‹ Play

Play With Algebra

The workshop where the equation is something you can grab. Classes 6 to 10.

Loading the atlas…

All 257 Play With Algebra lessons

Every lesson in the series, by class. Every lesson is free to play once you sign in.

Class 6

  • The Secret of Cross-Multiplication — When three terms of a proportion are known, the fourth is found by multiplying the means and dividing by the known extreme · Ratio and Proportion
  • Does the ratio change? — We use ratios in daily life. For example, to make rice we put 2 cups of water for 1 cup of rice — this is a 1:2 ratio. To make 2 cups of rice, multiply both numbers by 2: 2 cups of rice need 4 cups of water. This is called scaling a ratio. · Ratio and Proportion
  • Find the Fourth Proportional — Use cross-multiplication to turn a ratio puzzle into a simple equation. · Ratio and Proportion
  • The Proportion Test: Cross-Multiply — Check if 2:4 is equal to 5:10 by multiplying across the equals sign. · Ratio and Proportion
  • Ratios are Fractions — See how 3:5 is the same as 3/5 on the number line. · Ratio and Proportion
  • Unitary Method: Find the Cost of One — Use division to find the value of a single unit, then multiply for the answer. · Ratio and Proportion
  • Merging Like Terms: The 3x + 2x Puzzle — Learn to combine similar algebraic terms to simplify equations before solving for x. · Fundamental Concepts
  • Solving 3x + 2x = 20 — Combine like terms first, then divide to find x. · Fundamental Concepts
  • Combine Like Terms — Group the similar chips together before you divide. · Fundamental Concepts
  • Like Terms: The Sorting Hat — Only terms with the same variable part can combine. Watch 3x and 2x merge, but 3x and 5 stay apart. · Fundamental Concepts
  • Substituting values into expressions — Replace the variable with a number, then calculate the result step-by-step. · Fundamental Concepts
  • What is a Coefficient? — Spot the coefficient, variable, and constant in a term like 5x. · Fundamental Concepts
  • Is 'a' a letter or a number? — Treat the variable like a hidden number. Group the 'a' chips together. · Fundamental Concepts
  • From Words to Symbols: The First Equation — Learn to translate a sentence like 'Twice a number...' into algebra, then solve it step-by-step. · Framing Algebraic Expressions
  • From Words to Formula: Rectangle Perimeter — Turn 'length plus breadth, doubled' into a clean algebraic formula. · Framing Algebraic Expressions
  • From Pattern to Formula — Turn a repeating pattern into a single algebraic expression for the perimeter. · Framing Algebraic Expressions
  • From Pattern to Formula — Turn a growing shape pattern into a general rule for pattern number x. · Framing Algebraic Expressions
  • Order Matters in Subtraction — See why '5 less than x' means x - 5, not 5 - x. Order changes the answer! · Framing Algebraic Expressions
  • Crack the Code: Twice y plus Three — Translate 'three more than twice y' into algebra and solve for y. · Framing Algebraic Expressions
  • Three Times a Number — See why 'three times a number plus five' becomes 3x + 5, not 3(x + 5). · Framing Algebraic Expressions
  • Sharing the Pizza: x/4 — When we divide a variable by a number, we write it as a fraction. · Framing Algebraic Expressions
  • Five More Than x — Translate words into algebra. Watch 'x + 5' in action. · Framing Algebraic Expressions

