÷ 2 = (a+b) × h ÷ 2.
S semicircle = π R2 ÷ 2
S circle = S great circle -S small circle = π (R2-R2)
4. The units of area and surface area are: square kilometers, hectares, square meters, square decimeters and square centimeters.
1 km2 = 1 00ha1hectare =10000m2
5. If the perimeter of a rectangle = the perimeter of a square = the perimeter of a circle, then the circle has the largest area among them.
6、( 1 1―― 19)2
Eight, enlarge the radius by n times, enlarge the diameter by n times, enlarge the circumference by n times and enlarge the area by n times.
Second unit
1 .1,
1, right, equal, equivalent, meaning the same.
2. How much = How much?
1. 2. To improve, decrease, increase, decrease, save, and increase or decrease by a few percent, all use: a-b.
2. Third, the relationship between decimals, fractions and percentages.
1. Fourth, the general steps to solve the problem of score application
1. Found the unit "1"
2. Determine whether the unit "1" is known or unknown.
3. If the unit "1" is known, calculate by multiplication: unit "1"× corresponding score.
4. If the unit "1" is unknown, it is calculated by division: known quantity ÷ corresponding score = unit "1"; In addition, equations can also be used.
5. Negative = negative-differential divider = divider quotient
Verb (abbreviation of verb) common quantitative relationship
1, speed× time = distance/speed = time/distance/time = speed.
2. Unit price × quantity = total price/unit price = total quantity/quantity = unit price
3. Work efficiency × working hours = total workload ÷ work efficiency = working hours
Total workload ÷ working time = working efficiency
4. Number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
Intransitive verb equality
1, an equation with unknown numbers is called an equation.
2. Solving the equation is "playing the devil's advocate"
Seven. Interest = principal × interest rate× time
Third unit
Axisymmetry, translation and rotation are used for graphic transformation and pattern design.
1. Axisymmetric
2. Translation: Pay attention to whether to translate up and down or left and right, especially how many frames have been translated.
3. Rotation: Pay attention to whether to rotate clockwise or counterclockwise, and pay attention to the angle of rotation.
4. Operating rules:
Additive commutative law and nature.
a+b=b+a
associative law of addition
a+b+c = a+(b+c)25+37+63 = 25+(37+63)
Commutative law of multiplication
a×b×c=a×c×b 25×9×4=25×4×9
Multiplicative associative law
a×b×c =(a×c)×b 128×3×8 =( 125×8)×3
Powder companion
When the sum of two numbers is multiplied by a number, you can multiply the two addends by this number respectively, and then add the two levels.
a×(b+c)= a×b+a×c 8×( 125+25)= 8× 125+8×25
2.37×99
=2.37× ( 100- 1 )
=2.37× 100-2.37× 1
Operational properties of subtraction
a―b―c = a-(b+ c) 14.29―3.9―6. 1 = 14.29―3.9+6. 1
Fourth unit
1. The division of two numbers is also called the ratio of these two numbers. Among them, the number before the comparison sign is the former item of the ratio, and the number after the comparison sign is the latter item of the ratio, and the former item ÷ the latter item = the ratio.
2. The relationship between ratio, division and fraction
A ÷ b = a: b = (b ≠ 0, divisor, denominator and postterm cannot be 0)
For example: 15 ÷ 25 = (): () = ()% = () (fill in decimal) = () Fold = () into.
Another example is that the ratio of number A to number B is 4: 3, number A is (/) of number B, number B is (/) of number A, number A is ()% of number B, number B is ()% of number A, number A is more than number B, and number B is less than number A ()%.
(hint: a number = 4 B number = 3)
Simplified proportion
Simplifying a ratio is to change a ratio into the simplest integer ratio. That is, the former and the latter are integers, and the former and the latter can only have a common factor of 1.
4. Note: The ratio is a number, and the simplified result is a ratio.
For example, the simplest integer ratio of 0.75 is () and the ratio is ().
5. Application of ratio
Key points: It is known that the circumference of a rectangle is 28 cm and the length-width ratio is 4: 3. Find the length, width or area of a rectangle.
