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Beijing Union University College of Special Education

Description of Single Entrance Examination for the Disabled (Mathematics) (Visually Impaired Students)

I. Nature

Beijing Union University College of Special Education

Description of Single Entrance Examination for the Disabled (Mathematics) (Visually Impaired Students)

I. Nature of the examination

The separate entrance examination for special education college of Beijing Union University is a selective examination attended by qualified disabled high school graduates and disabled candidates with the same academic ability. According to the established enrollment plan and candidates' scores, the college selects the best candidates. Therefore, this kind of college entrance examination should have high reliability, validity, necessary discrimination and appropriate difficulty.

Two. Examination content

The proposition conforms to the actual learning ability of visually impaired students, further embodies the evaluation concept of mathematics curriculum standards formulated by the Ministry of Education in 2003, guides mathematics teaching in senior high schools, improves mathematics learning methods of visually impaired students, and effectively evaluates students' mathematics learning status.

The examination of mathematics subjects focuses on the basic knowledge, basic skills, basic ideas and methods of middle school mathematics, the ability of logical thinking, calculation, spatial imagination, analysis and problem solving, and the potential of visually impaired students to continue their studies in colleges and universities. According to the principle of "paying attention to ability while examining basic knowledge", the guiding ideology based on the actual ability of visually impaired students is established, and the examination of knowledge, ability and quality is integrated to comprehensively test the mathematical literacy of candidates.

I. Assessment objectives and requirements

(a) the knowledge requirements, ability requirements and personality quality requirements of the examination content

1.？ Knowledge demand

Knowledge refers to mathematical concepts, properties, laws, formulas, axioms, theorems, mathematical ideas and methods in some teaching contents stipulated by the mathematics curriculum standards.

The requirements for knowledge are in turn four levels: cognition, understanding, mastery and comprehensive application.

(1) Understanding: Have a preliminary understanding of the listed knowledge, and will identify it and directly apply it to related problems.

(2) Understanding: Have a rational understanding of the listed knowledge, be able to explain, give examples, deform and infer, and use the listed knowledge to solve simple problems.

(3) Mastery: Have a profound and rational understanding of the listed knowledge, form skills, and use the listed knowledge to solve related problems.

(4) Comprehensive application: systematically grasp the internal relationship of knowledge, and be able to use relevant knowledge to analyze and solve relatively comprehensive problems.

2.？ Ability requirement

Ability refers to thinking ability, calculating ability, spatial imagination ability, practical ability and innovative consciousness.

(1) Thinking ability: I can observe, compare, analyze, synthesize, abstract and summarize problems or data; Able to use analogy, induction and deduction for reasoning; Can be expressed logically and accurately.

(2) Calculation ability: it can perform correct operation, deformation and data processing according to laws and formulas; According to the conditions and objectives of the problem, find and design a reasonable and simple operation mode; Can estimate and approximate data as needed.

Computing ability is the combination of thinking ability and computing skills. Operations include calculation, estimation and approximate calculation of numbers, combined deformation and decomposition deformation of formulas, calculation and solution of geometric quantities of geometric figures, etc. Computational ability includes thinking ability in a series of processes, such as analyzing operational conditions, exploring operational direction, selecting operational formulas, and determining operational procedures. It also includes the ability to adjust the operation when encountering obstacles in the execution of the operation, and the skills to realize the operation and calculation.

(3) Space imagination: make correct graphics according to conditions, and imagine intuitive images according to graphics; Can correctly analyze the basic elements and their relationships in graphics; Can decompose, combine and transform graphics; Will use graphics and charts to vividly reveal the essence of the problem.

Spatial imagination is the ability to observe, analyze and abstract spatial forms. Mainly manifested in the ability to read, draw and imagine graphics. Understanding graphics refers to observing and studying the relationship between geometric elements in a given graphic; Drawing refers to the transformation of written language and symbolic language into graphic language, and the addition or various transformations of auxiliary graphics to graphics; The imagination of graphics mainly includes two kinds: there are pictures and there are no pictures, which is a high-level symbol of spatial imagination.

(4) Innovative consciousness: for novel information, situations and problems, choose effective methods and means to analyze information, comprehensively and flexibly use the learned mathematical knowledge, ideas and methods, conduct independent thinking, exploration and research, put forward ideas to solve problems, and creatively solve problems.

