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Mathematics explained step by step, with worked examples, visual reasoning, and explanations that show how and why each concept works.

Dois símbolos vermelhos de porcentagem sobre blocos de madeira com setas para baixo, ligados por uma seta curva, ao lado de um carrinho de compras e sacolas.

Fractions & Percentages26/09/2026

Successive percentages: why do two 20% discounts not add up to 40%?

Learn why two successive 20% discounts equal 36%, with a changing calculation base, formula, and worked examples.

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Caderno com três quadros coloridos de equações do segundo grau, cálculos do delta e parábolas que cruzam, tocam ou não encontram o eixo x.

Algebra & Equations22/09/2026

Quadratic formula with zero or negative discriminant: solve and check each case

Learn to identify a, b, and c, calculate the discriminant, and solve three quadratic equations, including repeated roots and cases with no real solution.

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Plano cartesiano com reta vermelha e dois pontos azuis, fórmulas para calcular a e b, exemplos com frações e uma reta vertical.

Functions & Graphs22/09/2026

Affine function from two points: find the equation and check the graph

Learn to calculate a and b from two points, verify the equation on a graph, and recognize when a vertical line is not a function of x.

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Quadro-negro com “0,999... = 1” escrito a giz acima de uma mesa com livros, caderno e um símbolo de infinito.

Fundamentals & Operations13/09/2026

Does 0.999... Equal 1? Three Proofs and the Mistake of Treating It as an Approximation

Understand why 0.999... is exactly 1 through three proofs: algebra, 1/3, and a series/limit argument — and why there is no “last 9.”

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Bolo dividido em porções ao lado de blocos de madeira que mostram 3/4 dividido por 1/4 igual a 3, em uma mesa de estudo.

Fractions & Percentages13/09/2026

Why does dividing by a fraction mean multiplying by its reciprocal? Three ways to understand it

See why fraction division becomes multiplication by the reciprocal using groups, scaling, and algebra — all with the same example.

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Composição educativa sobre porcentagem reversa com R$ 100 como valor original, R$ 80 após desconto de 20% e R$ 120 após aumento de 20%, além de calculadora e anotações.

Fractions & Percentages13/09/2026

Reverse percentages: how to find the original value after a discount or increase

Learn how to recover the original value from a known final value by using the correct multiplier for discounts and increases, with worked examples and checks.

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Mesa de estudo com caderno mostrando uma regra de três composta, cálculo com x igual a 8, blocos com setas, livros de matemática, calculadora e caneta.

Problems & Reasoning12/09/2026

Compound proportion with inverse quantities: decide by logic, not memorized arrows

Learn to identify direct and inverse relationships logically, solve two compound proportion problems, and check results with units and order of magnitude.

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Mesa de estudo com uma árvore de probabilidades desenhada em papel, marcadores coloridos sobre os ramos, calculadora e quadro ao fundo com notação de probabilidade condicional.

Statistics & Probability12/09/2026

Conditional probability tree: when to multiply, add, and renormalize without memorizing formulas

Learn to read a conditional probability tree: multiply paths, add alternatives, and renormalize after receiving new information.

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Mesa de estudos com caderno mostrando fórmulas de média simples e ponderada, tabela de notas e frequências, calculadora e material do Enem.

Statistics & Probability11/09/2026

Simple or weighted average? How to spot hidden weights in tables and Enem questions

Learn when to use a simple or weighted average, especially when frequencies, group sizes, and percentages act as weights.

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Notebook exibindo três boxplots coloridos para grupos A, B e C em uma mesa de estudos com livros de estatística, probabilidade e matemática.

Statistics & Probability11/09/2026

Boxplots without memorizing: how to read the median, quartiles, interquartile range, and outliers in problems

Learn to interpret boxplots step by step, compare location and spread across groups, and recognize possible outliers without confusing a statistical flag with an error.

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Mesa de estudos com livros de matemática e Enem, caderno com barras de 30% e 45%, anotações de diferença de 15 p.p. e variação de 50%, calculadora e quadro com símbolo de porcentagem.

Fractions & Percentages11/09/2026

Percentage points vs. percentages: how to avoid rate-change mistakes in Enem questions

Learn when to subtract rates in percentage points and when to calculate percent change, with examples and a practical method for Enem questions.

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Estudante resolvendo problemas de matemática em um caderno, com mapa de rotas, comparação de preços, tabela e calculadora ao redor.

Problems & Reasoning10/09/2026

PISA 2025: what Level 2 mathematics requires — with 3 step-by-step solved problems

Understand what the OECD associates with Level 2 mathematics in PISA 2025 and practice with three original teaching problems, fully solved and explained.

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