CSCA 수학 핵심 개념과 공식
시험 범위의 모든 개념과 그 공식 — 그리고 실제 기출에서 무엇이 나왔는지.
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집합
대수
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.
기출 5문항 · 5회Solving Inequalities
Solving quadratic and fractional inequalities through equivalence transformations, and comparing values via inequality properties.
기출 15문항 · 5회Arithmetic 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.
기출 14문항 · 5회Geometric Sequences
General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.
기출 10문항 · 5회
삼각함수
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.
기출 7문항 · 5회Fundamental Trigonometric Identities
The Pythagorean and quotient identities drive simplification and knowing-one-find-the-others problems, together with exact values of special angles.
기출 14문항 · 5회Double-Angle Formulas
Double-angle formulas for sine, cosine and tangent; the three equivalent forms of cos 2α do most of the simplification work.
기출 5문항 · 5회Half-Angle Formulas
Use the squared half-angle identities to find sine or cosine, then choose the sign from the quadrant of the half-angle.
기출 9문항 · 5회Tangent Function Graph
Use the period, vertical asymptotes and increasing branches of the tangent function to identify and interpret its graph.
기출 4문항 · 4회
복소수
함수
Exponents and Exponential Functions
Laws of rational exponents, monotonicity of exponential functions, and using monotonicity to compare powers.
기출 6문항 · 5회Logarithms and Logarithmic Functions
Logarithm laws, the change-of-base formula and logarithmic domains, with monotonicity used to compare logarithmic values.
기출 6문항 · 5회Function Parity
Definition and tests for even/odd functions: check the domain is symmetric about the origin first, then compare f(−x) with f(x).
기출 6문항 · 5회Function Monotonicity
The definition of monotonicity and reading monotonic intervals of standard functions such as power and quadratic functions.
기출 4문항 · 4회Function Domains
Read the domain from the expression: non-zero denominators, non-negative radicands, positive logarithm arguments — intersect all constraints.
기출 7문항 · 5회Inverse Functions
Swap the input and output, solve for the new function, and check how the original domain and range exchange roles.
기출 5문항 · 5회
통계와 확률
기하
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.
기출 2문항 · 2회Quadrants of the Coordinate Plane
Determine a point’s quadrant from the signs of its coordinates; points on an axis lie in no quadrant.
기출 8문항 · 5회Equations of Lines
Relate inclination angle to slope, form line equations, then find intersections and distances between points.
기출 24문항 · 5회Equations of Circles
Standard and general forms of the circle equation, reading centre and radius from each, and relative positions of two circles.
기출 10문항 · 5회Conic Sections: Basic Quantities
Standard equations of the ellipse, hyperbola and parabola, and converting between a, b, c, foci, directrix, asymptotes and eccentricity.
기출 12문항 · 5회Space 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.
기출 미출제