Class 7

  • The Sign Flip Secret — Move numbers across the equals sign, but never forget to change their mood. · Integers
  • Adding Negative Integers — Watch how adding a negative moves you left on the number line. · Integers
  • Dividing Signed Integers — Use multiplication to check your division. Same signs give positive, different signs give negative. · Integers
  • The Sign Flip: Negative Times Negative — Solve 4x = -12. See how dividing by a positive keeps the sign, but the answer is negative. · Integers
  • Subtracting Negatives on the Number Line — Subtracting a negative is like adding a positive. Watch the arrows flip. · Integers
  • The Fraction Balancer — Master the move that clears denominators and reveals the hidden value. · Rational Numbers
  • Adding Fractions: The Common Ground — You cannot add halves and thirds directly. Expand them to sixths first. · Rational Numbers
  • Plotting 3/4 on the Number Line — Split the gap between integers into equal parts to find fractions. · Rational Numbers
  • The Magic of Multiplying Fractions — See how fractions shrink when you multiply them. No cross-multiplying needed! · Rational Numbers
  • Where do fractions live? — See where -3/4 lives: divide the line from -1 to 1 into 8 equal parts. · Rational Numbers
  • The Power Slide: Watching Exponents Grow — See how a small change in the exponent creates a massive change in the result. · Exponents
  • What does 2^4 actually mean? — Expand the exponent into multiplication to see what it really is. · Exponents
  • The Power of a Power Rule — Unpack (2^3)^2 to discover why we multiply exponents, not add them. · Exponents
  • The Power of Product Rule — See how (ab)^n splits into a^n * b^n by expanding the brackets. · Exponents
  • Multiply Powers: Same Base Rule — See why 2^3 * 2^4 is not 2^12. Expand, count, and discover the exponent addition rule. · Exponents
  • Dividing Powers: The Subtraction Trick — See why dividing same bases means subtracting the exponents. · Exponents
  • The Mystery of Power Zero — Why does any number raised to the power of 0 equal 1? Let's find out by dividing. · Exponents
  • The Invisible Multiplier — Discover how one number controls the entire relationship between two quantities. · Ratio and Proportion
  • Direct Proportion: The Constant Ratio — Explore how y = kx represents a constant ratio between two quantities. · Ratio and Proportion
  • The Magic Rectangle: Inverse Proportion — Watch how length and width change together while the area stays fixed. · Ratio and Proportion
  • Find the Mean Proportional — If x is the mean proportional between 4 and 9, solve x^2 = 36. · Ratio and Proportion
  • The Interest Equation — See how Principal, Rate, and Time work together to grow your money. · Simple Interest
  • Find Simple Interest — Plug in P, R, and T into SI = PRT/100. Watch the calculation unfold. · Simple Interest
  • Find the Rate: Rearranging SI — We know the Interest, Principal, and Time. Now, let's isolate R to find the rate. · Simple Interest
  • The Great Merge: Combining Like Terms — Learn to spot which terms can team up and which must stay apart. The secret to simplifying algebra. · Fundamental Concepts
  • Adding Algebraic Expressions — Combine like terms to add expressions. Watch how variables group together. · Fundamental Concepts
  • Building Expressions from Words — Turn a word problem into an equation. Watch how '2 more than' becomes '+ 2'. · Fundamental Concepts
  • Dividing Monomials: The Chip Split — Split the coefficient and the variable separately. Watch 15x become 5x. · Fundamental Concepts
  • The Distributive Property — Multiply a number by a bracket: 2(x + 3) = 2x + 6. Watch the magic of distribution. · Fundamental Concepts
  • Multiply Monomials: The 3-Variable Swap — See how coefficients multiply and variables group when expanding a product. · Fundamental Concepts
  • Subtracting Algebraic Expressions — Subtracting is adding the opposite. Watch how signs flip when the minus sign distributes. · Fundamental Concepts
  • Solve 3x + 7 = 22 — Drag +7 across the equals sign and watch it become −7. · Simple Linear Equations
  • The Scale of Justice — Keep the equation balanced. Whatever you do to one side, you must do to the other. · Simple Linear Equations
  • Balance the scale: x + 8 = 15 — Learn to undo addition by subtracting the same number from both sides. · Simple Linear Equations
  • Solve 4x = 20 — Divide both sides by 4 to free x. Watch the balance stay equal. · Simple Linear Equations
  • The Equals Sign is a Bridge — Treat = like a balance scale. If you add to one side, you must add to the other. · Simple Linear Equations
  • The Sign-Flip Magic — Watch what happens to a term when it jumps across the equals sign. · Simple Linear Equations
  • Unlock the Mystery Box: 3x + 4 = 19 — Peel back the layers of a two-step equation using inverse operations. · Simple Linear Equations
  • From Words to Equations — Translate a word problem into a linear equation and solve it step by step. · Simple Linear Equations
  • The Flip Rule: Inequality Magic — Solve equations, then discover why inequalities flip when you divide by negatives. · Inequalities
  • Solving Inequalities: Add & Subtract — Adding or subtracting keeps the inequality sign pointing the same way. · Inequalities
  • Graphing x > 3 on a Number Line — Learn when to use open circles and how to shade the solution ray. · Inequalities
  • What does x > 5 really mean? — It's not one number. It's a whole team of numbers waiting to be found. · Inequalities
  • The Great Inequality Flip — Watch what happens to the < sign when you multiply by a negative number. · Inequalities
  • Multiplying Inequalities by Positive Numbers — When you multiply both sides by a positive number, the direction stays the same. · Inequalities

