Mathematics for the CSCA test

After this unit you know how the course works, read the key maths terms in English, and know where to start.

1. 1How to get the most from this courseHow the three levels fit together, how the exercise after each lesson works, and how to read the «To review» list after each result.
2. 2The language of maths in EnglishThe terms and symbols that keep coming up, such as domain, range and solution set, and how to read the question text.
3. 3Find where to startTake the free practice test to see which units you start from Foundation and which you can take straight in the Syllabus.

After this unit you simplify algebraic expressions and solve equations without arithmetic slips.

1. 1Numbers, powers and rootsKinds of numbers, the laws of exponents, and simplifying roots.
2. 2Algebraic expressions and factorisingExpanding brackets, the standard identities, and factorising.
3. 3Equations and systemsLinear and quadratic equations, and systems of two equations in two unknowns.

After this unit you work out areas and trigonometric ratios and handle points on the coordinate plane.

1. 1Plane shapes and areasTriangles, quadrilaterals and circles: their properties, perimeters and areas.
2. 2Trigonometric ratios in a right triangleSine, cosine and tangent, and the special angles.
3. 3The coordinate planeDistance between two points, the midpoint, and the slope of a line.

After this unit you handle sets and logical statements, and solve each kind of inequality and write its solution in interval notation.

1. 1Sets and set operationsMembership, subsets, intersection, union and complement, shown with Venn diagrams.
2. 2Necessary and sufficient conditions, quantifiers«If… then…» statements, necessary and sufficient conditions, and negating quantified statements.
3. 3Linear and quadratic inequalitiesSolving the inequality and showing the solution on the number line and in interval notation.
4. 4Rational and absolute-value inequalitiesSign tables, absolute-value cases, and the usual mistakes when multiplying by a negative.
5. 5The basic inequality and extreme valuesThe arithmetic–geometric mean inequality and using it to find maximum and minimum values.

After this unit you can study any function in the syllabus: its domain, range, properties and graph.

1. 1What a function is: domain and rangeThe definition, finding domain and range, and composite and inverse functions.
2. 2Properties: monotonicity, parity, periodicityIncreasing and decreasing functions, even and odd functions, and periodic functions.
3. 3Quadratic functionsThe vertex and axis of symmetry, maximum and minimum on an interval, and how the discriminant relates to the roots.
4. 4Exponential and logarithmic functionsLogarithm laws, the two graphs, and solving their equations and inequalities.
5. 5Power functions and graph transformationsCommon power functions, and shifting, stretching and reflecting graphs.
6. 6Trigonometric functions and their graphsRadians, the unit circle, and amplitude, period and phase shift in sin and cos graphs.
7. 7Trigonometric identities and solving trianglesSum, difference and double-angle identities, and the sine and cosine rules.
8. 8Arithmetic and geometric sequencesThe general term and the sum of terms, and how to tell the type of sequence from the question.
9. 9Introduction to derivativesWhat a derivative means, the basic rules, and using it to study monotonicity.

After this unit you solve problems on vectors, analytic geometry and solid geometry.

1. 1Vectors in the planeVector operations, the dot product, parallel and perpendicular vectors.
2. 2Lines and circlesThe equation of a line, the distance from a point to a line, the circle equation and how a line meets a circle.
3. 3Conic sectionsEllipse, hyperbola and parabola: their equations, foci and properties.
4. 4Solids: surface areas and volumesPrism, pyramid, cylinder, cone and sphere.
5. 5Lines and planes in spaceParallel and perpendicular lines and planes in space, and the angles between them.
6. 6Complex numbersAlgebraic form, basic operations, the conjugate and the modulus.

After this unit you count cases, compute probabilities and draw statistical measures from data.

1. 1Counting, permutations and combinationsWhen to add and when to multiply, and the difference between permutations and combinations.
2. 2The binomial theoremThe general term of the expansion and its coefficients.
3. 3Probability and eventsClassical probability, mutually exclusive and complementary events.
4. 4Conditional probability and independent eventsWhen two events are independent, and how to compute conditional probability.
5. 5Statistics and reading dataMean, median, mode and variance, and reading tables and histograms.

After this unit you spread your time across the paper and rule out wrong options quickly.

1. 1Reading a maths question in English, fastThe words that flip a question's meaning, such as not, except and at least, and how to catch them on the first reading.
2. 2Managing time on the paperA pace of about 75 seconds a question, based on the official paper format, and when to leave a question and come back.
3. 3Ruling out options and quick checksEstimating, plugging in the options, and checking units and signs before you commit to an answer.

After this unit you move between Syllabus units within one set without losing your pace.

1. 1Mixed set: sets and functionsVaried questions from the first two units at the official pace.
2. 2Mixed set: geometry and probabilityVaried questions from units three and four at the official pace.
3. 3Mixed set: every unitQuestions from all four units in random order, as on the paper.

After this unit you know your strong and weak points in every unit before your test date.

1. 1First full practice testA full paper in the official format, then a unit-by-unit reading of your result.
2. 2Your mistake logGo back to every question you missed and name the cause: an idea, a calculation, the reading, or time.
3. 3Final reviewA plan for the last days before the test, built from your «To review» list.
4. 4Before test dayWhat to check before you start. The test's rules and instructions are on csca.cn and on your admission ticket.