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**Candidates**
Completing Chinese Junior Middle school students or equivalent education background

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**About the exam**
Candidates are asked to participate in a 45 minutes long lesson. Candidates need to be fully engaged in class learning. They need to take meaning notes, interact with teachers and peers and contribute to team work. Also they are expected to solve two questions related to the new knowledge they have just learned in the lesson independently at the end of the lesson. The lesson will be delivered bilingually. Students can use both Chinese and English in class.

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**Assessment objectives**
.To know how well students learn new knowledge and apply new knowledge to solve problems

.To check candidates’ logic thinking skills

.To know how well candidates can communicate in Mathematical language

Candidates will be assessed through taking notes, participating in group discussions and solving problems independently.

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**Contents of the exam**
- Algebraic expressions, including their basic calculation, such as multiplication and division
- Equation and simultaneous equation
- Inequality and simultaneous inequality
- Quantitative analysis in the daily situation problems, such as their applications
- Factorization of polynomials, including quadratic functions
- Functions and their graphs: linear and quadratic functions, inverse functions, and how to sketch the graph of a given function
- Geometry in 2 dimensions, such as the equation of lines, gradients and intercepts; also the trigonometry
- Geometry in three dimensions, including the volume and the surface area of spheres, cones, cylinders and cubes
- Statistics and Probability, such as basic calculation involving mean/average, median and mode, and some simple probabilities

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**Candidates Students**
who are current Junior 2 or 3 students or equivalent.

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**Exam format and content**
The examination includes a computer-based test and an interview.

The computer-based test lasts for 80 minutes. It mainly evaluates the candidates' ability of Use of English (grammar and vocabulary) and Listening. The type of questions are multiple-choice and fill-in-the-blank. The test is computer adaptive, which means that the test adjusts the difficulty of questions based on the student’s responses.

The interview lasts for 10-15 minutes, and the foreign teachers will conduct one-on-one interviews. The interviewer will make an individual comprehensive assessment based on the candidates' communication skills and enthusiasm for learning.

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**Candidates**
Students who are current high school students or have equivalent study experience.

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**About the exam**
The exam is closed-book exam. There will be long and short answer questions. Candidates are required to write down the processes of solving the problems and present clear and logic thinking. The exam lasts 60 minutes and approximate 7 questions need to be answered. Grades are given when the papers are marked, which are A,B,C,D and U. Grade C is the admitted grade.

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**Contents of the exam**
**Set Theory:** basic concepts of set theory and operations of sets, as mathematical fundamentals;

**Function:** the concept of a function, the basic properties of the function (monotonic functions, even and odd functions), the concepts and operations of exponential functions, logarithmic function and power function;

**Trigonometry:** use trigonometric functions, and vector methods in the solution of triangles, with emphasis on the graphs of trigonometric functions and their properties;

**Plane vectors:** use vector as a tool to solve mathematical problems, conjointly with knowledge of analytic geometry;

**Trigonometric identities:** be able to use trigonometric identities and trigonometric functions to transform, simplify or study various expressions or equations;

**Series:** arithmetic series and its general formula, the sum of the first n items of an arithmetic series and the formulas for such geometric series and its general formula, the sum of the first n items of a geometric series and formulas. Understand the concept of arithmetic and geometric series and the formulas for the sum of the first n terms and the use of them in the solution of simple problems;

**Inequality:** understand the basic nature of inequalities, quadratic inequalities and their solutions; simple linear programming problems.

**Introduction to algorithm:** understand the basic use of computational algorithms and formulas;

**Statistics:** with reference to statistical case studies, understand the concept of random sampling and stratified sampling and how to use these concepts in simple practical problems. In case studies, know how to use of the frequency distribution calculated from the sample to estimate the population distribution, and the use of calculations from the sample to estimate population means and variance;

**Probability:** understand the concept of the probability of random events, and the calculation of probability of such events, use permutations and combinations and their basic formulas to calculate the probability of events in various situations. Know how to use the geometric probability model to find the probability of the occurrence of some evens.

**Solid geometry:** understand elementary plane or three dimensional geometrical diagrams, and simple calculations of geometrical properties such as surface area and volume;

**Points, lines and planes:** know the definition of points, lines and planes and their formulas or equations and the determination of relationship such as whether two lines are parallel or perpendicular and other relationships among geometric figures; Lines and their equations: understand the concept of the measurement of slope and direction of a straight line, know how to find the direction of a line defined by two points, how to find the equation of a line from a given point and a given direction, how to find the equation of a line from various given conditions, how to tell whether two lines are parallel or perpendicular, how to find the distance from a point to line, and to tell the relationship between two lines from their given equations.

**The derivative and its applications:** know how to find the derivatives of a function, and to find the extreme in a monotonic and closed interval;

**Derivative and its application:** know the definition and operation of derivative and the fundamental theorem of calculus; Extend the number system and introduce the complex number, be familiar with the algebraic operations of the complex number; Counting principal, the addition law and the multiplication law, permutation & combination, binomial theorem; Random variable and its distribution, discrete random variable and its distribution function, binomial distribution, mean and variance, normal distribution; statistics case, grasp the idea of regression and independent testing and its tapplication.

English test is online test. There are five parts in the test, including listening, reading, speaking, writing， grammar and vocabulary. The exam lasts 160 minutes.

The interview is face to face communication with school teachers and it may last from 10 to 15 minutes per candidate. The candidates need to demonstrate their verbal communication skills, enthusiasm about study, etc.

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**Content of the exam**
**Listeniing**
Listening lasts for about 40 minutes. Tasks include information recognition, information matching, inference-discussion and inference- longer monologues.

**Reading:**
Reading lasts for about 35 minutes. Tasks include sentence comprehension, text cohesion, opinion matching and long text comprehension.

**Speaking**
Speaking lasts for about 12 minutes. Tasks include Sentence comprehension, describe, express opinion and provide reasons and explanations, describe, compare and provide reasons and explanations and discuss personal experience and opinion on an abstract topic.

**Writing**
Writing lasts for 50 minutes. Tasks include word-level writing, short text writing, three written responses to questions and formal and informal writing.

**Vocabulary and grammar**
Vocabulary and grammar last for 25 minutes. Tasks include word definition, word pairs, word usage, word combinations and sentence completion by choosing the correct options.