Innovative consciousness is the advanced expression of rational thinking. Observing, guessing, abstracting, generalizing and proving mathematical problems is an important way to find and solve problems. The higher the degree of transfer, combination and integration of mathematical knowledge, the stronger the sense of innovation will be.

3.？ Personality quality requirements

Personality quality refers to the feelings, attitudes and values of candidates. Candidates are required to have a certain mathematical vision, understand the scientific and humanistic value of mathematics, advocate the rational spirit of mathematics, form the habit of prudent thinking, and appreciate the aesthetic significance of mathematics.

Candidates are required to overcome their nervousness, take the test with a peaceful mind, control the test time reasonably, answer the test questions with a scientific attitude of seeking truth from facts, establish confidence in overcoming difficulties, and embody the spirit of perseverance.

(2) Examination requirements

The systematicness and rigor of mathematics discipline determine the profound internal relationship between mathematical knowledge, including the vertical relationship between each part of knowledge in their respective development process and the horizontal relationship between each part of knowledge. We should be good at grasping these relations in essence, and then construct the structural framework of mathematics examination papers through classification, combing and synthesis.

1. The examination of the basic knowledge of mathematics should be comprehensive and focused, and the key contents supporting the subject knowledge system should occupy a large proportion, which constitutes the main body of the mathematics test paper.

2. The examination of mathematical thinking method is an abstract and generalized examination of mathematical knowledge at a higher level, which must be combined with mathematical knowledge to reflect the examinee's understanding of mathematical thinking method; Starting from the overall significance and ideological value of this topic, we should pay attention to general methods and downplay special skills, and effectively examine the examinee's mastery of mathematical ideas and methods contained in middle school mathematics knowledge.

3. The examination of mathematical ability emphasizes "taking the practical ability of blind students as the concept", that is, taking mathematical knowledge as the carrier, starting from problems, grasping the overall significance of the subject and organizing materials with a unified mathematical point of view. Focus on the understanding and application of knowledge, so as to test the ability of candidates to transfer knowledge to different situations, so as to test the breadth and depth of candidates' individual rational thinking and the potential for further learning.

4. The examination of practical ability mainly adopts the form of solving application problems. First, adhere to the principle of "close to life, fair background, and control difficulty", and the design of test questions should conform to the reality of mathematics teaching in middle schools for the blind in China, taking into account the age characteristics and practical experience of visually impaired students, so that the difficulty of mathematics application problems can meet the level of candidates.

The proposition of mathematics discipline, on the basis of examining basic knowledge, pays attention to the examination of mathematical thinking methods, mathematical ability, scientific value and humanistic value of mathematics, takes into account the foundation, comprehensiveness and reality of test questions, attaches importance to the hierarchy among test questions, and insists on multi-angle and multi-level examination, so as to achieve the requirements of comprehensive examination of mathematical literacy.

Second, the scope and requirements of the examination

( 1)? Setting, simple logic?

1. exam content:?

Assemble. Subset. Complement set intersection. Trade union. Logical connectives. Four propositions. Sufficient conditions and necessary conditions. ?

2. Examination requirements:?

(1) Understand the concepts of set, subset, complement, intersection and union. Understand the meaning of empty set and complete set. Understand the meaning of belonging, tolerance and equality. Master related terms and symbols, and use them to represent some simple sets correctly. ?

(2) Understand the meaning of logical connectives "or", "and" and ". Understand four propositions and their relationships. Understand the meaning of sufficient condition, necessary condition and necessary and sufficient condition. ?

(2)? Function?

1. exam content:?

Mapping. Function. Monotonicity of functions. Parity. Inverse function. The relationship between function images of reciprocal functions. Extension of the concept of exponent. Operational properties of rational exponential powers. Exponential function. The operational properties of logarithms. Logarithmic function. Application of functions. ?

2. Examination requirements:?

(1) Understand the concepts of mapping and function. ?

(2) Understand the concepts of monotonicity and parity of functions.

(3) Understanding the concept of inverse function and the relationship between function images which are mutually inverse functions, we will find the inverse functions of some simple functions. ?

(4) Understand the concept of fractional exponential power, master the operational properties of rational exponential power, and master the concept, image and properties of exponential function. ?

(5) Understand the concept of logarithm and master the operational nature of logarithm. Master the concept and properties of logarithmic function and understand logarithmic images.

