Online Math Solver With Steps — Algebra, Geometry, Calculus & More

Type your equation or pick a topic below. Each topic links to fully worked examples following Indian school (CBSE / ICSE / State Board) and university curriculum, with every step shown. For instant solving of algebra and calculus problems, type into the box above.

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Photo upload & OCR — coming soon. Once the image solver is ready, you'll be able to upload a photo of a handwritten or printed math problem and get a worked solution. We don't want to fake the feature, so for now please type the problem into the box above.

Grades 6–8 (CBSE / ICSE / State Board)

The middle-school topics below cover the foundations the rest of school maths is built on — numbers, factors, ratios, exponents, basic algebra, geometry, mensuration, the coordinate plane, and data handling. Each landing page collects fully solved CBSE / ICSE-style problems with every line of working shown.

Number System

Natural numbers, integers, rationals, fractions, decimals.

The number system is where everything starts. You meet natural numbers (1, 2, 3...), whole numbers (add 0), integers (add the negatives), and rationals (anything that can be written as a fraction). The CBSE Class 6–8 syllabus expects you to be confident with HCF, LCM, integer operations, and converting between fractions and decimals. The 12 solved problems walk through HCF by prime factorisation, LCM by the division method, adding and subtracting unlike fractions, decimal-to-fraction conversion, and a few common exam traps where a missing sign costs the whole answer.

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Factors & Multiples

Prime factorisation, HCF, LCM, divisibility rules.

Factors are numbers that divide a given number cleanly; multiples are what you get when you keep multiplying by an integer. This is where HCF and LCM live, and where most Class 6–8 board questions on numbers come from. The 10 solved examples cover prime factorisation using factor trees, finding HCF and LCM by both the factor-tree and division methods, and the divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11 — with CBSE-style questions that ask you to use those rules to test large numbers without dividing.

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Ratio & Proportion

Unitary method, direct and inverse proportion, percentages.

A ratio compares two quantities of the same kind; a proportion says two ratios are equal. From Class 6 onward, almost every word problem about mixing, sharing, scaling, or percentage has a ratio inside it. The 12 worked examples cover simplifying ratios, the unitary method for direct proportion (price, distance, work), inverse proportion (the classic men-and-days problems), and percentage problems set up as proportions. Each one shows the 'let the unknown be x' setup line explicitly, because that is the step where most students lose half their marks.

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Exponents & Roots

Laws of exponents, square and cube roots, radicals, scientific notation.

Exponents tell you how many times a number is multiplied by itself; roots ask the opposite question. This page also works as a radical calculator and exponent solver — type any expression with √ or ^ and you get the simplified form plus step-by-step working. The 10 step-by-step problems cover the seven laws of exponents (product, quotient, power of a power, zero and negative exponents, fractional exponents), square roots and cube roots by prime factorisation, simplifying radicals (e.g., √72 → 6√2), rationalising denominators, and scientific notation for very large and very small numbers. A few questions are picked specifically because the trick is to rewrite both sides with a common base — once you spot it, the answer falls out in a single line.

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Basic Algebra

Variables, simplifying expressions, linear equations.

Algebra is just arithmetic with one or two unknown values written as letters. The 14 solved examples take you from variables and constants, through simplifying expressions by combining like terms, to solving linear equations in one variable using transposition. The harder examples build a linear equation from a short word problem ("the sum of a number and 5 is 18") — that translation step is what catches students who can solve the equation but freeze when they have to write it down themselves. Each example ends with the verification step too, the one most students skip in exams.

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Geometry Basics

Lines, angles, triangles, quadrilaterals, circles.

Geometry rewards students who draw the figure neatly before writing a single calculation. This topic covers lines and angles (complementary, supplementary, vertically opposite), triangle properties (angle sum, exterior angle, isosceles), quadrilaterals (parallelogram, rhombus, trapezium), circles (chord, tangent, basic theorems), and the simple theorems Class 7–8 students are expected to apply. The 11 solved examples each include a clean diagram, the 'given' and 'to find' lines, and the standard step-marked layout that examiners look for in CBSE and ICSE answer booklets.

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Mensuration

Perimeter, area, volume, cylinder volume calculator and standard 3D shapes.

