A proposition principles 

Test students understanding of the basics of mathematics, the level of mastery and application, as well as operations, data processing, spatial imagination, the basic level of competence practices. 

Second, in the form of exam 

Closed book, written examination. 

Third, the questions of structure 

There are fill-in questions, multiple choice questions, such as reconciliation answer. Fill in the blank to fill in only requires a direct result of having to write the calculation process or push the certification process; choose a four-choice multiple-choice type; answer questions in various forms, for example: calculation problems, proofs, application questions, reading comprehension questions, open questions and exploratory questions, etc., should write the text to answer questions, calculus steps or push the certification process. Questions out of 120 points, the examination time was 120 minutes. 

Fourth, the examination of the content and requirements 

I. Number and Algebra 

1 Number and type 

(A) rational 

Exam content 

Rational, axes, opposite number, the absolute value of the number. Rational numbers to add, subtract, multiply, divide, involution, addition, multiplication law, rational simple mixing operations. 

Examination Requirements 

① understand the rational sense, can point axis represents the number of rational numbers, it would be more rational size. 

② With the number of axes understand the significance of the number and the absolute opposite, the opposite will seek rational numbers and absolute value. 

③ understand the meaning of involution, the master of rational numbers to add, subtract, multiply, divide, involution and simple mixing operations (mainly in three steps). 

④ understand the rational calculations law, and to apply the law to simplify the arithmetic operations. 

⑤ able to use rational arithmetic to solve simple problems. 

(2) Real 

Exam content 

Square root of the arithmetic square root, cube root, irrational numbers, real numbers, the approximate number of significant digits. 

Secondary radical, secondary radical of addition, subtraction, multiplication, division, real simple four operations. 

Examination Requirements 

① understand the square root of the arithmetic square root, cube root of the concept will be represented by the square root of the number of root, cube root. 

② understand prescribing and involution are inverse operations, will use certain non-squaring find the square root of a negative number, it will seek certain number of cubic cube root operation. 

③ understand the concept of irrational numbers and real numbers, real numbers that correspond with the number of points the shaft. 

④ understand the concept of the approximate number of significant figures, asking questions and then take the results of approximation. 

⑤ understand the concept and secondary radical addition, subtraction, multiplication, and division algorithms will use them to relevant real simple four operations (does not require denominator rationalized). 

(3) algebraic 

Exam content 

Algebra, algebraic values. 

Examination Requirements 

① understand the significance of the number represented by the letter. 

② able to analyze the relationship between the number of simple questions and expressed by algebraic. 

③ explain some simple algebraic or geometric meaning the actual context. 

④ will be evaluated algebraic. 

(4) Zhengshi and Fractional 

Exam content 

Zheng Shi, Zhengshi addition and subtraction, multiplication and division, multiplication formula. 

Factorization: mention common factor method, formula method. 

The basic properties of fractions, fractions, fractions of about points, common denominator, a simple fraction of addition, subtraction, multiplication, and division operations. 

Examination Requirements 

① Zhengshi understand the concept, and will Zhengshi simple addition, subtraction operation; Zhengshi will perform simple multiplication. 

② will use a simple formula to calculate the multiplication. 

③ will use to mention common factor method, factorization formula method. 

④ understand the concept of fractions, will make use of the basic properties of fractions for about points and common denominator. 

⑤ will conduct a simple fraction addition, subtraction, multiplication, and division operations. 

2 equations and inequalities 

(1) equations with the equations 

Exam content 

Solving equations and equations, one dollar equation method and its applications, linear equations solution and application group, a quadratic equation solution and application, can be turned into a dollar an equation Fenshifangcheng. 

Examination Requirements 

① will be a solution of one yuan equation, a simple set of linear equations, can be turned into an equation Fenshifangcheng one yuan. 

② can list the equation (s) according to the number of specific issues in the relationship, appreciate equation (group) is portrayed in the real world of a valid mathematical model. 

③ understanding with the method, factorization method, formula, will be solutions of a quadratic equation. 

(2) inequalities and inequalities 

Exam content 

Inequality, the inequality of the basic nature of the solution set of inequalities, inequalities in one unknown and its solution and application, inequalities in one unknown group and its solution and applications. 

Examination Requirements 

① able to understand the meaning of inequality based on the size of the specific issues in relation to master the basic nature of inequality. 

