How Much Is Tested in This Part
The first module in the official syllabus is "Sets and Inequalities." It covers the definition, operations and representation of sets, along with the basic properties and solution methods of inequalities (quadratic inequalities in one variable, rational inequalities and so on).
We counted 7 past papers, totaling 333 questions (each question is counted once, under the knowledge point its main key point tests): this module has 35 questions, about 11%.
- Sets: 12 questions: operations between sets 7 questions (tested in all 7 papers), relationships between sets 3 questions (3 papers), definition of sets 2 questions (2 papers)
- Inequalities: 23 questions: solving quadratic inequalities in one variable 10 questions (tested in all 7 papers), solving rational inequalities 7 questions (6 papers), properties of inequalities 6 questions (6 papers)
Sets: What You Need
For the sets part, you need to know intersection (A∩B), union (A∪B) and complement.
For example: A = {1, 2, 3}, B = {2, 3, 4}, so A∩B = {2, 3} and A∪B = {1, 2, 3, 4}.
Distinguish subsets from proper subsets: a set with n elements has 2ⁿ subsets.
When you tackle set questions, plot the solution set of the inequality on a number line first, then read off the intersection or union; this is the least error-prone method.
Quadratic Inequalities in One Variable
First solve the corresponding equation, then check the direction in which the parabola opens.
For example: for x² − 5x + 6 < 0, the two roots of the equation are 2 and 3, the parabola opens upward, and the solution set is 2 < x < 3.
When the coefficient of the quadratic term is negative, first multiply both sides by −1 and reverse the inequality sign.
Fractional Inequalities
Rational inequalities must be converted into polynomial inequalities, but the denominator cannot be 0.
For example: the solution set of (x − 1)/(x + 2) ≥ 0 is x < −2 or x ≥ 1 (x = −2 is excluded).
Properties of Inequalities
When you multiply or divide both sides of an inequality by the same negative number, you must reverse the direction of the inequality sign.
a > b does not necessarily imply a² > b²; for example, a = 1, b = −2.
Why Secure These Points
Of these 35 questions, 17 come from two knowledge points tested in all 7 papers (set operations and quadratic inequalities in one variable), and the question types are fixed.
These methods are also the foundation for domain and range questions on functions.
Next Steps
First take the 15-minute diagnostic, then practice by knowledge point in the Learning Center.