Mensuration is where geometry meets numbers — finding the perimeter, area, surface area, and volume of standard shapes. This page also works as a cylinder volume calculator, sphere volume calculator and cone volume calculator — type V = π r² h or whichever formula applies and the solver gives you the numerical answer with steps. The 13 worked problems cover squares, rectangles, triangles, parallelograms, trapeziums, and circles for 2D, then cubes, cuboids, cylinders (V = π r² h), cones (V = ⅓ π r² h), and spheres (V = ⁴⁄₃ π r³) for 3D. A few of the harder questions are combined-shape problems (a rectangle with a semicircular end, a cube with a cone on top) where you have to split the figure first. These are the ones that turn up in CBSE Class 8–10 board exams almost every year.

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Coordinate Basics

Plotting points, quadrants, distance on axes.

Coordinate geometry starts with the simple act of putting numbers on a graph paper. This topic covers plotting points (x, y) on the Cartesian plane, identifying which of the four quadrants a point belongs to (or whether it sits on an axis), and finding the distance between two points that lie on the same horizontal or vertical line. The 8 worked examples include a few questions that look harder than they are — for instance, finding the area of a triangle whose three vertices are given, using only horizontal and vertical distances on the grid.

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Data Handling

Mean, median, mode, bar graphs, pie charts.

Data handling is the first taste of statistics. The 9 solved problems cover the three measures of central tendency — mean (the arithmetic average), median (the middle value of the sorted data), and mode (the most frequent value) — along with reading and drawing bar graphs and pie charts. The questions follow the CBSE Class 7–8 pattern: you are given a short table or graph and asked to compute one or two measures, or to identify which measure is most appropriate for the kind of data shown.

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Grades 9–12 (CBSE / ICSE Board Preparation)

The Class 9–12 topics cover the heart of board-exam preparation — polynomials, sequences, trigonometry, coordinate geometry, matrices and vectors, and the introductory calculus chapter that runs from limits through to definite integrals. The solved problems follow the marking pattern that CBSE and ICSE examiners actually award marks for.

Polynomials

Degree, zeros, division, remainder & factor theorems.

A polynomial is an expression made of terms with non-negative integer powers of a variable. From Class 9 onward, you'll work with degree, zeros (roots), the division algorithm, the remainder theorem ("the remainder of p(x) ÷ (x − a) is p(a)"), and the factor theorem. The 12 solved problems cover finding zeros of quadratic and cubic polynomials, dividing one polynomial by another using long division and synthetic division, applying the factor theorem to factorise cubics, and CBSE/ICSE board-style questions that combine two of these ideas in a single problem.

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Sequences & Series

AP, GP, nth term, sum formulas.

An arithmetic progression (AP) adds the same number every time; a geometric progression (GP) multiplies by the same number every time. That single distinction unlocks most of the Class 10–11 chapter. The 13 solved examples cover the nth term and the sum of n terms for both AP and GP, the formulas for the sum of the first n natural numbers, their squares, and their cubes, and a few problems where the trick is to spot a hidden AP inside a word problem ("a man saves ₹100 in the first month and ₹50 more each month after").

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Trigonometry

Ratios, identities, equations, heights and distances.

Trigonometry starts as ratios in a right triangle (sin, cos, tan) and grows into one of the most-tested chapters in CBSE Class 10 and 11. The 15 worked problems cover the six ratios, the values of sin, cos, and tan at the standard angles (0°, 30°, 45°, 60°, 90°), the three fundamental identities (sin²θ + cos²θ = 1 and the two derived from it), simple trigonometric equations, and heights-and-distances problems (a tower, an aeroplane, a flagpole). Each problem starts with the figure, because drawing the right triangle correctly is honestly half the work.

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Coordinate Geometry

Distance, section formula, line equations, conics.

Coordinate geometry turns geometry problems into algebra. The 14 solved examples cover the distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²), the section formula (both internal and external division), the slope of a line, the four standard forms of the line equation (slope-intercept, point-slope, two-point, general), and an introduction to conic sections — the equations of the circle, parabola, ellipse, and hyperbola in their standard positions. A few of the harder problems use the determinant formula to find the area of a triangle from three vertices.

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Matrices & Vectors

Matrix operations, determinants, inverse matrix calculator, vector algebra.

