The Weight of Functions in CSCA Math
The official CSCA Mathematics Examination Syllabus (2025 Edition) states that the math exam lasts 60 minutes, contains 48 single-choice questions, and is worth 100 points. The paper is divided into four modules: Sets and Inequalities, Functions, Geometry and Algebra, and Probability and Statistics.
In the syllabus, the "functions" module contains four items: the concepts and properties of functions (domain, range, monotonicity, parity, and so on); basic elementary functions (power functions, exponential functions, logarithmic functions, and trigonometric functions); sequences; and basics of derivatives and calculus.
We counted 7 past papers, with 333 questions in total (each question was assigned to a single knowledge point according to its main tested point): the functions module had 198 questions, accounting for 59%. In other words, functions are the largest of the four modules and deserve priority.
This article covers only the first chapter within the functions module, "Function Basics": 8 knowledge points, with 80 questions across the 7 past papers, about 24% of all 333 questions. Trigonometric functions and sequences are covered in separate articles.
Question Counts for the 8 Knowledge Points
Start with this chapter's "weight table," then decide what to learn first:
- Cartesian coordinate plane: 23 questions, tested in all 7 papers
- Logarithms and logarithmic functions: 16 questions, tested in all 7 papers
- Concept of functions: 12 questions, tested in all 7 papers
- Inverse functions: 9 questions, tested in all 7 papers
- Parity of functions: 6 questions, tested in 6 of the 7 papers
- Monotonicity of functions: 6 questions, tested in 5 of the 7 papers
- Power functions: 5 questions, tested in 4 of the 7 papers
- Exponential functions: 3 questions, tested in 3 of the 7 papers
The first 5 knowledge points appear in every paper or nearly every paper, totaling 66 questions, and are the focus of this chapter. Power functions and exponential functions have fewer questions and appear less consistently; even so, exponential functions are the foundation for learning logarithms, so they cannot be skipped.
Suggested Study Order (Writing Suggestion, Not an Official Rule)
The order below follows the principle of "lay the foundation first, then build upward." It is not an official rule, and you can adjust it to your own situation:
- Concept of functions: begin by understanding the domain, range, and correspondence, and be able to find the domain of simple functions. All later questions build on this concept.
- Cartesian coordinate plane: coordinates of points, the distance between two points, and the midpoint. Later graph questions rely on it, and it also has the most questions (23).
- Learn exponents and logarithms together: logarithms are the inverse operations of exponents, so learning them together is easier than learning them separately. Memorize the logarithm rules:
- log_a(MN) = log_a M + log_a N - log_a(M/N) = log_a M − log_a N - log_a(M^n) = n·log_a M - Common result: lg 2 + lg 5 = 1
- Inverse functions: be able to find inverse functions, and know that the graphs of a function and its inverse are symmetric about the line y = x.
- Monotonicity and parity: f(−x) = f(x) defines an even function, and f(−x) = −f(x) defines an odd function; in addition, the domains of both odd and even functions must be symmetric about the origin.
- Power functions: recognize the graphs of y = x, y = x², y = x³, y = x^(1/2), and y = 1/x, and know roughly what they look like and which special points they pass through.
If time is very tight, prioritize making steps 1 to 3 solid: the concept of functions, the Cartesian coordinate plane, and logarithms and exponents total 54 questions, more than two-thirds of the 80 questions in this chapter.
Exam-Room Tips
- Calculators are not permitted in the CSCA, so logarithmic and exponential calculations must be done by hand. Do not rely on a calculator during practice.
- When finding the domain, do not overlook the restrictions: the denominator cannot be 0, the radicand under an even root must be greater than or equal to 0, and the argument of a logarithm must be greater than 0.
- The syllabus also lists "basics of derivatives and calculus." Our knowledge-point count does not include this item separately; when reviewing, simply make sure you understand the definition and geometric meaning of the derivative as set out in the syllabus.
Next Steps
At CSCA.PRO, you can first take a 15-minute diagnostic to see how well you have mastered the functions section, then go to the Learning Center to study and practice by knowledge point.