1 minutong basahin
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.
Learning Center: Mga Simpleng Aralin sa Math
Mga simpleng paliwanag para sa mga paksang pinakamadalas itanong ng mga estudyante. Bawat aralin ay nagsisimula sa ideya, naglulutas ng halimbawa nang hakbang-hakbang, at sinusuri ang sagot gamit ang math engine ng Sumzo — saka nagli-link sa isang calculator at mga tanong pansanay.
Aritmetika at mga numero
1 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
2 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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.
Geometry
1 minutong basahin
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
1 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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 minutong basahin
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.
Trigonometry
1 minutong basahin
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.
Statistics
1 minutong basahin
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 minutong basahin
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.
Calculus
1 minutong basahin
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.
Linear algebra
2 minutong basahin
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.
Pang-araw-araw na math
2 minutong basahin
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 minutong basahin
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
Paano matuto ng math sa mga araling ito
- Pumili ng paksa sa ibaba, o maghanap.
- Basahin ang maikling paliwanag, saka sundan ang mga halimbawang nalutas linya por linya — subukan ang bawat hakbang bago ito basahin.
- Tingnan ang mga karaniwang mali, para malaman mo kung ano ang dapat bantayan.
- Magsanay gamit ang mga naka-link na tanong. Mag-log in kung gusto mong ma-save ang iyong progreso.
Ganito ang hitsura ng simpleng halimbawa sa math
Lutasin ang .
- Ibawas ang 4 sa magkabilang panig: .
- Hatiin sa 3 ang magkabilang panig: .
- Pagsusuri: . ✓
Ganito gumagana ang bawat aralin: isang maliit na hakbang sa bawat pagkakataon, at sagot na nasuri.
Mga madalas itanong
May madali bang paraan para matutunan ang mahihirap na paksa?
Hatiin ang bawat paksa sa maliliit na hakbang na alam mo na. Ginagawa ito ng mga aralin para sa iyo — halimbawa, ang quadratic ay nagsisimula sa factoring bago ang quadratic formula.
Paano sinusuri ang mga halimbawang nalutas?
Nilulutas ulit ng math engine o mga calculator ng Sumzo ang mga halimbawa sa mga automated test, kaya nahuhuli ang maling sagot bago mailathala ang aralin.
Kailangan ko ba ng account?
Hindi. Libreng basahin ang lahat ng aralin. Ang account ay nagse-save lamang ng iyong progreso sa pagsasanay.