Class 8

  • The Division Key: Unlocking x — Discover how division is the reverse of multiplication to find hidden values. · Rational Numbers
  • The Rational Sandwich — Find a fraction between 1/3 and 1/2 by making denominators match. · Rational Numbers
  • Plot -7/4 on the Number Line — Divide the gap between -1 and -2 into four equal parts to find the spot. · Rational Numbers
  • Order Doesn't Matter: Commutativity — Swap the terms. Watch the sum stay the same. · Rational Numbers
  • The Power of Powers: Exponent Rules — Discover why multiplying powers with the same base means adding their exponents. · Exponents (Powers)
  • Power of a Quotient — Simplify (2x/3)^3 using exponent laws step-by-step. · Exponents (Powers)
  • Fractional Exponents: The 1/2 Rule — Discover that a^(1/2) is just another way to write the square root of a. · Exponents (Powers)
  • The Negative Exponent Flip — A negative power doesn't mean a negative number. It means 'move to the bottom'. · Exponents (Powers)
  • Speed of Light in Scientific Notation — Convert 300,000 km/s into a compact number using powers of 10. · Exponents (Powers)
  • The Square Number Lighthouse — Slide the number, watch the square grow. Spot the perfect squares before you calculate them. · Squares and Square Roots
  • Is it a Perfect Square? — x² = 25 has TWO roots, one on each side of zero. Find them both on the number line. · Squares and Square Roots
  • Square Roots by Factorisation — Break 144 into prime factors. Pair them up to find the root. · Squares and Square Roots
  • Square Root by Prime Factors — Factorise 144 into primes, pair them up, and pull one from each pair. · Squares and Square Roots
  • Unsquaring 144: Prime Factorisation — Pair up prime factors to find the square root without a calculator. · Squares and Square Roots
  • Square 49 in your head — Use (a-b)^2 to turn a hard multiplication into simple squares and a product. · Squares and Square Roots
  • The Cube Explosion — Why cubing a number makes it grow much faster than squaring. · Cubes and Cube Roots
  • Extracting Cube Roots — Group prime factors in threes to find the cube root. · Cubes and Cube Roots
  • Spotting Perfect Cubes — Factorise 27x³ into a single cubed bracket to see the pattern. · Cubes and Cube Roots
  • The Snowball Effect: CI vs SI — Watch how interest earns interest. See why Compound Interest grows faster than Simple Interest over time. · Interest (Simple and Compound)
  • The CI Formula: A = P(1+r/100)^n — Watch how repeated interest builds into a single powerful formula. · Interest (Simple and Compound)
  • Compound Interest: Year by Year — Watch how interest earns interest. No formula, just logic. · Interest (Simple and Compound)
  • Cracking the SI Formula — Use inverse operations to find Principal, Rate, or Time from the Simple Interest formula. · Interest (Simple and Compound)
  • The Constant Ratio: Direct Variation — When one quantity grows, the other grows at the same rate. Find the hidden constant. · Direct and Inverse Variations (Including Time and Work)
  • The 'k' in Direct Variation — Find the hidden constant that links two changing quantities. · Direct and Inverse Variations (Including Time and Work)
  • The Rectangle Area Mystery — Watch how length and width dance to keep area constant. · Direct and Inverse Variations (Including Time and Work)
  • Work = Rate × Time — If 4 men take 6 days, how long for 8 men? Use inverse variation. · Direct and Inverse Variations (Including Time and Work)