② will solve simple one dollar once inequality, and the solution set can be expressed in a number line. Inequality group will be composed of two inequalities in one unknown composition and determine the solution set. 

③ relationship can be based on the number of specific issues listed inequalities in one unknown (group), to solve simple problems. 

3 Functions 

(1) Function 

Exam content 

Constants, variables, functions and their representation. 

Examination Requirements 

① understand the significance of constants, variables, functions and understand the concept of three methods, can cite actual examples of functions. 

② a function capable of binding to a simple image to be analyzed in practical problems. 

③ use appropriate function notation portray some real problems in the relationship between variables. 

(2) a linear function 

Exam content 

A linear function, a function of the picture and the nature of the application. 

Examination Requirements 

① understand proportional function, meaning a function determines a function expression according to the known conditions. 

② According to the image and will be a function of the analytic formula y = kx + b (k ≠ 0) to understand its nature (k> 0 or k <0, the image changes). 

③ use a function to solve practical problems. 

(3) the inverse function 

Exam content 

Inverse proportion, inverse function of the image and its properties, applications. 

Examination Requirements 

① understand the significance of the inverse function, inverse function expression can be determined according to the known conditions. 

② can understand its nature (k> 0 k <0, the change or the image) based on the image and the analytical [removed]k ≠ 0). 

③ inverse function can be used to solve some practical problems. 

(4) a quadratic function 

Exam content 

Quadratic function, quadratic function image and its properties, applications. 

Examination Requirements 

① determine the expression of a quadratic function of the analysis of the actual problem situations, and to understand the meaning of a quadratic function. 

② able to understand the nature of the quadratic function based on the image and analytic. 

③ will determine the vertex, opening direction and the symmetry axis images according to the formula, and to solve practical problems. 

Second, space and graphics 

Understanding 1 graphic 

(1) point, line, surface, angle. 

Exam content 

Point, line, surface, angle, angle bisector and its properties. 

Examination Requirements 

① In the actual context awareness, understanding point, line, surface, the concept of angles. 

② would be more angular size, can estimate the size of an angle, it will calculate the angle of the sum and difference, recognizing degrees, minutes, seconds, and will carry out a simple conversion. 

③ understand its properties bisector theorem, inverse theorem. 

(2) parallel to the line of intersection with the line 

Exam content 

Supplementary angle, complementary angle, vertical angles, vertical, point to the distance from the line, the line segment perpendicular bisector theorem and its properties, inverse theorem. Distance parallel lines, parallel lines between two straight lines parallel to the nature and determination. 

Examination Requirements 

① understand supplementary angle, complementary angle, vertical angles definition and properties. 

② understand the concept of vertical, vertical segments, etc., to understand the nature of the shortest vertical segment, understanding the significance of the point to the straight line distance, know too little and only in a straight line perpendicular to the given line. 

③ line perpendicular bisector understand the definition and properties. 

④ understand the concept of parallel lines and parallel lines axiom, inference and their basic properties. 

⑤ appreciate the significance of the distance between the two parallel lines. 

(3) triangle 

Exam content 

Triangle, triangle bisector, middle and high, triangular median lines, congruent triangles, triangles congruent judgment and nature, isosceles triangle, equilateral triangle, triangle conditions and nature of the Pythagorean theorem, hook share theorem converse theorem. 

Examination Requirements 

① learn about the concept of a triangle (inner corner, outer corner, middle, high, angle bisector), to understand the stability triangle. 

② master bit line in the nature of a triangle. 

③ understand the concept of congruent triangles, two triangles congruent grasp determination and character. 

④ understand isosceles triangle, equilateral triangle, triangle of the concept, master isosceles triangle, equilateral triangle, triangle nature and determination. 

⑤ grasp the Pythagorean theorem, will use the Pythagorean Theorem to solve simple problems; will determine the right triangle with the Pythagorean theorem converse theorem. 

(4) quadrilateral 

Exam content 

Polygons, polygon interior angle and with the outer corner and, regular polygon, parallelogram, rectangle, diamond, square, trapezoid concept, conditions and nature of plane figures mosaic. 

Examination Requirements 

① understand the polygon interior angle and with the outer corner and formulas to understand the concept of a regular polygon. 

② master parallelogram, rectangle, rhombus, square, trapezoidal concept, to understand the relationship between them; understanding instability quadrilateral. 

