Math Lab

▶ Math Labs & Calculators

203 hands-on tools: 46 full calculators (EMI, GST, BMI, quadratic solver…) plus 157 slider-driven mini-labs.

🧰 Full calculators & tools

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🎚 Slider mini-labs (by class)

Class XII 25 labs

Integrals

∫₀^a sin x dx = 1 − cos a

Slide a , the running area under sin x bounces between 0 and 2 because of cancellation.

Integrals

∫₀^a x² dx = a³/3

Slide the upper limit a; the definite integral grows cubically.

Linear Programming

1-D LP: Max p·x s.t. x ∈ [0, M]

A single-variable LP. The optimum sits at an endpoint of the feasible interval , see which one.

Vector Algebra

2-D Dot Product a·b

Set components of vectors a and b in 2-D. See magnitudes, dot product and angle between them.

Matrices

2×2 Matrix Times a Vector

Set entries of a 2×2 matrix and a 2-vector. See the matrix-vector product compute live.

Three-Dimensional Geometry

3-D Line: Direction Ratios → Cosines

Set direction ratios (a, b, c) of a 3-D line. Convert to direction cosines (l, m, n).

Three-Dimensional Geometry

3-D Point Distance from Origin

Slide x, y, z components and read off the Euclidean distance √(x²+y²+z²).

Vector Algebra

Angle Between Two Vectors

Use the dot-product formula cos θ = (a·b)/(|a||b|) and report θ in degrees.

Probability

Bayes' Rule: Prior → Posterior

Pick the prior P(H), sensitivity P(E|H) and false-positive rate P(E|¬H). Read the posterior.

Probability

Binomial Distribution Mean & Variance

n trials, success probability p. See mean np, variance np(1−p) and the chance of exactly k successes.

Continuity and Differentiability

Continuity of a Piecewise Function

Piecewise: f(x) = x + a for x < 0 and bx + 1 for x ≥ 0. Tune a, b until the left and right limits match.

Application of Derivatives

Cubic with Adjustable Coefficients

Shape a cubic y = ax³ + bx² + cx + d. Find critical points and use the second derivative test.

Determinants

Determinant of a 2×2 Matrix

Set the four entries of a 2×2 matrix; the determinant updates instantly.

Three-Dimensional Geometry

Distance of Origin from a Plane

Plane ax + by + cz = d. Distance from origin is |d| / √(a² + b² + c²).

Differential Equations

dy/dx = k y, Solution y = y₀ e^(kx)

Pick growth/decay rate k and initial value y₀; the exponential curve responds.

Matrices

Inverse of a 2×2 Matrix

When det ≠ 0, the inverse exists: swap diagonals, negate off-diagonals, divide by det.

Inverse Trigonometric Functions

Inverse Trig: y = a · arcsin(b x)

Domain of arcsin is [-1, 1]. Scale x with b and watch where the curve is defined.

Differential Equations

Logistic Curve y = L / (1 + e^(−k(x − x₀)))

S-shaped growth bounded by capacity L. Set steepness k and midpoint x₀.

Probability

Normal Bell Curve N(μ, σ²)

Shift μ and resize σ. Peak height and spread react together , area under curve stays 1.

Continuity and Differentiability

Product Rule: (x^a · e^(bx))′

Watch the product rule in action on f(x) = x^a · e^(bx). The derivative has two terms.

Integrals

Riemann Sum: Area Under y = x²

Choose interval [0, a] and rectangle count n. Compare left-endpoint sum with the exact integral.

Application of Derivatives

Tangent Line at x₀ on y = x³ − 3x

A cubic with two turning points. Slide x₀ to see the tangent rotate and the slope go to zero at extrema.

Integrals

Trapezoidal Rule on sin x

Approximate ∫₀^a sin x dx by stacking n trapezoids. Compare to the exact value 1 − cos a.

Vector Algebra

Unit Vector of a 2-D Vector

Scale a vector to length 1 by dividing by its magnitude. Components show the direction cosines.

Continuity and Differentiability

y = ln(x) and its Tangent

Drag x₀. The tangent slope is 1/x₀ , and the tangent line is y = ln(x₀) + (x − x₀)/x₀.

Class XI 24 labs

Inequalities

AM ≥ GM Inequality

Choose two positive numbers , the arithmetic mean is always at least the geometric mean.

Sequences and Series

Arithmetic Progression: nth term & sum

Set first term a, common difference d and position n. Get a_n and S_n instantly.

