1 min de leitura
Fractions: simplifying, adding, multiplying and dividing
What a fraction means, how to simplify one, and the four operations — with a common denominator only when you need it.
Central de aprendizagem: aulas simples de matemática
Explicações simples dos temas sobre os quais os estudantes mais perguntam. Cada aula parte da ideia, resolve um exemplo passo a passo e verifica a resposta com o motor matemático do Sumzo — e depois leva a uma calculadora e a questões de prática.
Aritmética e números
1 min de leitura
Prime factors, GCD and LCM
Break numbers into primes, then use the prime factorisation to find the greatest common divisor and least common multiple.
2 min de leitura
Square roots explained: perfect squares, surds and estimating
What a square root is, the perfect squares to know, how to simplify surds such as √180, and how to estimate roots like √65 without a calculator.
Álgebra
5 min de leitura
Equations: what they are and how to solve them
What an equation is, what its solution means, and how to solve equations step by step — from one-step equations to fractions and two variables.
1 min de leitura
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 min de leitura
Quadratic equations: how to solve them
Factorising, completing the square, the quadratic formula and the discriminant — and how to tell which method to use.
1 min de leitura
Slope and the equation of a line
What slope measures, how to find it from two points, and how to write a line as y = mx + b.
4 min de leitura
How to simplify radicals (simplest radical form)
How to simplify radicals by taking out perfect-square factors, what simplest radical form means, and how to simplify radical expressions — with checked examples.
2 min de leitura
Rational equations: how to solve them
What a rational equation is, how to solve rational equations by multiplying by the lowest common denominator, and why every answer must be checked.
3 min de leitura
Factoring polynomials: a step-by-step guide
The steps for factoring polynomials — common factor first, then two, three or four terms — with worked examples, each checked by multiplying back out.
3 min de leitura
Solving inequalities: how to solve and graph them
Solving inequalities like equations — with one extra rule — and showing the answer on a number line, in interval notation and as a shaded region.
2 min de leitura
What is a solution in math? Examples with one, none or many
A solution is a value that makes an equation true. How to check one, and examples with one solution, no solution, all real numbers and two solutions.
2 min de leitura
How to solve a word problem: 5 steps that work
A five-step method for solving word problems, the key words that turn into maths, and worked examples — ages, consecutive numbers, discounts and tickets.
2 min de leitura
How to graph an equation: lines, parabolas and more
Three ways to graph an equation — a table of values, slope and intercept, and key points of a parabola — with worked examples and how to match a graph to its equation.
3 min de leitura
Functions: how to graph a function, domain, range and f(g(x))
Function notation, how to graph a function from its formula, how to find its domain and range, and how composite functions such as f(g(x)) work.
2 min de leitura
Polynomials: how to simplify, expand and solve them
What a polynomial is, how to simplify and expand polynomials, and how to solve polynomial equations by factoring — with checked examples.
2 min de leitura
Rational expressions: simplify, multiply, divide, add and subtract
What rational expressions are, their excluded values, and how to simplify, multiply, divide, add and subtract them — then solve rational equations.
2 min de leitura
How to solve literal equations (rearranging formulas)
A literal equation has several letters. Solving it means isolating one of them — the same moves as an ordinary equation, with letters instead of numbers.
1 min de leitura
How to simplify expressions and complex fractions
How to simplify the following kinds of expression: like terms, brackets, exponents and complex fractions (a fraction inside a fraction), each with checked examples.
1 min de leitura
Find x: how to solve for x in equations, angles and triangles
The questions that say “find x” — equations, angles on a line, triangle angles, Pythagoras and similar shapes — and the one idea behind all of them.
2 min de leitura
Systems of equations and graphing systems of linear inequalities
How to find the solution to a system of equations three ways, then how to graph a system of inequalities: boundary lines, shading and the overlap.
Geometria
1 min de leitura
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
1 min de leitura
Area of common shapes and circles
Area formulas for rectangles, triangles, trapeziums and circles — and why the triangle formula has a half in it.
2 min de leitura
Area of a trapezium (trapezoid): formula and examples
The formula for the area of a trapezium (a trapezoid in the US), why it works, and worked examples — including finding a missing height or side.
2 min de leitura
Types of triangles: scalene, isosceles and equilateral
Scalene, isosceles and equilateral triangles — how to tell them apart, their angles, and how to find their area, including the area of an equilateral triangle.
1 min de leitura
Polygons and quadrilaterals: is a square a quadrilateral?
Is a square a quadrilateral? Yes — and a rectangle, a rhombus and a parallelogram. How the family fits together, plus polygon angle sums and areas.
1 min de leitura
Triangular prism volume, cylinders, cones and other 3D shapes
How to find the volume and surface area of a triangular prism, and the volume of cylinders and cones — one idea (area of the cross-section × length) behind most of them.
Trigonometria
1 min de leitura
Trigonometry basics: SOH CAH TOA and exact values
The three trig ratios, the two special triangles that give exact values, and how degrees relate to radians.
Estatística
1 min de leitura
Averages and spread: mean, median, mode, range and standard deviation
Three ways to describe a typical value, two ways to describe how spread out data is, and when to use each.
2 min de leitura
Statistics basics: z-scores, percentiles, quartiles and combinations
Three statistics skills that come up again and again: turning a z-score into a percentile, finding quartiles in a data set, and counting with the combination formula.
Cálculo
1 min de leitura
Derivatives and the power rule
A derivative is the slope of a curve at a point. The power rule lets you differentiate any polynomial in one line.
Álgebra linear
2 min de leitura
How to find the determinant of a 2×2 or 3×3 matrix
How to find the determinant of a matrix: the ad − bc rule for 2×2, cofactor expansion for 3×3, a shortcut for triangular matrices, and what a zero determinant tells you.
Matemática do dia a dia
2 min de leitura
How to calculate percentages: the three types of problem
How to solve percentage problems of all three kinds — a percentage of an amount, one number as a percentage of another, and percentage change — with checked examples.
1 min de leitura
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
Como aprender matemática com estas aulas
- Escolha um tema abaixo ou pesquise.
- Leia a explicação curta e acompanhe os exemplos resolvidos linha por linha — tente cada passo antes de lê-lo.
- Veja os erros comuns, para saber no que prestar atenção.
- Pratique com as questões indicadas. Entre na conta se quiser salvar seu progresso.
Como é um exemplo simples de matemática
Resolva .
- Subtraia 4 dos dois lados: .
- Divida os dois lados por 3: .
- Verificação: . ✓
Todas as aulas funcionam assim: um pequeno passo de cada vez e uma resposta verificada.
Perguntas frequentes
Existe um jeito fácil de aprender temas difíceis de matemática?
Divida cada tema em pequenos passos que você já conhece. As aulas fazem isso por você — as quadráticas, por exemplo, começam pela fatoração antes da fórmula de Bhaskara.
Como os exemplos resolvidos são verificados?
Os exemplos são resolvidos de novo pelo motor matemático ou pelas calculadoras do Sumzo em testes automáticos, então uma resposta errada é detectada antes de a aula ser publicada.
Preciso de uma conta?
Não. Todas as aulas são gratuitas. Uma conta só salva seu progresso na prática.