(3)? Inequality?

1. exam content:?

Inequality. Basic properties of inequality. Proof of inequality. The solution of inequality. Inequalities with absolute values. ?

2. Examination requirements:?

(1) Understand the properties of inequalities. ?

(2) Understanding, analyzing, synthesizing and comparing to prove simple inequalities. ?

(3) Master the solution of simple inequality. ?

(3)? Trigonometric function?

1. exam content:?

Popularization of the concepts of angle and arc system. Trigonometric function at any angle. The trigonometric function line in the unit circle. Basic relations of trigonometric functions with the same angle. Inductive formulas of sine and cosine. Sine, cosine and tangent of sum and difference of two angles, sine, cosine and tangent of double angles. Images and properties of sine function and cosine function. Periodic function. Image of function y=Asin(ωx+). Images and properties of tangent function. It is known that trigonometric functions can find angles. Sine theorem. Cosine theorem. Solution of oblique triangle. ?

2. Examination requirements:?

(1) Understand the concept of arbitrary angle and the meaning of radian. Can correctly convert radian and angle. ?

(2) Understand the definition of sine, cosine and tangent at any angle. Understand the definitions of cotangent, secant and cotangent, and master the basic relationship of trigonometric functions with the same angle. Master the inductive formulas of sine and cosine. Understand the meaning of periodic function and minimum positive period. ?

(3) Master the sine, cosine and tangent formulas of the sum and difference of two angles. Master the sine, cosine and tangent formulas of double angles. ?

(4) The trigonometric formula can be used correctly to simplify, evaluate and prove the identities of simple trigonometric functions. ?

(5) Understand the images of sine function, cosine function and tangent function, understand the properties of sine function, cosine function and tangent function, and understand A,,? The physical meaning of. ?

(6) Master sine theorem and cosine theorem, and use them to solve oblique triangles. ?

(5)? Series?

1. exam content:?

Sequence. Arithmetic progression and his general formula. Arithmetic progression's first n terms and formulas. Geometric series and its general formula. The first n terms and formulas of geometric series. ?

2. Examination requirements:?

(1) Understand the concept of sequence and the meaning of the general term formula of sequence. Knowing the recursive formula is a way to give the sequence, and the first few items of the sequence can be written according to the recursive formula. ?

(2) Understand the concept of arithmetic progression, master arithmetic progression's general formula and the first n summation formulas, and solve simple practical problems. ?

(3) Understand the concept of geometric series, master the general formula of geometric series and the first n summation formulas, and solve simple practical problems. ?

(6)? Equation of straight line and circle (about 13%)

1. exam content:?

The inclination and slope of a straight line. Point inclination formula and two-point formula of linear equation. General formula of linear equation. ? The condition that two straight lines are parallel and perpendicular. The intersection of two straight lines. Distance from point to straight line. Concepts of curves and equations. The curve equation is listed by known conditions. Standard equation and general equation of circle. Parametric equation of a circle. ?

2. Examination requirements:?

(1) Understand the concepts of inclination angle and slope of a straight line, and master the slope formula of a two-point straight line. Master the point-oblique formula, two-point formula and general formula of one-dimensional linear equation, and be able to skillfully solve one-dimensional linear equation according to conditions. ?

(2) Master the conditions of parallelism and perpendicularity of two straight lines, the angle formed by two straight lines and the distance formula from point to straight line. Can judge the positional relationship between two straight lines according to the straight line equation. ?

(3) Master the standard equation and general equation of a circle, understand the concept of parametric equation and understand the parametric equation of a circle. ?

(7)? Conic curve equation (about 7%)

1. exam content:?

Ellipse and its standard equation. Simple geometric properties of ellipse. Parametric equation of ellipse. Hyperbola and its standard equation. Simple geometric properties of hyperbola. Parabola and its standard equation. Simple geometric properties of parabola. ?

2. Examination requirements:?

(1) Master the definition, standard equation and simple geometric properties of ellipse, and understand the parameter equation of ellipse. ?

(2) Master the definition of hyperbola, standard equation and simple geometric properties of hyperbola. ?

(3) Master the definition, standard equation and simple geometric properties of parabola. ?

(4) Understand the preliminary application of conic curve. ?

(8)? Solid geometry foundation (about 7%)

1. exam content:?