A matrix is a rectangular grid of numbers; a vector is a quantity with both magnitude and direction. This page works as an inverse matrix calculator, determinant calculator, and matrix multiplication solver — enter your 2×2 or 3×3 matrix and the tool returns A⁻¹, det(A), and step-by-step working. The 12 problems cover matrix addition, subtraction, scalar multiplication, and matrix-on-matrix multiplication, the determinant of a 2×2 and 3×3 matrix, finding the inverse using the adjoint method (A⁻¹ = adj(A) ÷ det(A)), solving a system of equations by Cramer's rule, and vector algebra — addition by the triangle and parallelogram laws, the dot product, and the cross product. Each problem shows the working in the row-by-column format that Class 12 board examiners expect.

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Intro Calculus

Limits, derivatives, integration basics.

Calculus is the maths of change. The 16 step-by-step examples introduce three big ideas. Limits — what happens to f(x) as x gets close to a value, including the 0/0 indeterminate form. Derivatives — the rate of change of a function, with the power rule, product rule, quotient rule, and chain rule. Integration — the reverse of differentiation, with simple substitutions and a few definite integrals. The set sticks to the CBSE Class 11–12 syllabus and stops short of the more abstract material that belongs in the graduate topics below.

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Graduate / Undergraduate Mathematics

The graduate-level topics cover the first-year B.Sc, B.Tech, and M.Sc curriculum — abstract algebra basics, rigorous limits and continuity, differentiation and integration techniques, infinite series, linear algebra, vector calculus, ordinary differential equations, and curve sketching. Each landing page sticks to the way university examiners expect the working to be written.

Advanced Algebra

Intro to groups, rings, and fields.

Once you have finished school algebra, the next layer is abstract algebra — the study of the structures themselves rather than specific numbers. The 8 introductory solved examples cover groups (closure, associativity, identity, inverse — the four axioms checked one by one), rings (two operations linked by the distributive law), and fields (every non-zero element has a multiplicative inverse). The problems are picked from the first chapter of most B.Sc and B.Tech mathematics syllabi, and each one is worked out the way an examiner expects: definitions stated, axioms verified one at a time.

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Limits & Continuity

Epsilon-delta, standard limits, L'Hôpital, continuity.

At university level, limits are no longer just "plug the value in and see what happens". The 12 worked problems include the formal epsilon-delta definition (the line a B.Sc student is asked to write on day one of analysis), the common limits worth memorising (sin x / x, (1 + 1/n)ⁿ, (1 − cos x) / x²), L'Hôpital's rule for 0/0 and ∞/∞ forms, and the three conditions a function must satisfy to be continuous at a point. A few problems test continuity of piecewise-defined functions, which is where most students slip.

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Differentiation

Chain, product, quotient, implicit, parametric, logarithmic.

Differentiation at undergraduate level reuses the school rules but layers them. The 18 examples cover the chain rule for nested functions, the product and quotient rules for combinations, implicit differentiation when y is tangled with x (find dy/dx when x² + y² = 25), parametric differentiation when both x and y depend on a third variable t, and logarithmic differentiation for products of many factors. Each example shows the 'let u = inner function' substitution step clearly — skipping it is the single biggest source of dropped marks in semester exams.

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Integration

Antiderivatives, substitution, by parts, partial fractions, definite integrals.

Integration is the part of calculus that takes practice rather than insight. This page works as an antiderivative calculator (also called indefinite integral calculator) and definite integral solver — enter ∫ f(x) dx and you get F(x) + C with step-by-step working. The 20 examples cover the four standard techniques: integration by substitution (let u = something, then du = something else), integration by parts (∫u dv = uv − ∫v du, with the LIATE rule for choosing u), partial fractions for rational functions, and definite integrals — including a few where the trick is to use symmetry or a property of the limits to skip half the work. Common antiderivatives included: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, ∫1/x dx = ln|x| + C, ∫eˣ dx = eˣ + C, ∫sin(x) dx = −cos(x) + C, ∫cos(x) dx = sin(x) + C. The problems sit at the level of a B.Sc or B.Tech first-year syllabus.

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Series & Convergence

Convergence tests, Taylor and Maclaurin series.