③ master parallelogram, rectangle, rhombus, square, has an isosceles trapezoid, properties related to master the quadrilateral is a parallelogram, rectangle, rhombus, square, trapezoid isosceles conditions. 

④ mosaic by exploring the plane figure, know any one triangle, square or hexagon can be mounted flat. 

(5) Round 

Exam content 

Circle relationship between the arc chord, the center angle, the point circle, and the circle line and the positional relationship between the circle and the circle, the central angle of the circumferential angle, and the inner triangle circumcenter nature, and determining the tangential arc length, fan-shaped area, the side area of the cone, the total area. 

Examination Requirements 

① Circle and understand the concepts, understand the relationship arc, chord, central angle, to understand the point, line and round and round and round and round the positional relationship. 

② understand the nature of the circle, to understand the relationship with the central angle of the circumferential angle, diameter circumferential angle of the feature. 

③ understand the inner triangle and circumcenter. 

④ understand the relationship between the radius of the concept of tangent, tangent point between overcutting; able to determine whether a line tangent to the circle. 

Area ⑤ calculates the arc length and fan, will calculate the area and the whole side of the cone area. 

(6) with the view projection 

Exam content 

Three simple geometry view, side straight prism cone expansion plan. 

Examination Requirements 

① understand the basic geometry (straight prism, cylinder, cone, sphere) of three views (front view, the left view, top view), will determine the three-view simple objects can basically geometry or physical prototypes described according to three views. 

② understand straight prism, an expanded view of the side of the cone, can determine three-dimensional model based on expansion plan. 

③ understand the basic geometry of its three-view, expand the diagram (except the ball) between; know this relationship applications (such as objects packaging) in real life. 

2 graphics and transform 

(A) symmetry axis graph, graphic translation, rotation graphics 

Exam content 

Axial symmetry, translation, rotation, center of symmetry. 

Examination Requirements 

① recognize axial symmetry (or pan, rotate) through specific examples, explore their basic properties. 

② understand simple plane figures through the axis of symmetry (or translation, rotation) after the graphics. 

③ explore basic graphics (isosceles triangle, rectangle, rhombus, isosceles trapezoid, regular polygon, circle) of axial symmetry properties and related properties, understand parallelogram, circle is the center of symmetry. 

④ explore the transformation of the relationship between graphic (axial symmetry, translation, rotation and combinations thereof), the use of axial symmetry (or translation, rotation) and the combination of graphic design; understanding and appreciation of the axis of symmetry (or translation, rotation) in real life application. 

(2) similar to the graphic 

Exam content 

The basic nature of the proportion of, is proportional to the line, similar to the graphic nature of the segment and the ratio of the conditions of similar triangles, graphics homothetic, acute trigonometric functions, trigonometric value 300,450,600 angle. 

Examination Requirements 

① understand the basic nature of proportion to understand segment than proportional segments, learn by example golden. 

② similar pattern recognized by way of example, to understand the nature of a similar pattern, similar to that corresponding to the angle of the polygon is equal to the ratio of the corresponding sides, the specific surface area is equal to the square of the ratio of the corresponding edge. 

③ understand the concept of two triangles similar to master two triangles similar conditions. 

④ homothetic understand graphics can be utilized like a bit pattern is enlarged or reduced. 

⑤ learn through examples similar objects using graphics similar to solve some practical problems (such as the use of a similar measure the height of the flagpole). 

⑥ acute awareness through examples trigonometric (sinA, cosA, tanA), know the value of 300,450,600 trigonometric angle; will seek to use its trigonometric value calculator from known acute angle, find the value of it by the known trigonometric corresponding acute angle. 

⑦ using simple trigonometric functions to solve practical problems related with the right triangle. 

3 graphics and coordinate 

Exam content 

Cartesian coordinate system. 

Examination Requirements 

① know and be able to draw a plane rectangular coordinate system; given Cartesian coordinate system, will delineate the location of the point based on coordinates, its location coordinates of the point of writing. 

② to establish appropriate Cartesian coordinate system on graph paper, describe the location of the object. 

③ In the same Cartesian coordinate system, feel the changes after the graphics transformation coordinate points. 

④ flexible use of different ways to determine the position of the object. 

4 graphics and prove 

(1) to understand the meaning of proof 

Exam content 

Proved definition, proposition, reverse proposition, theorem, theorem, reductio ad absurdum. 

Examination Requirements 

① prove the necessity of understanding. 

