港澳台联招数学考试大纲（The math exam outline of Hong Kong and Macao Taiwan） 港澳台联招数学考试大纲（The math exam outline of Hong Kong and Macao Taiwan） 2) Mathematics Examination requirements 1。 correctly understand and master the basic knowledge, basic skills, basic ideas and methods of middle school mathematics。 2。。 Skillfully use the mathematical knowledge and methods in the syllabus to solve the problem (including simple application problems)。 II。 Examination content Algebra (Algebra) 1。 number (Number) Rational number, irrational number and real number, absolute value, complex number and its vector (Vector) representation, four operations of complex number。
2。 algebraic formula (Algebraic expression) Type, fraction and its operation, factorization, and radical operation, two radical rationalization。 3。 equation (Equation) The solution and application of the unary two equation, the relation between the root and the coefficient of the unary two equation, the solution of the simultaneous equations of two variables and the simultaneous equations of three variables。 4。 inequality (Inequality) Inequality and its properties, the proof of simple inequality, the solution of the unary inequality, the solution of the two inequality of one variable。
5。 set (Set) Set, subset, intersection, well set, complement。 6。 function (Function) Function, function symbol, domain of function, increasing and decreasing of function, parity,inverse function香港澳台联招, function of inverse function and relation between their images。 7。 a function (y = ax+b, a = 0), quadratic function (y=ax2+bx+c, a = 0), inverse proportion function (y=k/x, k = 0) power function (y=xa), which Images and properties。 8。 exponential function (y=ax, a > 0 and a = 1), logarithmic function (y=logax, a > 0 and a = 1, the common logarithm of the base 10 written LG x), and their image The nature of the formula, logarithmic, exponential and logarithmic equations for the simple。
9。 series (Sequence): arithmetic sequence and its general term formula and the formula N and the geometric series and its general formula and formula n and。 10。 limit (Limit): limit of sequence and the function and four operations, the absolute value of the ratio is less than 1 and the infinite geometric series。 The 11。 addition principle, the principle of multiplication, arrangement and arrangement number formula, combination and composite formula。 12。 binomial theorem, mathematical induction (Mathematical induction) 13。
polynomials (Polynomial): polynomial, remainder theorem and factor theorem。 Two, triangle (Trigonometry) 1。 angle measurement and angle arc system, sine a (sin a), angle cosine (COS a) (Tan, a) and tangent cotangent (COT a) definition。 2。 formulas of trigonometric function with arbitrary angle trigonometric function (induced formula) and trigonometric function of same angle are given。 Trigonometric function value, angle and sine function are known The image and properties of number, cosine function and tangent function。
The solution of 3。 right triangle and its application, sine theorem and cosine theorem and their application in solving oblique triangle。 4。 corners and trigonometric function and difference, sine, cosine and tangent angle formula of two times, sine, cosine and tangent half angle formula。 5。 anti sine, anti cosine, and tangent functions and their images。 Three, solid geometry (Solid geometry) The position relation of two straight lines in space 1。, the angles parallel to the straight line, the corresponding edges being parallel, and the angles formed by the straight lines of different planes。
2。 the relation between the line and the plane, the judgment and the nature of the line and the plane parallel, the judgment and the nature of the line and the plane vertical, the projection of the oblique line on the plane, the straight line The angle formed by the plane is perpendicular to the diagonal line, if it is perpendicular to the line of the plane and the oblique line of the plane (called the three perpendicular theorem) And its converse theorem。 3。 two position plane, two plane parallel and determine the nature, dihedral angle, two perpendicular to the plane of judgment and property。
The volume and side area is 4。 prism, pyramid, it is crystal, cylinder, cone and frustum of a cone, Volume and surface area of spheres。 The relations between 5。 positive propositions, inverse propositions, negative propositions and inverse negative propositions, necessary conditions and sufficient conditions。 Four, analytic geometry (Analytical geometry) 1。 coordinate system (Coordinate) The plane rectangular coordinate system, the distance formula between two points, the definite fraction of line segment。
2。 vector (Vector) Vector, directed line segment and vector, inner product of plane vector。 3。, the slope angle and slope of the straight line, point oblique, oblique cut, two-point, intercept and general equations, two lines parallel and vertical conditions, two straight The angle formed by a line, the intersection point of two straight lines, and the distance from point to line。 4。 curves and equations, simple trajectory problems。 The standard equation and general equation of the 5。 circle, the definition of ellipse, the standard equation, the graph and its property, the definition of hyperbola, the standard equation,the graph and its property香港澳台联招, the parabola Line definition, standard equation, graph and their properties。
The translation of 6。 coordinate axes, using the coordinate axis translation, will be missing XY term of two variables two equation into standard equation。 The interaction of polar coordinate system, polar coordinate and rectangular coordinate in 7。 polar coordinates。 8。 space rectangular coordinate system, straight line and plane in space, plane equation, space straight line equation。 Five, calculus (Differential and integral calculus) 1。 the concept of continuous function and derivative (Derivative) and its geometric significance, several common functions [C, XM (M is rational), ex, ax, LN x, logax] The derivative, the sum, difference, product, quotient derivative of two functions, derivative of compound function, fundamental derivative formula。
2。 use derivative to study the monotonicity, extreme value (Extremum), maximum and minimum of function。 Six, probability and Statistics (Probability and Statistic) 1。 probability of random event, probability of equal probability event, probability addition formula of mutual exclusion event, probability multiplication formula of independent event and independent repeated test。 2。 sampling methods (random sampling, systematic sampling, stratified sampling, etc。), estimation of population distribution, estimation of normal distribution and population characteristics。
III。 examination form and structure of test paper 1。 test time is 120 minutes, 150 points。 2。 closed book exam writing style, with a pen or a ballpoint pen with a red pen to answer, the not in pencil。 3。 students of science and science use the same test paper, which includes different examination questions for students of Arts and science。 4。 examination can use calculators and compasses, rulers and other drawing instruments。 5。 the proportion of knowledge content in each part Algebra about 35% Triangle about 15% The solid geometry is about 10% The analytic geometry is about 20% Calculus about 10% Probability and statistics are about 10% 6。
the proportion of various types of questions The test paper includes three types of questions: multiple-choice questions, filling in the blanks and answering questions。 Choose a single choice question of "four selection"; fill in the blanks only ask to fill in the result directly, and don't write it Calculation or deduction process; answer questions include calculation questions, argumentation questions and application questions, answers should write text description, calculation steps or push the certificate process。 Three types of test papers are accounted for Fraction proportion: Selective questions about 35% Fill in the blanks about 25% Answer questions about 40%