Binomial Theorem

Binomial Coefficient C(n, r)

Pick n and r , see C(n, r), the symmetric partner C(n, n − r) and the central row max.

Conic Sections

Circle (x − h)² + (y − k)² = r²

Move the center (h, k) and resize the radius r. Both halves of the circle are plotted.

Complex Numbers

Complex Number in Polar Form

Set real and imaginary parts of z = x + iy. See modulus |z| and argument arg(z) live.

Coordinate Geometry

Distance Between Two Points

Pick two points in the plane; see the Pythagorean distance and midpoint coordinates.

Conic Sections

Ellipse: (x/a)² + (y/b)² = 1

Drag semi-axes a and b , the upper half of the ellipse redraws. a > b is horizontal; a < b is vertical.

Relations and Functions

Function Family Mixer

Mix linear, quadratic, modulus and reciprocal pieces with coefficient sliders to see compound shapes.

Sequences and Series

Geometric Progression: nth term & sum

First term a, common ratio r, position n. Try |r| < 1 vs |r| > 1 for growth or decay.

Conic Sections

Hyperbola (x/a)² − (y/b)² = 1

Two branches and oblique asymptotes , adjust a, b to see the shape stretch.

Limits and Derivatives

Limit of sin(x)/x near 0

Zoom h toward 0 and watch sin(h)/h hug the value 1. The famous limit, made visible.

Straight Lines

Line Through Two Points

Choose two points (x₁,y₁) and (x₂,y₂); the line and its slope update automatically.

Statistics

Mean, Variance, SD of Five Numbers

Set five data values; mean, variance and standard deviation update instantly.

Conic Sections

Parabola y² = 4ax

Slide the parameter a , the parabola opens right (a > 0) or left (a < 0).

Permutations and Combinations

Permutations vs Combinations

Pick n and r. Compare P(n,r) (order matters) with C(n,r) (order does not).

Complex Numbers / Quadratic Equations

Quadratic Roots & Discriminant

Slide a, b, c of ax² + bx + c. Discriminant tells you real vs complex roots.

Sets

Set Cardinality: |A ∪ B|

Pick sizes of A, B and their intersection , watch how union and difference cardinalities update.

Trigonometry

Sin + Cos + Tan Mixer

Blend sin, cos and tan with three weight sliders. Useful for spotting Fourier-like sums.

Straight Lines

Slope–Intercept Line: y = mx + c

Drag m and c , see how slope tilts and intercept slides the line.

Limits and Derivatives

Tangent Slope on y = sin x

Slide a point along sin x. The tangent uses slope cos(x₀) , confirm d/dx sin x = cos x.

Limits and Derivatives

Tangent Slope on y = x²

Slide a point x₀ along y = x². The tangent line uses slope 2x₀ , see it follow the curve.

Trigonometry

y = A cos(ωx + φ)

Cosine version , same controls as sine, but the wave starts at its peak when φ = 0.

Trigonometry

y = A sin(ωx + φ)

Tune amplitude, angular frequency and phase and see the sine wave change shape.

Trigonometry

y = A tan(ωx + φ)

Vertical asymptotes appear wherever the argument equals π/2 + nπ , try shifting φ.

Class X 15 labs

Coordinate Geometry

Area of a Triangle from Vertices

Place three vertices and compute the signed and unsigned triangle area.

Arithmetic Progressions

Arithmetic Progression: Term & Sum

Choose first term a, common difference d, and term count n; get nth term and total sum.

Statistics

Class-Mark Method: Mean of Grouped Data

Three class-intervals share a common width. Slide their frequencies to see the assumed-mean shift.

Coordinate Geometry

Distance Between Two Points

Drag two points A(x1,y1) and B(x2,y2) and watch the distance update.

Surface Areas and Volumes

Frustum of a Cone

Slide the two radii and height of a frustum; read slant height, CSA, TSA, and volume.

Trigonometry Applications

Heights and Distances

From distance d and elevation angle, compute the tower's height.

Surface Areas and Volumes

Hemisphere on Top of a Cylinder

A common composite: a cylindrical vessel capped by a hemisphere. Compute combined surface area and capacity.

Linear Equations

Pair of Linear Equations: Intersection Point

Two lines a1 x + b1 y = c1 and a2 x + b2 y = c2 , see where they meet (or don't).

Polynomials

Polynomial Remainder Theorem

Divide p(x) = x^3 + bx^2 + cx + d by (x - k) and read off the remainder p(k).

