Concepts et formules de Mathématiques CSCA
Chaque concept au programme avec ses formules — et ce que les annales ont réellement demandé.
L'épreuve CSCA se passe en chinois ou en anglais, au choix du candidat. Les concepts et formules sont donc donnés dans ces deux langues ; cette page affiche la version anglaise.
Ensembles
Algèbre
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 questions d'annales · 5 sessionsSolving Inequalities
Solving quadratic and fractional inequalities through equivalence transformations, and comparing values via inequality properties.
15 questions d'annales · 5 sessionsArithmetic 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 questions d'annales · 5 sessionsGeometric Sequences
General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.
10 questions d'annales · 5 sessions
Trigonométrie
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 questions d'annales · 5 sessionsFundamental Trigonometric Identities
The Pythagorean and quotient identities drive simplification and knowing-one-find-the-others problems, together with exact values of special angles.
14 questions d'annales · 5 sessionsDouble-Angle Formulas
Double-angle formulas for sine, cosine and tangent; the three equivalent forms of cos 2α do most of the simplification work.
5 questions d'annales · 5 sessionsHalf-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 questions d'annales · 5 sessionsTangent Function Graph
Use the period, vertical asymptotes and increasing branches of the tangent function to identify and interpret its graph.
4 questions d'annales · 4 sessions
Nombres complexes
Fonctions
Exponents and Exponential Functions
Laws of rational exponents, monotonicity of exponential functions, and using monotonicity to compare powers.
6 questions d'annales · 5 sessionsLogarithms and Logarithmic Functions
Logarithm laws, the change-of-base formula and logarithmic domains, with monotonicity used to compare logarithmic values.
6 questions d'annales · 5 sessionsFunction 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 questions d'annales · 5 sessionsFunction Monotonicity
The definition of monotonicity and reading monotonic intervals of standard functions such as power and quadratic functions.
4 questions d'annales · 4 sessionsFunction Domains
Read the domain from the expression: non-zero denominators, non-negative radicands, positive logarithm arguments — intersect all constraints.
7 questions d'annales · 5 sessionsInverse Functions
Swap the input and output, solve for the new function, and check how the original domain and range exchange roles.
5 questions d'annales · 5 sessions
Statistiques et probabilités
Géométrie
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 questions d'annales · 2 sessionsQuadrants of the Coordinate Plane
Determine a point’s quadrant from the signs of its coordinates; points on an axis lie in no quadrant.
8 questions d'annales · 5 sessionsEquations of Lines
Relate inclination angle to slope, form line equations, then find intersections and distances between points.
24 questions d'annales · 5 sessionsEquations of Circles
Standard and general forms of the circle equation, reading centre and radius from each, and relative positions of two circles.
10 questions d'annales · 5 sessionsConic Sections: Basic Quantities
Standard equations of the ellipse, hyperbola and parabola, and converting between a, b, c, foci, directrix, asymptotes and eccentricity.
12 questions d'annales · 5 sessionsSpace 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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