阅读约 1 分钟
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.
学习中心：简单数学课
针对学生最常问的主题的简单讲解。每节课从思路讲起，一步步解一道例题，并用 Sumzo 数学引擎检验答案——然后链接到计算器和练习题。
算术与数
阅读约 1 分钟
Prime factors, GCD and LCM
Break numbers into primes, then use the prime factorisation to find the greatest common divisor and least common multiple.
阅读约 2 分钟
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.
代数
阅读约 5 分钟
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.
阅读约 1 分钟
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
阅读约 2 分钟
Quadratic equations: how to solve them
Factorising, completing the square, the quadratic formula and the discriminant — and how to tell which method to use.
阅读约 1 分钟
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.
阅读约 4 分钟
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.
阅读约 2 分钟
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.
阅读约 3 分钟
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.
阅读约 3 分钟
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.
阅读约 2 分钟
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.
阅读约 2 分钟
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.
阅读约 2 分钟
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.
阅读约 3 分钟
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.
阅读约 2 分钟
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.
阅读约 2 分钟
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.
阅读约 2 分钟
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.
阅读约 1 分钟
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.
阅读约 1 分钟
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.
阅读约 2 分钟
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.
几何
阅读约 1 分钟
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
阅读约 1 分钟
Area of common shapes and circles
Area formulas for rectangles, triangles, trapeziums and circles — and why the triangle formula has a half in it.
阅读约 2 分钟
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.
阅读约 2 分钟
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.
阅读约 1 分钟
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.
阅读约 1 分钟
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.
三角学
阅读约 1 分钟
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.
统计
阅读约 1 分钟
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.
阅读约 2 分钟
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.
微积分
阅读约 1 分钟
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.
线性代数
阅读约 2 分钟
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.
生活数学
阅读约 2 分钟
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.
阅读约 1 分钟
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
如何用这些课程学数学
- 在下方选择一个主题，或搜索。
- 阅读简短讲解，然后逐行跟着例题做——每一步先自己试，再看答案。
- 看看常见错误，知道要注意什么。
- 用相关练习题巩固。想保存进度请登录。
一道简单的数学例题是什么样的
解 。
- 两边同时减 4：。
- 两边同时除以 3：。
- 检验：。✓
每节课都是这样：一次一小步，答案经过检验。
常见问题
有没有轻松学难点的办法？
把每个主题拆成你已经会的小步骤。课程会帮你做到这一点——比如二次方程先学因式分解，再学求根公式。
例题是怎样检验的？
例题会在自动化测试中由 Sumzo 的数学引擎或计算器重新求解，因此错误答案会在课程上线前被发现。
我需要账户吗？
不需要。所有课程都免费阅读。账户只用于保存你的练习进度。