6. The ratio of degrees of three internal angles of a triangle is 1: 2: 3 or 1: 1: 2. This triangle is a (right angle) triangle.
7. Mass units: tons, kilograms and grams
8. unit of volume: liters of milliliters.
9. unit of volume: cubic meter cubic decimeter cubic centimeter.
1 l = 1 cubic decimeter 1 ml = 1 cubic centimeter
10, RMB unit: jiao yuan fen.
1 1, numbers greater than 0 are called positive numbers, and numbers less than 0 are called negative numbers. Positive and negative numbers can be used to represent quantities with opposite meanings. 0 is neither positive nor negative.
12, positive and negative numbers can cancel out, for example, +5 and -5 can completely cancel out; -8 and +3 cancel each other to get -5.
13. Statistical charts include: (composite) bar chart, (composite) line chart and fan chart.
14, bar graph: it is easy to see the quantity of various quantities.
15, broken line statistical chart: not only can you see the quantity, but also can indicate the increase or decrease of the quantity.
16, pie chart: percentage and total of each part can be displayed.
(1) knowledge of plane graphics; (2) the perimeter and area of the plan; (3) Understanding of three-dimensional graphics; (4) the surface area and volume of three-dimensional graphics.
(1) knowledge of plane graphics
① Characteristics, connections and differences of straight lines, rays and line segments.
② Characteristics, classification and measurement methods of angles.
③ Vertical and parallel.
(4) Characteristics and classification of triangles (by edge and angle).
⑤ quadrilateral. The characteristics of each kind of graphics, the relationship between special and general.
⑥ Circle and sector. The characteristics of circle, diameter and radius, and the relationship between sector and circle.
⑦ Axisymmetric graphics. (Can draw the symmetry axis of the learned axisymmetric figure)
Requirements: ① Grasp the characteristics, establish contact, and let students feel the connection from point to line, from line to surface, and from surface to body.
② Reasonable judgments and choices can be made according to the graphic features.
(2) the perimeter and area of the plan
① Understand the concepts of perimeter and area.
(2) Master the calculation formula and derivation process of the perimeter and area of each figure.
③ Formulas can be used flexibly to solve problems.
① Features of cuboids, cubes, cylinders and cones.
(2) The relationship between length and cube.
(3) the surface area and volume of three-dimensional graphics
② Find the surface area and volume of cuboid, cube and cylinder; The volume of a cone.
(3) Establish the connection of volume calculation of these four kinds of three-dimensional graphics.
④ Strengthen the contrast training of the difference between volume and surface area and the difference between volume and volume.
Suggestion: This part of geometry preparation knowledge contains a lot of knowledge. In order to let students really participate in learning and improve learning efficiency, teachers should design some thoughtful, challenging and comprehensive questions, stimulate students' positive thinking, arouse their enthusiasm, give full play to students' main role, and let them further understand and consolidate what they have learned in the process of inquiry, experience the happiness of success and master the learning methods.
For example, the knowledge network diagram of the plane graphic area is completed by students independently (thinking independently, consulting materials and asking for help); The surface areas of cuboids and cubes allow students to bring their own tape boxes and design packaging schemes-
Avoid: cover everything, keep explaining, keep asking questions, practice a lot, and only seek results, not process.
6. Simple statistics
Review points and requirements:
(1) average: understand the meaning of average; Master the method of averaging; Can apply the average to solve practical problems.
(2) Statistics and charts: Understand the types, characteristics and production methods of statistics and charts, and analyze the charts.
Suggestion: When reviewing, avoid mechanical exercises, fill in forms and make statistical charts monotonously, and design some practical activities in combination with students' real life. In the activity, students can apply statistical knowledge, which not only consolidates knowledge, but also mobilizes students' enthusiasm and initiative, and gives play to students' practice and innovation ability.
For example, starting from students' study and life, according to the various characteristics of shopping discounts in shopping malls, let students design their own shopping plans and choose the best shopping plan, and complete the task of reviewing statistical knowledge in this process.
Be sure to learn well, the first volume of the first day of junior high school and the second volume of the first, second and seventh volumes can all be learned well!