Gaokao Mathematics study guide
Gaokao Mathematics · Work through your exam, one topic at a time.
The Gaokao mathematics paper is the mathematics component of China's National College Entrance Examination, the main route into undergraduate study for senior secondary graduates. Candidates sit it at the end of three years of senior high school, and the score enters the composite that provincial admission offices use when placing students into universities and programmes. The Gaokao Mathematics study guide has 10 sections and about 2,331 words.
01Sets and Common Logical Connectives
A set is fixed by its elements; master union, intersection, set difference, complement relative to a universal set, subsets, and cardinality for finite sets, including A∪B = A + B − A∩B . Remember that ∅⊆A and A⊆A always hold, and distinguish an element x∈A from a subset {x}⊆A.
249 words, about 1 min02Functions and Derivatives
A function is a rule with a domain; before differentiating or solving, state the domain forced by denominators, even roots, and logarithms. Know composition, inverse functions (domain and range swap), symmetry, periodicity, and transformations of graphs.
269 words, about 1 min03Trigonometric Functions and Triangle Solving
Master the unit circle, radian measure, reference angles, and the graphs of sine, cosine, and tangent, including amplitude, period, phase shift, and asymptotes. Know the Pythagorean identities, sum and double-angle formulas, and the transformations used to reduce expressions to a single trigonometric function.
280 words, about 1 min04Sequences
Distinguish arithmetic sequences (constant difference) from geometric sequences (constant ratio), and know the general term, the sum formulas, and the behavior of each. For arithmetic, aₙ=a₁+(n−1)d and Sₙ=n(a₁+aₙ)/2.
214 words, about 1 min05Inequalities
Solve inequalities by transforming them into equivalent forms, tracking the domain and the direction of the inequality. For quadratics, factor or use a sign chart; for rational inequalities, bring everything to one side and use critical points, never multiply blindly by an expression whose sign is unknown.
249 words, about 1 min06Plane Vectors and Complex Numbers
A vector has magnitude and direction; in coordinates, addition and scalar multiplication are componentwise, while the dot product a·b= a b cos θ measures projection and detects perpendicularity. Know collinearity (b=λa), the projection formula, and the geometric meaning of the dot product's sign.
201 words, about 1 min07Solid Geometry and Space Vectors
Know the axioms and positional relations of lines and planes: parallel, intersecting, skew, perpendicular, and the theorems that justify them. In space coordinates, a plane has equation ax+by+cz+d=0 with normal vector (a,b,c); a line is described by a point and direction.
248 words, about 1 min08Analytic Geometry and Conic Sections
Master the line forms and the standard equations of circles, ellipses, hyperbolas, and parabolas, including centers, vertices, foci, directrices, asymptotes, and eccentricity. For an ellipse x²/a²+y²/b²=1 with a b 0, c²=a²−b² and e=c/a; for a hyperbola x²/a²−y²/b²=1, c²=a²+b² and the asymptotes are y=±(b/a)x.
215 words, about 1 min09Probability and Statistics
Know classical probability, the addition and multiplication rules, conditional probability, independence, and the complement rule. For a random variable, compute the distribution, expectation, and variance; for binomial settings, use C(n,k)p^k(1−p)^{n−k}.
199 words, under 1 min10Counting Principles and Binomial Theorem
Use the addition principle for mutually exclusive cases and the multiplication principle for successive choices. Distinguish permutations, where order matters, from combinations, where it does not; the binomial coefficient C(n,k) counts k-element subsets.
207 words, about 1 min