Plane and its basic properties. Parallel lines. The angle of a parallel side. The angle formed by straight lines on different planes. The common perpendicular of straight lines in different planes. The distance of straight lines on different planes. Determination and properties of parallelism between straight line and plane. Determination and properties of perpendicularity between straight line and plane. Distance from point to plane. Projection of diagonal lines on a plane. The angle formed by a straight line and a plane. Three vertical theorems and their inverse theorems. Determination and properties of parallel planes. Distance between parallel planes. Dihedral angle and its plane angle. Determination and properties of two planes being perpendicular. A polyhedral regular polyhedral prism. Pyramid. Ball. ?

2. Examination requirements:?

(1) Understand the basic properties of a plane.

(2) Understand the judgment theorem and property theorem that two straight lines are parallel and vertical. Understand the concepts of angle and distance formed by two straight lines. For the distance of straight lines in different planes, it is only necessary to calculate the distance given the common perpendicular. ?

(3) Understand the judgment theorem and property theorem of parallelism between straight lines and planes. Understand the judgment theorem and property theorem of vertical line and plane. Understand the concepts such as the projection of diagonal lines on the plane, the angle between straight lines and the plane, and the distance between straight lines and the plane. Understand the three vertical theorems and their inverse theorems. ?

(4) Understand the judgment theorem and property theorem of two parallel planes. Understand the concepts of dihedral angle, plane angle of dihedral angle and distance between two parallel planes. Understand the judgment theorem and property theorem of two planes perpendicular. ?

(5) Understand the concepts of polyhedron, convex polyhedron and regular polyhedron. ?

(6) Understand the concept and properties of prism. ?

(7) Understand the concept of pyramids and the nature of regular pyramids. ?

(8) Understand the concept and properties of the ball, and understand the surface area formula and volume formula of the ball. ?

(9)? Permutation, combination and binomial theorem

1. exam content:?

Classification counting principle and step counting principle. Arrange. Formula of permutation number. Combination. Combination number formula. Two properties of combinatorial numbers. Binomial theorem. Properties of binomial expansion. ?

2. Examination requirements:?

(1) Understand the principles of classified counting and step-by-step counting. ?

(2) Understand the meaning of permutation and the calculation formula of permutation number. ?

(3) Understand the meaning of combination, the calculation formula of combination number and the nature of combination number. ?

(4) Understand the binomial theorem and the properties of binomial expansion. ?

Ⅲ. Examination form and examination paper structure

First, the answer method: closed book, written test.

Second, the examination time: 150 minutes

3. Marking paper: The total score of the test paper is 150, of which multiple-choice questions and fill-in-the-blank questions account for about 1 10, and the answer questions account for about 40.

Fourth, the question type:

The test paper includes multiple-choice questions, fill-in-the-blank questions and solution questions. Multiple choice questions are single choice questions of four choices and one type; Fill in the blanks only by filling in the results directly, without writing out the calculation process or derivation process; Solution questions include calculation questions, proof questions, application questions, etc. Solution questions should be written in words, calculation steps or derivation process.

Fifth, the difficulty of the test paper.

The difficulty ratio of the test questions is: about 80% of the basic questions; Improve the number of questions by about 20%.

Sixth, the principle of composition

The test questions are mainly arranged according to the type and difficulty. Multiple choice questions come first, non-multiple choice questions come last. Try to arrange the same type of questions in order from easy to difficult.

Beijing Union University College of Special Education

Description of the Single Recruitment Examination for Disabled Persons (Physical and Chemical Physics)

(Acupuncture and Massage Major)

I. Nature of the examination

The separate entrance examination for special education college of Beijing Union University is a selective examination attended by qualified disabled high school graduates and disabled candidates with the same academic ability. According to the established enrollment plan and candidates' scores, the college selects the best candidates. Therefore, this kind of college entrance examination should have high reliability, validity, necessary discrimination and appropriate difficulty.

Two. Examination content

According to the requirements of our college for the cultural quality of disabled freshmen, and according to the Curriculum Scheme (Experiment) and Curriculum Standard (Experiment) for Ordinary High Schools promulgated by People's Republic of China (PRC) and the Ministry of Education in 2003, the content of physics examination in our college is determined. The examination content includes two aspects: knowledge and ability.