After AP and GP, the natural question is: what about infinite series with a general nth term? The 10 problems work through the standard convergence tests — the comparison test, the ratio test, the root test, and the integral test — and apply them to series you'll meet in any analysis course. The set also includes Taylor and Maclaurin expansions of eˣ, sin x, cos x, log(1 + x), and a few problems where you find the radius of convergence of a power series. Each test is stated formally before it is used.

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Linear Algebra

Eigenvalues, eigenvectors, diagonalisation.

Linear algebra is the working language of modern science and engineering. The 12 solved examples cover eigenvalues and eigenvectors of 2×2 and 3×3 matrices (the characteristic polynomial, solving det(A − λI) = 0, then finding the corresponding null space), the conditions for a matrix to be diagonalisable, and the actual diagonalisation step P⁻¹AP = D. A couple of the problems use diagonalisation to compute a high power of a matrix without multiplying it out by hand — exactly the kind of trick B.Tech and M.Sc exams keep coming back to.

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Vector Calculus

Gradient, divergence, curl, line integrals, partial derivatives, double integrals.

Vector calculus extends single-variable calculus into three-dimensional space. This page works as a partial derivative calculator (∂f/∂x, ∂f/∂y, ∂f/∂z) and double integral calculator (∬ f(x,y) dA) for multi-variable functions — enter your expression and get step-by-step solutions. The 10 worked problems cover the gradient ∇f of a scalar field (which is built from partial derivatives), the divergence ∇·F and curl ∇×F of a vector field, line integrals of vector fields along a curve, double integrals over rectangular and general regions (with both dxdy and dydx orders, plus polar form ∬ f(r,θ) r dr dθ), and a first look at the integral theorems (Green's, Stokes', divergence) without going too deep on the proofs. The examples follow the B.Tech engineering mathematics syllabus, with each step shown in full Cartesian coordinates so you can map the answer back to the formula sheet.

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Differential Equations

First-order, second-order, separable, linear ODEs.

A differential equation is one that involves a function and its derivatives. The 14 examples cover first-order separable equations (dy/dx = f(x)g(y), separate and integrate both sides), first-order linear equations (the integrating-factor method), exact equations, and second-order linear equations with constant coefficients — both homogeneous (characteristic equation, three cases for the roots) and non-homogeneous (the method of undetermined coefficients). The problems are picked from B.Sc and B.Tech first-year mathematics, and each one ends with the general solution written out clearly.

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Graphs & Intersections

Curve sketching and points of intersection.

Curve sketching is a skill engineering and physics students lean on almost every day. The 8 worked examples cover the standard checklist — find the domain, the x and y intercepts, the symmetry, the asymptotes (vertical, horizontal, oblique), the critical points from f′(x) = 0, the points of inflection from f″(x) = 0, and the behaviour at infinity. Two of the problems are intersection problems where two curves cross and you have to solve a system of two equations to find the exact crossing points.

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How to Use This Solver

The fastest way in is the box at the top of the page. For algebra equations, type using standard symbols: +, -, *, /, ^ for power, and sqrt for square root. Example inputs that work straight away: 3x + 7 = 22, x^2 + 5x + 6 = 0, sin(45). If you want a step-by-step explanation rather than just the answer, include the word solve or factor at the start of your line, like solve x^2 - 5x + 6 = 0.

For topic-based practice — the part most students actually need before an exam — skip the box and click straight into the relevant grade level below. The Grades 6–8 grid is the right starting point if you are revising CBSE Class 6, 7, or 8 material. The Grades 9–12 grid covers the board-exam years. The Graduate grid is for B.Sc, B.Tech, and M.Sc first-year mathematics. Each topic card has a short description so you can tell at a glance whether you are in the right place, and a "View solved problems →" link that drops you straight into the worked examples for that topic.