② through specific examples, understand the meaning of the definitions, propositions, theorems, and will differentiate the proposition conditions (title design) and conclusions. 

③ with specific examples, understand the concept of inverse proposition, will identify two reciprocal proposition, and know the original proposition holds its inverse proposition is not necessarily true. 

④ understand the role of counter-examples, that the use of counter-examples can prove a proposition is wrong. 

⑤ By way of example, the experience of the meaning of reductio ad absurdum. 

⑥ grasp an integrated method to prove the format, experience step by step process requires proof of evidence. 

(2) proof is based on master 

Exam content 

A straight line obtained by parallel straight lines cut two corresponding angles are equal. 

Two lines being cut third line, if corresponding angles are equal, then the two lines are parallel. 

If the angle between the two sides of the triangle and equal, respectively, the two triangles are congruent. 

And the two corners of the triangle are equal to each side of the folder, the two triangles are congruent. 

Three sides of the triangle are equal to two, the two triangles are congruent. 

Corresponding sides congruent triangles, corresponding angles are equal. 

Examination Requirements 

The use of more than six "basic facts" as proof basis. 

(3) the use of (2) of the basic facts to prove the following proposition 

Exam content 

Theorems of parallel lines (the wrong angle equal to the same side interior angles complementary) and decision theorem (the wrong angle with the side interior angles are equal or complementary, the two parallel lines). 

Angles and triangles theorem and corollary (triangle exterior angle equal to the two non-adjacent interior angles, triangle exterior angle is greater than any one and it is not adjacent interior angles). 

Right triangles congruent judgment theorem. 

Nature bisector theorem and converse theorem; triangular three bisector intersect at one point (the heart). 

The nature of the perpendicular bisector theorem and converse theorem; triangular cross perpendicular bisector trilateral dry point (circumcenter). 

Bit line triangles theorem. 

Isosceles triangle, equilateral triangle, triangle theorem nature and determination. 

Parallelogram, nature rectangle, diamond, square, isosceles trapezoid and decision theorem. 

Examination Requirements 

① will use the (2) the basic facts that the above proposition. 

② will use the above theorem proving new propositions. 

③ exercises and exam topics related to the difficulty of proof should be quite a difficult proposition with the argument listed above. 

④ by Euclid "original" presentation, perceived value of the mathematical geometric interpretation system development and human civilization. 

Third, Statistics and Probability 

1 Statistics 

Exam content 

Data, data collection, collation, description and analysis. 

Sampling, overall, individual samples. 

Fan charts. 

The weighted average, the degree of concentration and degree of dispersion of data, range and variance. 

Frequency, frequency, frequency distribution, frequency tables, histograms, line charts. 

The overall sample estimates, the sample mean, variance, mean overall variance. 

Statistics and Decision, data, statistics and scientific applications in the field of social life.

Examination Requirements 

① will collect, organize, describe and analyze the data, the calculator can handle more complex statistics. 

② understand the necessity of sampling, can point out the overall and individual samples, know different sampling may get different results. 

③ will represent data using fan charts. 

④ understand and will calculate the weighted average, according to the specific problem, select the appropriate statistic indicates the degree of concentration of the data. 

⑤ will explore how to represent the degree of dispersion of a set of data, calculates poor and variance, and will use them to represent the degree of dispersion of the data. 

⑥ understand the frequency, concept frequency, frequency distribution to understand the significance and role, will be listed frequency distribution table, using frequency distribution histograms and frequency line graph, solve simple practical problems. 

⑦ overall experience of using the sample estimate of thinking, can sample mean, variance to estimate the overall mean and variance. 

⑧ can make reasonable judgments and predictions based on the statistical results, the statistical effect of decisions on experience, can more clearly express their views, and to communicate. 

⑨ able to find relevant information according to the problem, to obtain data, daily life will express their views on some of the data. 

⑩ statistical knowledge can be applied to solve some simple practical problems in the social and scientific spheres of life. 

2 Probability 

Exam content 

Probability event, the event, citing law (including a list of tree) calculate the probability of a simple event. 

Frequency experiments and events, the estimated value of the probability of a large number of duplicate experiments when the event occurs. 

Using probabilistic knowledge to solve practical problems. 

Examination Requirements 

① understand the significance of the specific context probability, using probability enumeration method (including a list of tree) calculation is simple events. 

