CSCA Math Syllabus 2026: Topics, Examples and Calculator Rules

What is in the CSCA math syllabus for 2026?

The CSCA math syllabus covers senior high school mathematics. Its purpose is to check that you have the foundation needed for first-year university courses in China. It is one paper inside the wider CSCA exam format, which also includes Physics, Chemistry and Professional Chinese for some programs. Here is the official outline, module by module.

• Sets and inequalities: the definition, operations and representation of sets; basic properties of inequalities; solving quadratic and rational inequalities
• Functions: domain, range, monotonicity (increasing and decreasing) and parity (odd and even); power, exponential, logarithmic and trigonometric functions; arithmetic and geometric sequences (general terms and sums); basics of derivatives
• Geometry and algebra: plane analytic geometry (lines, circles, ellipses, hyperbolas and parabolas); vectors; complex numbers; solid geometry using a space rectangular coordinate system
• Probability and statistics: classical probability; mean and variance; the normal distribution

A warning about older study guides: some list matrices, determinants, Boolean algebra, Karnaugh maps or number-base conversion as CSCA topics. None of these appear in the official module list. If your time is limited, spend it on the four modules above. The same applies to topic percentages. The official syllabus does not say how many questions come from each module, so treat any weighting chart as a guess. For the wider picture of subjects, dates and fees, see our CSCA exam 2026–27 guide.

Sets and inequalities: what does the CSCA test?

Sets and inequalities is the first module on the CSCA syllabus. The two topics are tested together because the answer to an inequality is usually written as a set or an interval. These are the skills to practice until they feel automatic:

• Reading set-builder notation, such as {x | x > 2}, and writing answers in interval notation
• Union, intersection and complement, including Venn diagram counting questions
• Subsets: a set with n elements has 2 to the power n subsets
• Properties of inequalities, especially that multiplying or dividing by a negative number reverses the sign
• Quadratic inequalities: find the roots, then use the shape of the parabola to choose the correct interval
• Rational inequalities: use a sign chart and always exclude values that make the denominator zero

Example 1: Let A = {x | x² − 4x + 3 < 0} and B = {x | x > 2}. Factor to get (x − 1)(x − 3) < 0, so A = (1, 3) and A ∩ B = (2, 3). Example 2: Solve (x − 1)/(x + 2) ≤ 0. The critical values are 1 and −2, so the solution is −2 < x ≤ 1. The value x = −2 is excluded because the denominator cannot be zero.

Functions, sequences and derivatives

Functions is the broadest CSCA math module. It joins the properties of functions, the standard function families, sequences and an introduction to derivatives. Make sure you can do each of these by hand:

• Find the domain and range, especially for logarithms, square roots and fractions
• Test parity: f is even if f(−x) = f(x), and odd if f(−x) = −f(x)
• Decide where a function increases or decreases
• Use exponent and logarithm laws, and sketch y = a to the power x and y = log base a of x
• Trigonometry: exact values at 0°, 30°, 45°, 60° and 90°, the main identities, and the period and shape of graphs like y = A sin(ωx + φ)
• Arithmetic sequences: aₙ = a₁ + (n − 1)d and the sum formula
• Geometric sequences: aₙ = a₁rⁿ⁻¹ and Sₙ = a₁(1 − rⁿ)/(1 − r)
• Derivatives: the power rule, the slope of a tangent line, and finding maximum and minimum values

Example 3: The domain of f(x) = log₂(x − 1) is x > 1. Example 4: f(x) = x³ − x is odd, because f(−x) = −x³ + x = −f(x). Example 5: A geometric sequence starts 2, 6, 18, 54. The sum of the first four terms is 2(3⁴ − 1)/(3 − 1) = 80. Example 6: For f(x) = x³ − 3x, f′(x) = 3x² − 3, which is zero at x = ±1, so f decreases on (−1, 1).

How much calculus should you study? The official wording is basics of derivatives. Focus on derivative rules and what they tell you about a graph. Integration is not listed as a separate topic, so give it a lower priority unless the current syllabus on csca.cn says otherwise.