Probability

Probability: Drawing from a Bag

A bag has R red and B blue balls; compute the probability of each colour on one draw.

Quadratic Equations

Quadratic Roots and Discriminant

Tune a, b, c and see the nature of roots flip between real/distinct, repeated, or complex.

Coordinate Geometry

Section Formula (Internal Division)

Divide segment AB in ratio m:n internally and read off the dividing point P.

Circles

Tangent Length from an External Point

From a point at distance d from the centre of a circle of radius r, find the tangent length.

Trigonometry

Trig on the Unit Circle

Sweep an angle in degrees and read off sin, cos, tan instantly.

Trigonometry

Trig Ratios in a Right Triangle

Set opposite and adjacent legs; compute hypotenuse and all six trig ratios.

Class IX 15 labs

Circles

Circle: Area, Circumference, Sector

Spin a radius and a sector angle to see area, circumference, sector area, and arc length react.

Surface Areas and Volumes

Cone: Slant, Surface Area, Volume

Slide r and h; slant height, CSA, TSA, and volume update together.

Polynomials

Cubic Polynomial Explorer

Shape y = ax^3 + bx^2 + cx + d and observe up-to-three real zeros.

Surface Areas and Volumes

Cylinder: Surface Area and Volume

Pick radius r and height h to compute CSA, TSA, and volume of a right circular cylinder.

Polynomials

Factor Theorem Checker

Pick a candidate k. Is (x - k) a factor of p(x) = x^3 + bx^2 + cx + d?

Heron's Formula

Heron's Formula Area

Enter the three sides; Heron computes the area without any height.

Number Systems

Irrational Numbers on the Number Line

Pick a positive integer n and locate sqrt(n) precisely on the number line.

Linear Equations

Linear Equation in Two Variables

Visualize ax + by + c = 0 as a straight line by tuning a, b, c.

Polynomials

Linear Polynomial Explorer

Adjust the slope m and intercept c of y = mx + c to see the line tilt and slide.

Statistics

Mean, Median, Mode of Five Numbers

Slide five data values and watch mean, median, and range respond.

Coordinate Geometry

Plot a Point in the Cartesian Plane

Slide x and y and see where the point lands. Which quadrant is it in?

Probability

Probability with a Single Die

Pick a target value k; see P(roll = k), P(roll <= k), P(roll > k) on a fair six-sided die.

Polynomials

Quadratic Polynomial Explorer

Tune a, b, c and watch y = ax^2 + bx + c bend and shift.

Surface Areas and Volumes

Sphere: Surface Area and Volume

Increase the radius and watch surface area grow as r^2 while volume grows as r^3.

Triangles

Triangle Inequality Checker

Pick three side lengths a, b, c. Do they form a valid triangle?

Class VIII 15 labs

Factorisation

Common Factor Pull-Out

For a x + a y, slide a, x, y and see the factored form a (x + y).

Comparing Quantities

Compound Interest

Compare simple vs compound interest as you change principal, rate and time.

Mensuration

Cone Volume and Surface

Slide radius and height of a cone; see its slant, volume and surface area.

Cubes and Cube Roots

Cubes and Cube Roots

Slide n for its cube and N for its cube root.

Mensuration

Cuboid Volume and Surface

Slide length, breadth and height to see volume and surface area.

Mensuration

Cylinder Volume and Surface

Choose radius and height; see volume, lateral surface and total surface area.

Factorisation

Difference of Two Squares

Check that a^2 - b^2 always equals (a - b)(a + b).

Direct and Inverse Proportion

Direct Proportion

When y = k x, slide the constant k and see how y grows with x.

Comparing Quantities

Discount and Selling Price

Set marked price and discount percent; see selling price and savings.

Exponents and Powers

Exponent Rules

Verify a^m * a^n = a^(m+n) and (a^m)/(a^n) = a^(m-n) by sliders.

Direct and Inverse Proportion

Inverse Proportion

When x y = k, slide k and see y fall as x grows.

Rational Numbers

Rational Number on the Line

Pick numerator p and denominator q; locate p/q on the number line.

Exponents and Powers

Scientific Notation

Build a number as m x 10^k and see its decimal value.

Squares and Square Roots

Squares and Square Roots

Slide n to see its square and slide N to see its square root.

Simple Graphs

Two-Variable Linear Graph

Plot a x + b y = c by isolating y. Slide a, b, c.