The college entrance examination focuses on examining candidates' knowledge, ability and scientific literacy, integrating theory with practice, attaching importance to the relationship between science and technology and social and economic development, and paying attention to the extensive application of physical knowledge in production and life, which is conducive to selecting freshmen in our college, stimulating candidates' interest in learning science, cultivating a realistic attitude, forming correct values, and promoting the three-dimensional courses of "knowledge and skills", "process and method" and "emotional attitude and values"

I. Assessment objectives and requirements

Physics in college entrance examination pays attention to ability while examining knowledge, and puts ability examination in the first place. Identify candidates' abilities by examining knowledge and its application, but don't simply correspond some knowledge with some abilities.

At present, the ability to be assessed by the physics department of the college entrance examination mainly includes the following aspects:

(a) Ability to understand the exact meaning of physical concepts and laws, the applicable conditions of physical laws, and their application in simple situations; Be able to clearly understand the expressions of concepts and laws (including written expression and mathematical expression); Be able to identify specious statements about concepts and laws; Understand the differences and connections of related knowledge.

(2) Reasoning ability can logically reason and demonstrate physical problems according to known knowledge and physical facts and conditions, draw correct conclusions or make correct judgments, and correctly express the reasoning process.

(3) Comprehensive analysis ability can independently analyze and study the problems encountered, find out the physical state, physical process and physical situation, and find out the factors and related conditions that play an important role; Be able to decompose a complex problem into several simpler problems and find out the relationship between them; Be able to put forward solutions to problems and use physical knowledge to comprehensively solve problems encountered.

(four) the ability to apply mathematics to deal with physical problems, to list the relationship between physical quantities according to specific problems, to deduce and solve them, and to draw physical conclusions according to the results; If necessary, geometric figures and function images can be used for simple expression and analysis.

(V) Experimental ability: For the experiments in the three modules of Physics 1, Physics 2 and Elective 3- 1, I can clearly define the experimental purpose, understand the experimental principles and methods, analyze experimental phenomena, process experimental data, draw conclusions, and analyze and evaluate the conclusions.

These five capacity requirements are not isolated. We focus on a certain ability, and at the same time we examine related abilities to varying degrees. At the same time, the process of applying a certain ability to deal with or solve specific problems is also accompanied by the process of finding and asking questions. Therefore, the college entrance examination examines the ability of candidates to find and ask questions, which permeates the examination of the above ability.

Second, the scope and requirements of the examination

The physical knowledge to be tested is mechanics and electromagnetism. Considering the arrangement of physics knowledge in the curriculum standard and the basic requirements of enrollment in our college, the examination content includes three modules: physics 1, physics 2, elective 3- 1.

The degree of knowledge required for each part is represented by numbers I and II. I and II have the following meanings:

First, knowing the content and significance of the listed knowledge can be directly identified and applied in related issues, which is equivalent to "understanding" and "cognition" in the curriculum standards.

Two. Understanding the exact meaning of listed knowledge and its connection with other knowledge can describe and explain it, and can be used in the process of analyzing, synthesizing, reasoning and judging practical problems, which is equivalent to "understanding" and "application" in curriculum standards.

See the following table for specific modules, themes, contents and requirements:

package

theme

content

ask

explain

Physics 1

(Required 1)

Linear motion of particles

Reference system, particle

Ⅰ

Displacement, velocity and acceleration

Ⅱ

Uniform linear motion and its formula and image

Ⅱ

Interaction and Newton's law of motion

Sliding friction, dynamic friction coefficient and static friction.

Ⅰ

1.？ The synthesis and decomposition of mutually angled forces mainly focus on the understanding of drawing methods. In terms of calculation, we only need to apply the knowledge of right triangle to solve it. It should be understood that vectors and scalars have different operation rules.

2.？ In Newton's laws of motion, we should examine the basic idea of comprehensively applying kinematics and dynamics knowledge to solve mechanical problems, but we should not deal with conjunctions.

3.？ The stress analysis of an object only needs to deal with the simple stress situation.

Deformation, elasticity, Hooke's law

Ⅰ

Vector and scalar

Ⅰ

Composition and decomposition of forces

Ⅱ

* * * Point force balance

Ⅱ

Newton's law of motion and its application

Ⅱ

Overweight and weightlessness

Ⅰ

Physics II

(Compulsory 2)

mechanical energy

Work and power

Ⅱ

1.？ Understand that work is a measure of energy conversion.

