Přijímačky VŠE Matematika cheat sheet

Match model type to the pattern: constant rate, constant percent, or periodic.

Exponential growth uses b = 1 + r; decay uses b = 1 − r.

The quadratic extremum sits at x = −b/(2a).

Use the constraint to reduce the objective to a single variable.

Track units through every step and report answers in context.

Round only at the end to avoid propagated error.

State domain restrictions before simplifying; cancelled factors still exclude values.

Composition f(g(x)) is evaluated inside-out and is generally not commutative.

Inverses require one-to-one functions; domain and range swap.

Horizontal transformations act opposite to the sign or factor shown.

Log laws convert sums to products, enabling solution of log equations.

Always check candidate solutions against original domain restrictions.

AP sum: n/2 × (first + last) or n/2(2a + (n − 1)d).

GP sum to infinity exists only for |r| < 1 and equals a/(1 − r).

The general binomial term C(n, r)a^(n−r)b^r gives any coefficient directly.

Count the number of terms carefully when the index starts at zero.

A negative common ratio alternates signs, so check the parity of the power.

Similarity scales lengths by k, areas by k², volumes by k³.

Inscribed angle equals half the intercepted central arc.

Sine law requires a known side–opposite-angle pair; watch the ambiguous case.

Cosine law handles SAS and SSS configurations.

Arc length and sector area formulas require radians.

Pythagorean identity sin²θ + cos²θ = 1 underpins most simplifications.

i² = −1; division uses multiplication by the conjugate.

|z| = √(a² + b²), and the argument must be placed in the correct quadrant.

Modulus–argument form is re^(iθ); multiplication adds arguments.

Real-coefficient polynomials have non-real roots in conjugate pairs.

|z − z₀| = r is a circle centred at z₀.

Consistency requires rank A = rank [A|b]; uniqueness also needs full column rank.

det A = 0 means no unique solution, not necessarily no solution.

Trace = sum of eigenvalues; determinant = product of eigenvalues.

a×b is perpendicular to both vectors; its magnitude is the parallelogram area.

Distance from point to plane: |n·P − d| / |n|.

An implication and its contrapositive are equivalent; the converse is not.

Negating a quantified statement flips the quantifier and negates the predicate.

Induction needs a base case, a stated hypothesis, and the step.

Inclusion–exclusion corrects for double counting.

Pigeonhole principle forces a collision when items exceed categories.

Sum of vertex degrees equals twice the edge count.