Dakika 1 za kusoma
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.
Kituo cha Kujifunzia: Masomo Rahisi ya Hisabati
Maelezo rahisi ya mada ambazo wanafunzi huuliza zaidi. Kila somo huanza na wazo, hutatua mfano hatua kwa hatua, na hukagua jibu kwa injini ya hisabati ya Sumzo — kisha huunganisha na kikokotoo na maswali ya mazoezi.
Hesabu na namba
Dakika 1 za kusoma
Prime factors, GCD and LCM
Break numbers into primes, then use the prime factorisation to find the greatest common divisor and least common multiple.
Dakika 2 za kusoma
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.
Aljebra
Dakika 5 za kusoma
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.
Dakika 1 za kusoma
Solving linear equations
Use inverse operations to get the unknown on its own, keep the equation balanced, and always check your answer.
Dakika 2 za kusoma
Quadratic equations: how to solve them
Factorising, completing the square, the quadratic formula and the discriminant — and how to tell which method to use.
Dakika 1 za kusoma
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.
Dakika 4 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 3 za kusoma
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.
Dakika 3 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 3 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 1 za kusoma
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.
Dakika 1 za kusoma
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.
Dakika 2 za kusoma
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.
Jiometri
Dakika 1 za kusoma
The Pythagorean theorem
How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.
Dakika 1 za kusoma
Area of common shapes and circles
Area formulas for rectangles, triangles, trapeziums and circles — and why the triangle formula has a half in it.
Dakika 2 za kusoma
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.
Dakika 2 za kusoma
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.
Dakika 1 za kusoma
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.
Dakika 1 za kusoma
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
Dakika 1 za kusoma
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.
Takwimu
Dakika 1 za kusoma
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.
Dakika 2 za kusoma
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.
Kalkulasi
Dakika 1 za kusoma
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.
Aljebra ya mstari
Dakika 2 za kusoma
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.
Hisabati ya kila siku
Dakika 2 za kusoma
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.
Dakika 1 za kusoma
Ratios and proportions
Simplify ratios, share amounts in a ratio, and solve proportions — the maths behind recipes, maps and scale models.
Jinsi ya kujifunza hisabati kwa masomo haya
- Chagua mada hapa chini, au itafute.
- Soma maelezo mafupi, kisha fuata mifano iliyotatuliwa mstari kwa mstari — jaribu kila hatua kabla ya kuisoma.
- Pitia makosa ya kawaida, ili ujue cha kuangalia.
- Fanya mazoezi kwa maswali yaliyounganishwa. Ingia kama unataka maendeleo yako yahifadhiwe.
Mfano rahisi wa hisabati unavyoonekana
Tatua .
- Toa 4 pande zote mbili: .
- Gawanya pande zote mbili kwa 3: .
- Kagua: . ✓
Kila somo linafanya kazi hivi: hatua ndogo moja kwa wakati, na jibu lililokaguliwa.
Maswali yanayoulizwa mara kwa mara
Je, kuna njia rahisi ya kujifunza mada ngumu?
Gawa kila mada katika hatua ndogo unazozijua tayari. Masomo hukufanyia hivyo — kwa mfano, kipeo cha pili huanza na kuweka vigawo kabla ya fomula ya kipeo cha pili.
Mifano iliyotatuliwa hukaguliwaje?
Mifano iliyotatuliwa hutatuliwa tena na injini ya hisabati au vikokotoo vya Sumzo katika majaribio ya kiotomatiki, kwa hiyo jibu lisilo sahihi hugunduliwa kabla somo halijachapishwa.
Je, ninahitaji akaunti?
Hapana. Masomo yote ni bure kusoma. Akaunti huhifadhi tu maendeleo yako ya mazoezi.