1 min di lettura
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.
Centro di apprendimento: lezioni di matematica semplici
Spiegazioni semplici degli argomenti su cui gli studenti chiedono di più. Ogni lezione parte dall’idea, svolge un esempio passo per passo e verifica la risposta con il motore matematico di Sumzo — poi rimanda a una calcolatrice e a esercizi.
Aritmetica e numeri
1 min di lettura
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 di lettura
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.
Algebra
5 min di lettura
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 di lettura
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 min di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
1 min di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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 di lettura
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.
Statistica
1 min di lettura
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 di lettura
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.
Analisi
1 min di lettura
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.
Algebra lineare
2 min di lettura
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.
Matematica di tutti i giorni
2 min di lettura
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 di lettura
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
Come imparare la matematica con queste lezioni
- Scegli un argomento qui sotto o cercalo.
- Leggi la breve spiegazione, poi segui gli esempi svolti riga per riga — prova ogni passaggio prima di leggerlo.
- Guarda gli errori comuni, così sai a cosa fare attenzione.
- Esercitati con le domande collegate. Accedi se vuoi salvare i tuoi progressi.
Com’è un semplice esempio di matematica
Risolvi .
- Sottrai 4 da entrambi i lati: .
- Dividi entrambi i lati per 3: .
- Verifica: . ✓
Ogni lezione funziona così: un piccolo passo alla volta e una risposta verificata.
Domande frequenti
C’è un modo facile per imparare argomenti difficili?
Dividi ogni argomento in piccoli passi che conosci già. Le lezioni lo fanno per te — il secondo grado, per esempio, parte dalla scomposizione prima della formula risolutiva.
Come vengono verificati gli esempi svolti?
Gli esempi vengono risolti di nuovo dal motore matematico o dalle calcolatrici di Sumzo in test automatici, quindi una risposta sbagliata viene scoperta prima che la lezione sia pubblicata.
Mi serve un account?
No. Tutte le lezioni sono gratuite. Un account salva solo i progressi negli esercizi.