② through experiments, to obtain frequency events; frequency that a large number of repeated tests as an estimate of the probability of occurrence of an event. 

③ will be the probability of events through experiments, and can use probabilistic knowledge to solve some practical problems. 

Sample questions: 

First, the choice :( total of 12 questions, each question three points, a total of 36 points) 

1, the absolute value of all integers less than 5 and equal () 

A, 30 B, 20 C, 10 D, 02, is calculated: 2 × [5+] = () 

A, 8 B, -8 C, -6 D, 6 

3, the following formula is correct () 

A, (ab4) 4 = ab8 B, (- 3pq) 2 = -6p2q2 

C, a6 ÷ a3 = a2 D, a10 ÷ a9 = a 

4, a root of the equation is known about -2, the m value () 

A, 13 B, -13 C, 7 D, -7 

5, which set the following number can be used as long trilateral triangle () 

A, 4,5,6 B, 5,12,13 C, 6,8,9 D, 9,12,16 

6, the following statements is false number is () 

(1) is the square root of 2; (2) 4a3b ÷ (-2a2b) = -2a; 

Image (3) a function after the first, second and fourth quadrant; 

(4) the inner triangle sides of the triangle is the intersection of the perpendicular bisectors; 

(5) the point (2,3) and point (-2, -3) about an axis of symmetry; 

A, 2 个 B, 3 个 C, 4 个 D, 5 个 

7, the side of the isosceles triangle is equal to the known 4cm, while equal 9cm, it is equal to the circumference () 

A, 13cm B, 17cm C, 22cm D, 17 or 22cm 

8, on the root of the equation in the case of x is () 

A, there are two real roots is not equal B, there are two equal real roots 

C, no real roots D, can not be determined 

9, on the function is the inverse function, the value of () 

A, -3 B, 1 C, 1 or -3 D, -1, or 3 

10, known parabola, the following statement is in error () 

A, the parabola axis of symmetry is a straight line B, the third quadrant of the parabola vertices 

C, the parabola opening up D, the parabola through the origin 

11, when the diameters of the two circles 8cm and 10cm, the positional relationship of the center distance of 9cm, the two circles are () 

A, endo-B, the intersection C, from the outside of D, exo 

12, to make the quadrilateral is a square, then the two diagonals of the quadrilateral should meet each other () 

A, vertical split B, vertical shear equal 

C, split and equal D, vertical split and equal 

Second, fill in the blank (a total of eight questions, each question 4 points) 

13, calculate: sin45 ° + cos60 ° = ______. 

14, ranging from the variable function is __________. 

15 If, then = ________ 

16, set up, then _________ 

17, if the interior angle of a polygon, and is 1080 °, the number of sides of the polygon is ____. 

18, in a radius of a circle has a length of 5cm 5cm of the chord, then the degree of the angle of circumference of the pair of strings _____. 

19 Data -2, -1, 0 variance for ___________. 

20 randomly flip a coin twice a uniform probability at least once tails is ______. 

Third, the answers to questions (a total of 6 items 21 --- 24 questions each question 8 points, 25 and 26 questions each question 10 points) 

21, the solution of equations: 22, Inequality Group: 23, first simplify, then evaluated:, where 24 columns equation word problems: a worker process 300 parts, due to improved methods of operation, work efficiency to the original two-fold. Reprocessing 300 parts, two hours ahead of schedule to complete. Two methods of the process before asking how many parts per hour? 

25, it is known on the equation x x2 + (2k-1) x + k2-1 = 0, 

(1) Why when k value equation has two real roots are not equal? 

(2) If the equation is equal to the square root of two 9, find the value of k. 

26, a mall purchase of a number of shirts priced at 16 yuan, after the sale for some time, in order to gain more profit, the mall decided to raise the selling price, the experiment found that, if the price of 20 yuan per piece 

A proposition principles 

Test students understanding of the basics of mathematics, the level of mastery and application, as well as operations, data processing, spatial imagination, the basic level of competence practices. 

Second, in the form of exam 

Closed book, written examination. 

Third, the questions of structure 

There are fill-in questions, multiple choice questions, such as reconciliation answer. Fill in the blank to fill in only requires a direct result of having to write the calculation process or push the certification process; choose a four-choice multiple-choice type; answer questions in various forms, for example: calculation problems, proofs, application questions, reading comprehension questions, open questions and exploratory questions, etc., should write the text to answer questions, calculus steps or push the certification process. Questions out of 120 points, the examination time was 120 minutes. 