Solved Problem Sets — Index

Grades 6–8 (CBSE / ICSE middle school). Nine topic landing pages cover the foundations: the number system, factors and multiples, ratio and proportion, exponents and roots, basic algebra, geometry, mensuration, coordinate basics, and data handling. Together they hold around 95 fully worked problems. The problems are picked from the parts of the syllabus that come up year after year in CBSE Class 6–8 papers — HCF and LCM, unitary-method word problems, simplifying expressions, triangle properties, and the surface area / volume of standard shapes. Jump to the Grades 6–8 index →

Grades 9–12 (CBSE / ICSE board preparation). Six topic landing pages cover the board-exam heart of the syllabus: polynomials, sequences and series, trigonometry, coordinate geometry, matrices and vectors, and the introductory calculus chapter. Together they hold around 82 worked problems, every one written with the step-marking pattern that examiners reward. The trigonometry set in particular includes heights-and-distances questions in the exact format the Class 10 paper has used for years. Jump to the Grades 9–12 index →

Graduate / undergraduate mathematics. Nine topic landing pages cover B.Sc, B.Tech, and M.Sc first-year material: advanced algebra (groups, rings, fields at intro level), limits and continuity (with the epsilon-delta definition), differentiation, integration, series and convergence, linear algebra, vector calculus, differential equations, and curve sketching with intersection problems. Together they hold around 110 worked examples, each kept inside the standard B.Sc / B.Tech syllabus rather than wandering into research-level material. Jump to the Graduate index →

Why Step-by-Step Matters in Math

Examiners give partial marks. That is the single most important fact about how Indian board exams and university semester exams are scored. Forgetting to write a step costs marks even when your final answer is correct, because the marking scheme awards specific marks for specific intermediate lines. The page you are on shows every intermediate calculation precisely for that reason.

Here is what it looks like in practice. Take the equation x² − 5x + 6 = 0.

The version that loses marks:
x = 2, x = 3

The version that gets full marks:
Compare with ax² + bx + c = 0 → a = 1, b = -5, c = 6
Factorise: x² - 5x + 6 = (x - 2)(x - 3) = 0
So either x - 2 = 0 or x - 3 = 0
Therefore x = 2 or x = 3

Same answer, four extra lines, full marks instead of half. The worked examples linked from every topic page on this site are written in the second style, line by line, so you can copy the layout into your own answer sheet.

Limits — What This Solver Can And Cannot Do

Honest version. The solver handles linear and quadratic equations, basic algebraic simplification, the standard calculus operations from the CBSE Class 11–12 syllabus (derivatives, common indefinite and definite integrals, simple limits), common trigonometric values and identities, and matrix and vector basics. The 24 topic landing pages cover the bulk of the Indian school and undergraduate maths syllabus in solved-example form.

What it does not do, and won't pretend to: abstract algebra proofs at research level, image-upload OCR (in development — see the note above), word problems that require interpretation rather than just calculation, and partial differential equations beyond first-order separable ones. For those, the right tools are Wolfram Alpha, Symbolab, or your textbook. We will keep adding worked examples here, but we won't fake features the engine does not actually support.

Quick Reference — Most-Used Formulas

The formulas below come up so often that it is worth keeping them in working memory. Each one carries a short note on when it applies.

Quadratic formula
x = (-b ± √(b² − 4ac)) / 2a
Solves any quadratic ax² + bx + c = 0 when factorising is awkward. The discriminant b² − 4ac tells you whether the roots are real and distinct, real and equal, or complex.
Distance formula
d = √((x₂ − x₁)² + (y₂ − y₁)²)
The straight-line distance between two points (x₁, y₁) and (x₂, y₂) on the Cartesian plane. The foundation of nearly every coordinate-geometry question.
Power rule (derivative)
d/dx (xⁿ) = n · xⁿ⁻¹
The single most-used derivative rule. Combined with the linearity of differentiation, it handles every polynomial you'll meet in school calculus.
Power rule (integral)
∫xⁿ dx = xⁿ⁺¹ / (n + 1) + C (for n ≠ −1)
The reverse of the derivative power rule. The exception n = −1 is the case ∫(1/x) dx = ln|x| + C — worth memorising separately.
Pythagorean trig identity
sin²θ + cos²θ = 1
Divide both sides by cos²θ to get 1 + tan²θ = sec²θ, or by sin²θ to get 1 + cot²θ = cosec²θ. Three identities for the price of one.
Logarithm product rule
log(ab) = log(a) + log(b)
Together with log(a/b) = log(a) − log(b) and log(aⁿ) = n · log(a), it lets you turn a multiplication problem into an addition problem — exactly how log tables and slide rules worked.