Geometry and algebra: conics, vectors and complex numbers

This module is where students from some school systems find gaps. Conic sections, complex numbers and three-dimensional coordinates are not taught in every curriculum, so check each item against what you studied in school:

• Lines: slope, the forms of a line equation, parallel and perpendicular lines, and the distance from a point to a line
• Circles: standard form, completing the square, and whether a line cuts, touches or misses a circle
• Ellipses and hyperbolas: standard equations, a, b and c, foci, eccentricity, and the asymptotes of a hyperbola
• Parabolas: the focus and directrix from the standard equation
• Vectors: coordinates, magnitude, the dot product, the angle between vectors, and perpendicular vectors (dot product zero)
• Complex numbers: i² = −1, the four operations, the conjugate and the modulus
• Solid geometry with space coordinates: points in three dimensions, distances and vectors in space

Example 7: x² + y² − 4x + 6y − 3 = 0 becomes (x − 2)² + (y + 3)² = 16, a circle with center (2, −3) and radius 4. Example 8: For the ellipse x²/25 + y²/9 = 1, a = 5 and b = 3, so c = 4. The foci are (±4, 0) and the eccentricity is 4/5. Example 9: (1 + i)² = 2i, and |3 + 4i| = 5. Example 10: If a = (1, 2) and b = (3, −1), then a · b = 3 − 2 = 1.

Probability and statistics

The official list for this module is short: classical probability, mean and variance, and the normal distribution. Classical probability means counting equally likely outcomes, so you also need basic counting. For statistics, be able to calculate a mean, variance and standard deviation from a small data set. For the normal distribution, know that the curve is symmetric about the mean μ and that a larger σ means a wider, flatter curve.

Example 11: Two fair dice are rolled. Six of the 36 outcomes give a sum of 7, so the probability is 1/6. Example 12: The data 2, 4, 6, 8 has mean 5 and variance (9 + 1 + 1 + 9)/4 = 5. Example 13: If X follows a normal distribution with mean μ, then P(X > μ) = 0.5. Questions like these are quick to solve if you have learned the definitions well, so they are good places to save time. For ten more questions in exam style, with worked answers, try our CSCA math sample questions.

Does CSCA allow a calculator?

Plan to work without one. The published exam rules do not list a calculator among permitted items, and prep guides to the online test give the same advice. The official syllabus itself does not mention calculators, so read the candidate rules in your session notice to be sure. For the home-based online test, published guides describe a small whiteboard, or a blank sheet inside a clear plastic sleeve, instead of loose paper, and you erase it on camera at the end.

The good news is that the questions are written to be solved by hand. You will not need to calculate sin 37°. What you need is fast, accurate mental arithmetic. These habits save the most time:

• Memorize squares up to 20², powers of 2 up to 2¹⁰, and powers of 3 up to 3⁵
• Know the exact trigonometric values for 30°, 45° and 60° in degrees and radians
• Factor quadratics on sight instead of using the quadratic formula every time
• Estimate first, then check which answer choice fits, before doing long working
• Practice on a whiteboard if you plan to take the online test, so exam day feels normal

How should you study the CSCA math syllabus?

You can start step one today with free CSCA math practice questions. No sign-up is needed, so it takes only a few minutes to see which CSCA math topics need the most work. For fully worked examples before a timed set, read our original CSCA exam questions and answers.

If you want a structured path through the CSCA syllabus, our self-paced CSCA Mathematics lessons are organized into units and lessons, with a mini test at the end of each one.

Students who learn better with a teacher can join our teacher-led live CSCA classes. Every class is recorded, so you can replay the hard topics.

Mathematics is only one part of your plan. Physics or Chemistry may also be required, depending on your major, so check which CSCA subjects you need by major early.

Then pick a session that leaves time for a retake. Our CSCA exam dates and registration guide explains how the session months and registration windows work.

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