Saarland Abitur Technik-Mathematik cheat sheet

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.

Chain rule: never drop the inner derivative g'(x).

Integration by parts: choose u so du is simpler than u.

Change limits immediately when substituting in a definite integral.

Improper integrals require an explicit limit, not direct substitution.

Implicit differentiation collects dy/dx terms after differentiating both sides.

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|.

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.

Equilibrium of a particle: the sums of resolved components in two perpendicular directions are zero.

Lami's theorem applies only to exactly three concurrent forces.

On a weight-only incline at impending downward slip, tan θ = μ_s; additional applied forces change the relation.

A pulling force at angle φ reduces the normal reaction: R = mg − P sin φ.

Choose axes along and perpendicular to the surface to minimise unknowns.

Moment = force × perpendicular distance, with clockwise or anticlockwise sense stated.

Rigid body equilibrium needs both zero resultant force and zero total moment.

Take moments about a point where an unknown acts to eliminate it.

A couple has moment Fd, identical about any point.

Uniform rods carry their weight at the midpoint; toppling occurs when the centre of mass passes outside the base.