Fourth, the examination of the content and requirements 

I. Number and Algebra 

1 Number and type 

(A) rational 

Exam content 

Rational, axes, opposite number, the absolute value of the number. Rational numbers to add, subtract, multiply, divide, involution, addition, multiplication law, rational simple mixing operations. 

Examination Requirements 

① understand the rational sense, can point axis represents the number of rational numbers, it would be more rational size. 

② With the number of axes understand the significance of the number and the absolute opposite, the opposite will seek rational numbers and absolute value. 

③ understand the meaning of involution, the master of rational numbers to add, subtract, multiply, divide, involution and simple mixing operations (mainly in three steps). 

④ understand the rational calculations law, and to apply the law to simplify the arithmetic operations. 

⑤ able to use rational arithmetic to solve simple problems. 

(2) Real 

Exam content 

Square root of the arithmetic square root, cube root, irrational numbers, real numbers, the approximate number of significant digits. 

Secondary radical, secondary radical of addition, subtraction, multiplication, division, real simple four operations. 

Examination Requirements 

① understand the square root of the arithmetic square root, cube root of the concept will be represented by the square root of the number of root, cube root. 

② understand prescribing and involution are inverse operations, will use certain non-squaring find the square root of a negative number, it will seek certain number of cubic cube root operation. 

③ understand the concept of irrational numbers and real numbers, real numbers that correspond with the number of points the shaft. 

④ understand the concept of the approximate number of significant figures, asking questions and then take the results of approximation. 

⑤ understand the concept and secondary radical addition, subtraction, multiplication, and division algorithms will use them to relevant real simple four operations (does not require denominator rationalized). 

(3) algebraic 

Exam content 

Algebra, algebraic values. 

Examination Requirements 

① understand the significance of the number represented by the letter. 

② able to analyze the relationship between the number of simple questions and expressed by algebraic. 

③ explain some simple algebraic or geometric meaning the actual context. 

④ will be evaluated algebraic. 

(4) Zhengshi and Fractional 

Exam content 

Zheng Shi, Zhengshi addition and subtraction, multiplication and division, multiplication formula. 

Factorization: mention common factor method, formula method. 

The basic properties of fractions, fractions, fractions of about points, common denominator, a simple fraction of addition, subtraction, multiplication, and division operations. 

Examination Requirements 

① Zhengshi understand the concept, and will Zhengshi simple addition, subtraction operation; Zhengshi will perform simple multiplication. 

② will use a simple formula to calculate the multiplication. 

③ will use to mention common factor method, factorization formula method. 

④ understand the concept of fractions, will make use of the basic properties of fractions for about points and common denominator. 

⑤ will conduct a simple fraction addition, subtraction, multiplication, and division operations. 

2 equations and inequalities 

(1) equations with the equations 

Exam content 

Solving equations and equations, one dollar equation method and its applications, linear equations solution and application group, a quadratic equation solution and application, can be turned into a dollar an equation Fenshifangcheng. 

Examination Requirements 

① will be a solution of one yuan equation, a simple set of linear equations, can be turned into an equation Fenshifangcheng one yuan. 

② can list the equation (s) according to the number of specific issues in the relationship, appreciate equation (group) is portrayed in the real world of a valid mathematical model. 

③ understanding with the method, factorization method, formula, will be solutions of a quadratic equation. 

(2) inequalities and inequalities 

Exam content 

Inequality, the inequality of the basic nature of the solution set of inequalities, inequalities in one unknown and its solution and application, inequalities in one unknown group and its solution and applications. 

Examination Requirements 

① able to understand the meaning of inequality based on the size of the specific issues in relation to master the basic nature of inequality. 

② will solve simple one dollar once inequality, and the solution set can be expressed in a number line. Inequality group will be composed of two inequalities in one unknown composition and determine the solution set. 

③ relationship can be based on the number of specific issues listed inequalities in one unknown (group), to solve simple problems. 

3 Functions 

(1) Function 

Exam content 

Constants, variables, functions and their representation. 

Examination Requirements 

① understand the significance of constants, variables, functions and understand the concept of three methods, can cite actual examples of functions. 

② a function capable of binding to a simple image to be analyzed in practical problems. 

③ use appropriate function notation portray some real problems in the relationship between variables. 

