CSCA Mathematics Concepts & Formulas
Every concept on the syllabus with the formulas it uses — and what the real exams have actually asked.
Sets
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 real-exam questions · 5 sittingsSolving Inequalities
Solving quadratic and fractional inequalities through equivalence transformations, and comparing values via inequality properties.
15 real-exam questions · 5 sittingsArithmetic 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 real-exam questions · 5 sittingsGeometric Sequences
General term, partial sums (mind the q = 1 case) and the geometric mean of a geometric sequence.
10 real-exam questions · 5 sittings
Trigonometry
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 real-exam questions · 5 sittingsFundamental Trigonometric Identities
The Pythagorean and quotient identities drive simplification and knowing-one-find-the-others problems, together with exact values of special angles.
14 real-exam questions · 5 sittingsDouble-Angle Formulas
Double-angle formulas for sine, cosine and tangent; the three equivalent forms of cos 2α do most of the simplification work.
5 real-exam questions · 5 sittingsHalf-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 real-exam questions · 5 sittingsTangent Function Graph
Use the period, vertical asymptotes and increasing branches of the tangent function to identify and interpret its graph.
4 real-exam questions · 4 sittings
Complex numbers
Functions
Exponents and Exponential Functions
Laws of rational exponents, monotonicity of exponential functions, and using monotonicity to compare powers.
6 real-exam questions · 5 sittingsLogarithms and Logarithmic Functions
Logarithm laws, the change-of-base formula and logarithmic domains, with monotonicity used to compare logarithmic values.
6 real-exam questions · 5 sittingsFunction 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 real-exam questions · 5 sittingsFunction Monotonicity
The definition of monotonicity and reading monotonic intervals of standard functions such as power and quadratic functions.
4 real-exam questions · 4 sittingsFunction Domains
Read the domain from the expression: non-zero denominators, non-negative radicands, positive logarithm arguments — intersect all constraints.
7 real-exam questions · 5 sittingsInverse Functions
Swap the input and output, solve for the new function, and check how the original domain and range exchange roles.
5 real-exam questions · 5 sittings
Statistics & probability
Geometry
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 real-exam questions · 2 sittingsQuadrants of the Coordinate Plane
Determine a point’s quadrant from the signs of its coordinates; points on an axis lie in no quadrant.
8 real-exam questions · 5 sittingsEquations of Lines
Relate inclination angle to slope, form line equations, then find intersections and distances between points.
24 real-exam questions · 5 sittingsEquations of Circles
Standard and general forms of the circle equation, reading centre and radius from each, and relative positions of two circles.
10 real-exam questions · 5 sittingsConic Sections: Basic Quantities
Standard equations of the ellipse, hyperbola and parabola, and converting between a, b, c, foci, directrix, asymptotes and eccentricity.
12 real-exam questions · 5 sittingsSpace 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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