Year 2 · 16 years old
Year 2 — Differential Calculus and Probability
Here the student formally meets the derivative. Alongside, they gain descriptive statistics and probability — the foundations for everything that follows in a Master's in Engineering, Economics, or Finance.
JP Math II + Math B · DE Klasse 11 LK · SG JC 1 (H2 Math início)
Schedule by term
Click a term to see Classes and Lessons (each Lesson opens the content). Lessons grouped into Classes didactic groups (3-5 lessons per Class). Or use the tabs below to browse by subject.
Term 5 — Limits and Continuity
open →Formalization of the limit concept, light ε-δ, continuity.
10 lessons · ~32h of study
- ~6hClass A — Formal limit and properties(2 lessons)
- ~6hClass B — Continuity and one-sided limits(2 lessons)
- ~12hClass C — Fundamental limits and IVT(4 lessons)
- ~6hClass D — Limit of a sequence + synthesis(2 lessons)
Term 6 — Derivatives: Concept and Rules
open →Definition via limit, rules (chain, product, quotient), notable derivatives.
10 lessons · ~32h of study
- ~6hClass A — Definition of the derivative and basic rules(2 lessons)
- ~6hClass B — Chain rule and implicit differentiation(2 lessons)
- ~9hClass C — Higher order, inverse and linear approximation(3 lessons)
- ~9hClass D — Related rates + smoothness(3 lessons)
Term 7 — Applications of the Derivative
open →Optimization, related rates, curve sketching, introductory Taylor.
10 lessons · ~32h of study
- ~9hClass A — Maxima, minima and optimization(3 lessons)
- ~9hClass B — L'Hôpital and Taylor(3 lessons)
- ~6hClass C — Marginal analysis and kinematics(2 lessons)
- ~6hClass D — Newton-Raphson + synthesis(2 lessons)
Term 8 — Descriptive Statistics and Probability
open →Distributions, normal, intuitive Central Limit Theorem.
10 lessons · ~32h of study
- ~9hClass A — Descriptive statistics(3 lessons)
- ~6hClass B — Random variable and binomial distribution(2 lessons)
- ~6hClass C — Normal distribution and the Central Limit Theorem(2 lessons)
- ~9hClass D — Correlation, regression, Bayes + synthesis(3 lessons)
Lessons organized by subject
Limits
Light ε-δ, continuity — formalization of "what does it approach".
- Lesson 41publishedFormal ε-δ definition, intuition
- Lesson 42publishedSum, product, quotient, composition of limits
- Lesson 43publishedDefinition by ε-δ, types of discontinuity
- Lesson 44publishedlim from the left and right, piecewise functions
- Lesson 45publishedlim (sin x)/x = 1, lim (1+1/n)ⁿ = e
- Lesson 46publishedIntermediate Value Theorem, bisection, applications
- Lesson 47publishedVertical, horizontal, oblique asymptotes
- Lesson 48publishedlim sin x, cos x, with substitution
- Lesson 49publishedConvergence, monotone bounded sequences
- Lesson 50publishedSynthesis: 50 mixed limit problems
Derivatives
Definition via limit, rules (chain, product, quotient), notable derivatives.
- Lesson 51publishedf'(a) = lim (f(a+h)-f(a))/h, tangent line
- Lesson 52published(f+g)', (fg)', (f/g)', power rule
- Lesson 53published(f∘g)' = f'(g)·g'
- Lesson 54publishedF(x,y)=0, dy/dx
- Lesson 55publishedf''(x), f^(n)
- Lesson 56published(f⁻¹)'(y) = 1/f'(x)
- Lesson 57publishedL(x) = f(a) + f'(a)(x-a), differentials
- Lesson 58publishedSliding ladder, volume of expanding sphere, etc.
- Lesson 59publishedContinuity, corners, vertical tangents, cusps
- Lesson 60publishedSynthesis: 60 mixed derivative problems
Applications of the Derivative
Optimization, related rates, curve sketching, introductory Taylor polynomial.
- Lesson 61publishedCritical points, 1st and 2nd derivative tests
- Lesson 62publishedOptimal box, minimum cost, applications
- Lesson 63publishedIncrease/decrease intervals, concavity, inflection
- Lesson 64published0/0, ∞/∞ indeterminate forms
- Lesson 65publishedPₙ(x) = Σ f^(k)(a)(x-a)ᵏ/k!, applications
- Lesson 66publishedf'', inflection points, sketching graphs
- Lesson 67publishedMarginal cost, elasticity, applications
- Lesson 68publishedv(t), a(t), motion problems
- Lesson 69publishedIterative method for f(x) = 0
- Lesson 70publishedSynthesis: 50 mixed derivative-application problems
Descriptive Statistics
Summary statistics, distributions, normal, intuitive Central Limit Theorem.
- Lesson 71publishedMean, median, mode — when each is appropriate
- Lesson 72publishedσ², σ, dispersion, comparison of datasets
- Lesson 73publishedQ1, Q2, Q3, IQR, boxplots
- Lesson 74publishedP(X=x), E[X], Var(X)
- Lesson 75publishedB(n,p), success/failure trials
- Lesson 76publishedN(μ,σ²), z-scores, applications
- Lesson 77publishedDistribution of sample means, intuitive proof
- Lesson 78publishedPearson r, interpretation, caveats
- Lesson 79publishedP(A|B), Bayes' theorem, applications
- Lesson 80publishedSynthesis: 60 mixed statistics + probability problems