Frequently Asked Questions

How do I solve a quadratic equation step-by-step?
For a quadratic in the form ax² + bx + c = 0, first try factorising. Find two numbers that multiply to ac and add to b — split the middle term, group, and pull out the common factor. If factorising is awkward, use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. The value b² - 4ac is the discriminant: positive means two real roots, zero means one repeated root, negative means a complex pair. Always write the comparison line (a = ?, b = ?, c = ?) before substituting — that single step is worth a mark in CBSE Class 10 and 11 board exams.
What's the difference between a derivative and an integral?
A derivative measures the rate of change of a function at a point — the slope of the tangent line. If f(x) = x³, then f′(x) = 3x², which tells you how steeply the curve rises at any x. An integral does the reverse: it adds up infinitesimal pieces to recover the area under a curve, or the original function from its rate of change. The two are linked by the fundamental theorem of calculus, which says integration and differentiation undo each other (up to a constant). In short: derivative = slope, integral = accumulated area.
How do I convert from degrees to radians?
A full circle is 360° in degrees and 2π radians in radians. So 180° equals π radians, which gives the conversion factor π/180. To convert degrees to radians, multiply by π/180. To go the other way, multiply by 180/π. Quick examples: 30° = 30 × π/180 = π/6, 45° = π/4, 60° = π/3, 90° = π/2. In calculus and physics, always use radians — the standard limit sin(x)/x → 1 and the derivative formulas d/dx (sin x) = cos x only hold when x is in radians.
Can this solver handle CBSE/ICSE Class 12 problems?
Yes, for the standard calculus, algebra, matrices, and coordinate-geometry chapters in the Class 12 syllabus. The solver handles derivatives (chain, product, quotient), basic indefinite and definite integrals, matrix operations and determinants, the quadratic formula and polynomial roots, and standard trigonometric and logarithmic expressions. It does not yet handle full proof-based questions (\"prove that...\") or word problems that need interpretation — for those, use the topic landing pages, which include CBSE-style fully solved examples with every step written out.
How do I factor a polynomial?
For a quadratic x² + bx + c, find two numbers that multiply to c and add to b — those are the roots, and the factors are (x − root₁)(x − root₂). For a general polynomial p(x), use the factor theorem: if p(a) = 0 for some value a, then (x − a) is a factor; divide p(x) by (x − a) to find the remaining factor. Common shortcuts: a² − b² = (a − b)(a + b), a³ ± b³ = (a ± b)(a² ∓ ab + b²), and the perfect-square trinomials a² ± 2ab + b² = (a ± b)². Always check by expanding the factors back.
What are the laws of exponents?
There are seven that cover almost every Class 6–10 exam question. Product: aᵐ × aⁿ = aᵐ⁺ⁿ. Quotient: aᵐ / aⁿ = aᵐ⁻ⁿ. Power of a power: (aᵐ)ⁿ = aᵐⁿ. Power of a product: (ab)ⁿ = aⁿbⁿ. Power of a quotient: (a/b)ⁿ = aⁿ/bⁿ. Zero exponent: a⁰ = 1 (a ≠ 0). Negative exponent: a⁻ⁿ = 1/aⁿ. The fractional-exponent rule a^(m/n) = ⁿ√(aᵐ) bridges exponents and roots. The single most useful trick: rewrite both sides of an equation with the same base, then equate the exponents.
How do I find the area of a triangle without a height?
You have three options. If all three sides are known, use Heron's formula: s = (a + b + c)/2, then area = √(s(s − a)(s − b)(s − c)). If two sides and the included angle are known, use area = ½ × a × b × sin C. If the three vertices of the triangle are given as coordinates (x₁, y₁), (x₂, y₂), (x₃, y₃), use the determinant form: area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Each of these avoids drawing or measuring the perpendicular height.
Can I get help with integration by parts?
Yes. Integration by parts uses the rule ∫u dv = uv − ∫v du. The hard step is choosing which factor is u and which is dv. The LIATE rule gives the priority order: Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential — pick u as the one that comes first in this list. Example: for ∫x cos x dx, x is algebraic and cos x is trigonometric, so u = x and dv = cos x dx. Then du = dx and v = sin x, giving ∫x cos x dx = x sin x − ∫sin x dx = x sin x + cos x + C.