CSCA-Mathematik: Konzepte und Formeln
Jedes Konzept des Lehrplans mit seinen Formeln — und was in den echten Prüfungen tatsächlich gefragt wurde.
Die CSCA-Prüfung wird auf Chinesisch oder Englisch geschrieben — die Kandidaten wählen selbst. Konzepte und Formeln stehen hier deshalb in diesen beiden Sprachen; diese Seite zeigt die englische Fassung.
Mengen
Algebra
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 Prüfungsaufgaben · 5 TermineSolving Inequalities
Solving quadratic and fractional inequalities through equivalence transformations, and comparing values via inequality properties.
15 Prüfungsaufgaben · 5 TermineArithmetic 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 Prüfungsaufgaben · 5 TermineGeometric Sequences
General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.
10 Prüfungsaufgaben · 5 Termine
Trigonometrie
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 Prüfungsaufgaben · 5 TermineFundamental Trigonometric Identities
The Pythagorean and quotient identities drive simplification and knowing-one-find-the-others problems, together with exact values of special angles.
14 Prüfungsaufgaben · 5 TermineDouble-Angle Formulas
Double-angle formulas for sine, cosine and tangent; the three equivalent forms of cos 2α do most of the simplification work.
5 Prüfungsaufgaben · 5 TermineHalf-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 Prüfungsaufgaben · 5 TermineTangent Function Graph
Use the period, vertical asymptotes and increasing branches of the tangent function to identify and interpret its graph.
4 Prüfungsaufgaben · 4 Termine
Komplexe Zahlen
Funktionen
Exponents and Exponential Functions
Laws of rational exponents, monotonicity of exponential functions, and using monotonicity to compare powers.
6 Prüfungsaufgaben · 5 TermineLogarithms and Logarithmic Functions
Logarithm laws, the change-of-base formula and logarithmic domains, with monotonicity used to compare logarithmic values.
6 Prüfungsaufgaben · 5 TermineFunction 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 Prüfungsaufgaben · 5 TermineFunction Monotonicity
The definition of monotonicity and reading monotonic intervals of standard functions such as power and quadratic functions.
4 Prüfungsaufgaben · 4 TermineFunction Domains
Read the domain from the expression: non-zero denominators, non-negative radicands, positive logarithm arguments — intersect all constraints.
7 Prüfungsaufgaben · 5 TermineInverse Functions
Swap the input and output, solve for the new function, and check how the original domain and range exchange roles.
5 Prüfungsaufgaben · 5 Termine
Statistik und Wahrscheinlichkeit
Geometrie
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 Prüfungsaufgaben · 2 TermineQuadrants of the Coordinate Plane
Determine a point’s quadrant from the signs of its coordinates; points on an axis lie in no quadrant.
8 Prüfungsaufgaben · 5 TermineEquations of Lines
Relate inclination angle to slope, form line equations, then find intersections and distances between points.
24 Prüfungsaufgaben · 5 TermineEquations of Circles
Standard and general forms of the circle equation, reading centre and radius from each, and relative positions of two circles.
10 Prüfungsaufgaben · 5 TermineConic Sections: Basic Quantities
Standard equations of the ellipse, hyperbola and parabola, and converting between a, b, c, foci, directrix, asymptotes and eccentricity.
12 Prüfungsaufgaben · 5 TermineSpace 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.
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