(2) a linear function 

Exam content 

A linear function, a function of the picture and the nature of the application. 

Examination Requirements 

① understand proportional function, meaning a function determines a function expression according to the known conditions. 

② According to the image and will be a function of the analytic formula y = kx + b (k ≠ 0) to understand its nature (k> 0 or k <0, the image changes). 

③ use a function to solve practical problems. 

(3) the inverse function 

Exam content 

Inverse proportion, inverse function of the image and its properties, applications. 

Examination Requirements 

① understand the significance of the inverse function, inverse function expression can be determined according to the known conditions. 

② can understand its nature (k> 0 k <0, the change or the image) based on the image and the analytical [removed]k ≠ 0). 

③ inverse function can be used to solve some practical problems. 

(4) a quadratic function 

Exam content 

Quadratic function, quadratic function image and its properties, applications. 

Examination Requirements 

① determine the expression of a quadratic function of the analysis of the actual problem situations, and to understand the meaning of a quadratic function. 

② able to understand the nature of the quadratic function based on the image and analytic. 

③ will determine the vertex, opening direction and the symmetry axis images according to the formula, and to solve practical problems. 

Second, space and graphics 

Understanding 1 graphic 

(1) point, line, surface, angle. 

Exam content 

Point, line, surface, angle, angle bisector and its properties. 

Examination Requirements 

① In the actual context awareness, understanding point, line, surface, the concept of angles. 

② would be more angular size, can estimate the size of an angle, it will calculate the angle of the sum and difference, recognizing degrees, minutes, seconds, and will carry out a simple conversion. 

③ understand its properties bisector theorem, inverse theorem. 

(2) parallel to the line of intersection with the line 

Exam content 

Supplementary angle, complementary angle, vertical angles, vertical, point to the distance from the line, the line segment perpendicular bisector theorem and its properties, inverse theorem. Distance parallel lines, parallel lines between two straight lines parallel to the nature and determination. 

Examination Requirements 

① understand supplementary angle, complementary angle, vertical angles definition and properties. 

② understand the concept of vertical, vertical segments, etc., to understand the nature of the shortest vertical segment, understanding the significance of the point to the straight line distance, know too little and only in a straight line perpendicular to the given line. 

③ line perpendicular bisector understand the definition and properties. 

④ understand the concept of parallel lines and parallel lines axiom, inference and their basic properties. 

⑤ appreciate the significance of the distance between the two parallel lines. 

(3) triangle 

Exam content 

Triangle, triangle bisector, middle and high, triangular median lines, congruent triangles, triangles congruent judgment and nature, isosceles triangle, equilateral triangle, triangle conditions and nature of the Pythagorean theorem, hook share theorem converse theorem. 

Examination Requirements 

① learn about the concept of a triangle (inner corner, outer corner, middle, high, angle bisector), to understand the stability triangle. 

② master bit line in the nature of a triangle. 

③ understand the concept of congruent triangles, two triangles congruent grasp determination and character. 

④ understand isosceles triangle, equilateral triangle, triangle of the concept, master isosceles triangle, equilateral triangle, triangle nature and determination. 

⑤ grasp the Pythagorean theorem, will use the Pythagorean Theorem to solve simple problems; will determine the right triangle with the Pythagorean theorem converse theorem. 

(4) quadrilateral 

Exam content 

Polygons, polygon interior angle and with the outer corner and, regular polygon, parallelogram, rectangle, diamond, square, trapezoid concept, conditions and nature of plane figures mosaic. 

Examination Requirements 

① understand the polygon interior angle and with the outer corner and formulas to understand the concept of a regular polygon. 

② master parallelogram, rectangle, rhombus, square, trapezoidal concept, to understand the relationship between them; understanding instability quadrilateral. 

③ master parallelogram, rectangle, rhombus, square, has an isosceles trapezoid, properties related to master the quadrilateral is a parallelogram, rectangle, rhombus, square, trapezoid isosceles conditions. 

④ mosaic by exploring the plane figure, know any one triangle, square or hexagon can be mounted flat. 

(5) Round 

Exam content 

Circle relationship between the arc chord, the center angle, the point circle, and the circle line and the positional relationship between the circle and the circle, the central angle of the circumferential angle, and the inner triangle circumcenter nature, and determining the tangential arc length, fan-shaped area, the side area of the cone, the total area. 