2.？ When dealing with the relationship between work and energy, we don't have to say negative work.

3.？ Elastic potential energy only needs qualitative understanding.

Kinetic energy and kinetic energy theorem

Ⅱ

Gravitational work and gravitational potential energy

Ⅱ

Function relation, law of conservation of mechanical energy and its application

Ⅱ

Projectile motion and circular motion

Composition and decomposition of motion

Ⅱ

1.？ The oblique throwing action is only qualitative.

2.？ Only centripetal acceleration's formula an=v2/r=rω2 needs to be used correctly, and it is not necessary to deduce the formula.

Parabolic motion

Ⅱ

Uniform circular motion, angular velocity, linear velocity and centripetal acceleration.

Ⅰ

Centripetal force of uniform circular motion

Ⅱ

Centrifugal phenomenon

Ⅰ

law of universal gravitation

Law of universal gravitation and its application

Ⅱ

The understanding of the law of universal gravitation can be related to the achievements made by human beings in exploring the laws of celestial bodies and developing space technology.

Circumferential/orbital speed

Ⅰ

The Second Universe Speed and third cosmic velocity

Ⅰ

Classical and relativistic views of time and space.

Ⅰ

Elective course 3- 1

(scientific tendency)

electric field

Electrical structure and charge conservation of matter

Ⅰ

The quantitative analysis of the motion of charged particles in uniform electric field is limited to the case that charged particles enter the uniform electric field vertically or parallel.

Explanation of electrostatic phenomenon

Ⅰ

point charge

Ⅰ

Coulomb law

Ⅱ

electrostatic field

Ⅰ

Field strength of point charge

Ⅱ

electric field line

Ⅰ

electric potential energy

Ⅰ

potential difference

Ⅱ

Relationship between potential difference and electric field strength in uniform electric field

Ⅰ

Motion of charged particles in uniform electric field

Ⅱ

oscilloscope tube

Ⅰ

Common capacitor

Ⅰ

Relationship among voltage, charge and capacitance of capacitor

Ⅰ

circuit

Ohm's Law

Ⅱ

Law of resistance

Ⅰ

Series and parallel connection of resistors

Ⅰ

Electromotive force and internal resistance of power supply

Ⅱ

Ohm's law of closed circuit

Ⅰ

Electric power, Joule's law

Ⅰ

magnetic field

Magnetic field, magnetic induction intensity, magnetic induction line

Ⅰ

1.？ The calculation of ampere force is limited to the case that the current is perpendicular to the magnetic induction intensity.

2.？ The calculation of Lorentz force is limited to the case that the velocity is perpendicular to the magnetic field direction.

3.？ The quantitative analysis of the motion of charged particles in a uniform magnetic field is limited to the case that charged particles enter the uniform magnetic field in the direction of vertical or parallel magnetic field.

Direction of magnetic field around charged straight line and charged coil

Ⅰ

Ampere force, the direction of Ampere force

Ⅰ

Ampere force in uniform magnetic field

Ⅱ

Lorentz force, the direction of Lorentz force

Ⅰ

lorentz force

Ⅱ

Motion of charged particles in uniform magnetic field

Ⅱ

Mass spectrometer and cyclotron

Ⅰ

Ⅲ. Examination form and examination paper structure

First, the answer method

1. Physics and chemistry (physics and chemistry) exams are the same.

2. Closed book and written test.

Second, the examination time

Physical chemistry (physics and chemistry) examination time 150 minutes.

Third, the volume surface assignment

Physical and chemical (physical and chemical) scores 150, of which physics accounts for 40%, that is, physics scores 60.

Fourth, the question type

Examination papers generally include single-choice questions, multiple-choice questions, fill-in-the-blank questions and calculation questions.

Verb (abbreviation of verb) content ratio

The knowledge proportion of each module in the test paper is: compulsory module physics 1, physics 2 each accounts for about 35%, and elective module 3- 1 accounts for about 30%.

Sixth, the difficulty of the test paper.

The difficulty ratio of the test questions is: about 80% of the basic questions; Improve the number of questions by about 20%.

Seven, the principle of composition

The test questions are mainly arranged according to the type and difficulty. Multiple choice questions come first, non-multiple choice questions come last. Try to arrange the same type of questions in order from easy to difficult.