IB Mathematics: Analysis and Approaches HL cheat sheet

Arithmetic and geometric formulas differ mainly by d versus r and by the n − 1 exponent.

S∞ exists only for a geometric series with |r| < 1.

Change of base converts any log to ln or log10 for calculator use.

In binomial expansion, the general term contains C(n,r)a^(n−r)b^r.

Financial growth and depreciation are geometric models with multiplier (1 ± r).

Domain restrictions come from denominators, even roots, and log arguments.

Composite domain requires both g(x) defined and g(x) in the domain of f.

An inverse exists only on a one-to-one domain; swap domain and range.

Transformations: a affects vertical scale, b horizontal scale, h horizontal shift, k vertical shift.

Complete the square to read a quadratic vertex and range.

Choose cosine rule when the angle is included between two known sides.

Sine rule can produce an ambiguous case when given SSA.

sin^2 θ + cos^2 θ = 1 and tan θ = sin θ/cos θ are core identities.

Dot product gives angle information; zero dot product means perpendicular.

Check calculator mode and interval endpoints for trig equations.

P(A|B) uses P(B) in the denominator, not P(A).

Mutually exclusive and independent are different conditions.

Binomial requires fixed n, two outcomes, constant p, independent trials.

Normal calculations use z = (x − μ)/σ and calculator area functions.

Correlation measures linear association; it does not prove causation.

f'(a) is the tangent slope; normal slope is −1/f'(a).

Stationary points require f'(x) = 0, then a sign or second-derivative test.

Chain rule is needed for composite functions.

Indefinite integrals need +C; definite integrals give signed area.

Area below the x-axis must be handled by splitting or taking absolute value as required.