Ключевые понятия и формулы: Математика CSCA
Все понятия программы вместе с формулами — и то, что на самом деле спрашивали на реальных экзаменах.
Экзамен CSCA сдаётся на китайском или английском языке — абитуриент выбирает сам. Поэтому понятия и формулы здесь даны на этих двух языках; на этой странице показан английский вариант.
Множества
Алгебра
Quadratic Functions and Equations
The parabola of a quadratic function, the roots of a quadratic equation and root–coefficient relations; the discriminant links the equation, function and inequality views.
5 заданий с экзаменов · 5 сессийSolving Inequalities
Solving quadratic and fractional inequalities through equivalence transformations, and comparing values via inequality properties.
15 заданий с экзаменов · 5 сессийArithmetic Sequences
General term, partial sums and the arithmetic mean of an arithmetic sequence, plus the index-sum property: two terms whose indices sum to the same value have the same sum.
14 заданий с экзаменов · 5 сессийGeometric Sequences
General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.
10 заданий с экзаменов · 5 сессий
Тригонометрия
Trigonometric Induction Formulas
Reduce any angle to an acute one: whether the function name changes depends on the multiple of π/2, and the sign follows the quadrant of the original angle.
7 заданий с экзаменов · 5 сессийFundamental Trigonometric Identities
The Pythagorean and quotient identities drive simplification and knowing-one-find-the-others problems, together with exact values of special angles.
14 заданий с экзаменов · 5 сессийDouble-Angle Formulas
Double-angle formulas for sine, cosine and tangent; the three equivalent forms of cos 2α do most of the simplification work.
5 заданий с экзаменов · 5 сессийHalf-Angle Formulas
Use the squared half-angle identities to find sine or cosine, then choose the sign from the quadrant of the half-angle.
9 заданий с экзаменов · 5 сессийTangent Function Graph
Use the period, vertical asymptotes and increasing branches of the tangent function to identify and interpret its graph.
4 задания с экзаменов · 4 сессии
Комплексные числа
Функции
Exponents and Exponential Functions
Laws of rational exponents, monotonicity of exponential functions, and using monotonicity to compare powers.
6 заданий с экзаменов · 5 сессийLogarithms and Logarithmic Functions
Logarithm laws, the change-of-base formula and logarithmic domains, with monotonicity used to compare logarithmic values.
6 заданий с экзаменов · 5 сессийFunction Parity
Definition and tests for even/odd functions: check the domain is symmetric about the origin first, then compare f(−x) with f(x).
6 заданий с экзаменов · 5 сессийFunction Monotonicity
The definition of monotonicity and reading monotonic intervals of standard functions such as power and quadratic functions.
4 задания с экзаменов · 4 сессииFunction Domains
Read the domain from the expression: non-zero denominators, non-negative radicands, positive logarithm arguments — intersect all constraints.
7 заданий с экзаменов · 5 сессийInverse Functions
Swap the input and output, solve for the new function, and check how the original domain and range exchange roles.
5 заданий с экзаменов · 5 сессий
Статистика и вероятность
Геометрия
Vectors and the Dot Product
Vector addition/subtraction rules and the dot product in definition and coordinate form, used for magnitudes and angles; the coordinate form extends to space vectors.
2 задания с экзаменов · 2 сессииQuadrants of the Coordinate Plane
Determine a point’s quadrant from the signs of its coordinates; points on an axis lie in no quadrant.
8 заданий с экзаменов · 5 сессийEquations of Lines
Relate inclination angle to slope, form line equations, then find intersections and distances between points.
24 задания с экзаменов · 5 сессийEquations of Circles
Standard and general forms of the circle equation, reading centre and radius from each, and relative positions of two circles.
10 заданий с экзаменов · 5 сессийConic Sections: Basic Quantities
Standard equations of the ellipse, hyperbola and parabola, and converting between a, b, c, foci, directrix, asymptotes and eccentricity.
12 заданий с экзаменов · 5 сессийSpace Rectangular Coordinates
Coordinates of points reflected in the axes, coordinate planes and origin (keep the coordinates of what you reflect in), plus the space distance formula.
На экзаменах пока не встречалось