Examination Requirements 

① Circle and understand the concepts, understand the relationship arc, chord, central angle, to understand the point, line and round and round and round and round the positional relationship. 

② understand the nature of the circle, to understand the relationship with the central angle of the circumferential angle, diameter circumferential angle of the feature. 

③ understand the inner triangle and circumcenter. 

④ understand the relationship between the radius of the concept of tangent, tangent point between overcutting; able to determine whether a line tangent to the circle. 

Area ⑤ calculates the arc length and fan, will calculate the area and the whole side of the cone area. 

(6) with the view projection 

Exam content 

Three simple geometry view, side straight prism cone expansion plan. 

Examination Requirements 

① understand the basic geometry (straight prism, cylinder, cone, sphere) of three views (front view, the left view, top view), will determine the three-view simple objects can basically geometry or physical prototypes described according to three views. 

② understand straight prism, an expanded view of the side of the cone, can determine three-dimensional model based on expansion plan. 

③ understand the basic geometry of its three-view, expand the diagram (except the ball) between; know this relationship applications (such as objects packaging) in real life. 

2 graphics and transform 

(A) symmetry axis graph, graphic translation, rotation graphics 

Exam content 

Axial symmetry, translation, rotation, center of symmetry. 

Examination Requirements 

① recognize axial symmetry (or pan, rotate) through specific examples, explore their basic properties. 

② understand simple plane figures through the axis of symmetry (or translation, rotation) after the graphics. 

③ explore basic graphics (isosceles triangle, rectangle, rhombus, isosceles trapezoid, regular polygon, circle) of axial symmetry properties and related properties, understand parallelogram, circle is the center of symmetry. 

④ explore the transformation of the relationship between graphic (axial symmetry, translation, rotation and combinations thereof), the use of axial symmetry (or translation, rotation) and the combination of graphic design; understanding and appreciation of the axis of symmetry (or translation, rotation) in real life application. 

(2) similar to the graphic 

Exam content 

The basic nature of the proportion of, is proportional to the line, similar to the graphic nature of the segment and the ratio of the conditions of similar triangles, graphics homothetic, acute trigonometric functions, trigonometric value 300,450,600 angle. 

Examination Requirements 

① understand the basic nature of proportion to understand segment than proportional segments, learn by example golden. 

② similar pattern recognized by way of example, to understand the nature of a similar pattern, similar to that corresponding to the angle of the polygon is equal to the ratio of the corresponding sides, the specific surface area is equal to the square of the ratio of the corresponding edge. 

③ understand the concept of two triangles similar to master two triangles similar conditions. 

④ homothetic understand graphics can be utilized like a bit pattern is enlarged or reduced. 

⑤ learn through examples similar objects using graphics similar to solve some practical problems (such as the use of a similar measure the height of the flagpole). 

⑥ acute awareness through examples trigonometric (sinA, cosA, tanA), know the value of 300,450,600 trigonometric angle; will seek to use its trigonometric value calculator from known acute angle, find the value of it by the known trigonometric corresponding acute angle. 

⑦ using simple trigonometric functions to solve practical problems related with the right triangle. 

3 graphics and coordinate 

Exam content 

Cartesian coordinate system. 

Examination Requirements 

① know and be able to draw a plane rectangular coordinate system; given Cartesian coordinate system, will delineate the location of the point based on coordinates, its location coordinates of the point of writing. 

② to establish appropriate Cartesian coordinate system on graph paper, describe the location of the object. 

③ In the same Cartesian coordinate system, feel the changes after the graphics transformation coordinate points. 

④ flexible use of different ways to determine the position of the object. 

4 graphics and prove 

(1) to understand the meaning of proof 

Exam content 

Proved definition, proposition, reverse proposition, theorem, theorem, reductio ad absurdum. 

Examination Requirements 

① prove the necessity of understanding. 

② through specific examples, understand the meaning of the definitions, propositions, theorems, and will differentiate the proposition conditions (title design) and conclusions. 

③ with specific examples, understand the concept of inverse proposition, will identify two reciprocal proposition, and know the original proposition holds its inverse proposition is not necessarily true. 

④ understand the role of counter-examples, that the use of counter-examples can prove a proposition is wrong. 

⑤ By way of example, the experience of the meaning of reductio ad absurdum. 

⑥ grasp an integrated method to prove the format, experience step by step process requires proof of evidence.