1 دقیقه مطالعه
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.
مرکز یادگیری: درس‌های سادهٔ ریاضی
توضیح‌های ساده برای موضوع‌هایی که دانش‌آموزان بیشتر از همه می‌پرسند. هر درس از ایده شروع میکند، یک مثال را گام‌به‌گام حل میکند و پاسخ را با موتور ریاضی Sumzo بررسی میکند — سپس به یک ماشین‌حساب و پرسش‌های تمرینی پیوند می‌دهد.
حساب و اعداد
1 دقیقه مطالعه
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 دقیقه مطالعه
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.
جبر
5 دقیقه مطالعه
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 دقیقه مطالعه
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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.
هندسه
1 دقیقه مطالعه
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
1 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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 دقیقه مطالعه
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.
مثلثات
1 دقیقه مطالعه
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.
آمار
1 دقیقه مطالعه
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 دقیقه مطالعه
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.
حسابان
1 دقیقه مطالعه
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.
جبر خطی
2 دقیقه مطالعه
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.
ریاضی روزمره
2 دقیقه مطالعه
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 دقیقه مطالعه
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
چگونه با این درسها ریاضی یاد بگیریم
- موضوعی را از پایین انتخاب کنید یا جست‌وجو کنید.
- توضیح کوتاه را بخوانید، سپس مثالهای حلشده را سطربه‌سطر دنبال کنید — هر مرحله را پیش از خواندن خودتان امتحان کنید.
- اشتباه‌های رایج را ببینید تا بدانید به چه چیزی دقت کنید.
- با پرسش‌های پیوندشده تمرین کنید. اگر می‌خواهید پیشرفتتان ذخیره شود وارد شوید.
یک مثال سادهٔ ریاضی چه شکلی است
را حل کنید.
- از هر دو طرف ۴ کم کنید: .
- هر دو طرف را بر ۳ تقسیم کنید: .
- بررسی: . ✓
هر درس این‌طور پیش می‌رود: هر بار یک گام کوچک، و پاسخی که بررسی شده است.
پرسش‌های متداول
آیا راه آسانی برای یادگیری موضوعهای سخت هست؟
هر موضوع را به گامهای کوچکی که از قبل میدانید بشکنید. درسها این کار را برایتان انجام میدهند — مثلاً معادلهٔ درجهٔ دوم پیش از فرمول دلتا با تجزیه شروع میشود.
مثالهای حلشده چگونه بررسی میشوند؟
مثالها در آزمونهای خودکار دوباره توسط موتور ریاضی یا ماشینحسابهای Sumzo حل میشوند، پس پاسخ نادرست پیش از انتشار درس پیدا میشود.
آیا به حساب کاربری نیاز دارم؟
نه. خواندن همهٔ درسها رایگان است. حساب کاربری فقط پیشرفت تمرینهایتان را ذخیره میکند.