  • The Lighthouse: Cutting Through the Noise — Learn to merge like terms with different signs to reveal the hidden structure of an equation. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • Add Polynomials: Group Like Terms — Align terms with same variables and powers. Combine coefficients. Watch the mess disappear. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • What is the Degree? — Find the highest power in a polynomial. Watch how terms combine. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • Divide a Polynomial by a Monomial — Split the fraction term-by-term. Do not cancel the whole denominator. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • Counting Terms: Mono, Bi, Tri — Use combine-like-terms to reveal the true number of terms in an algebraic expression. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • The Rectangle of Algebra — Expand (x+3)(x+5) by splitting it into four parts. No magic, just multiplication. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • The Distributive Property: Don't Forget the Last Term! — Watch how a monomial multiplies every single term inside the bracket. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • Subtracting Polynomials: The Sign Trap — Watch how the minus sign distributes to every term inside the bracket. · ALGEBRAIC EXPRESSIONS (Including Operations on Algebraic Expressions)
  • The Mystery of the Missing 40 — Why (a+b)^2 is not a^2 + b^2. Discover the hidden term that makes the identity work. · Identities
  • Mental Math: Square 98 Instantly — Use (a - b)^2 to solve 98^2 without long multiplication. · Identities
  • The Cube of a Sum — Expand (a + b)^3 step-by-step. Watch the identity emerge from multiplication. · Identities
  • Equation or Identity? — Test values to see if a statement is always true or only sometimes true. · Identities
  • The Difference of Squares Trick — See why (a+b)(a-b) always equals a² - b². No long multiplication needed. · Identities
  • The (a - b)² Identity Trap — Why (10 - 3)² is NOT 100 - 9. Watch the middle term appear. · Identities
  • The Trap of Squaring a Sum — Why (a + b)² is NOT a² + b². Watch the 'middle term' appear. · Identities
  • Splitting the Middle: The Factorisation Key — Unlock quadratic equations by splitting the middle term into two friends. · Factorisation
  • Factorise: Pulling out the Common — Think of brackets as a shared wrapper. Pull the common part out, keep the rest inside. · Factorisation
  • The Difference of Squares Pattern — See how x² - 25 splits into two factors. No middle term? That's the clue. · Factorisation
  • Factorise by Grouping: The Pair Game — Split the four terms into two teams. Find the common link in each team. · Factorisation
  • Detective Algebra: Factorise 2x^2 + 5x - 3 — No common factor? No difference of squares? Split the middle term to crack the code. · Factorisation
  • Spotting the Perfect Square — Recognise x^2 + 10x + 25 as (x + 5)^2 and factor it. · Factorisation
  • Splitting the Middle Term — Break x^2 + 7x + 12 into two binomials by splitting the 7x. · Factorisation
  • The Fraction Vanisher — Multiply both sides to clear fractions. Turn messy ratios into clean integers instantly. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • Solving Equations with Fractions — Clear the fractions by multiplying both sides by the LCM, then solve. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • Cracking the Code: Brackets in Equations — Use the distributive property to remove brackets before solving. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • Cracking Open Brackets in Equations — Expand first, then simplify. Don't let the brackets hide the path to x. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • Tug-of-War: x on Both Sides — When x appears on both sides, collect them on one side to solve. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • The Age Mystery: Solving Word Problems — Translate a story about ages into an equation, then solve it step-by-step. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • The Mystery of the Ages — Translate a word problem into an equation and solve for the unknown age. · LINEAR EQUATIONS IN ONE VARIABLE (With Problems Based on Linear Equations)
  • The Lighthouse Rule: When Inequalities Flip — Solve equations, then see how inequalities behave differently when multiplied by negatives. · LINEAR INEQUATIONS (Including Number Lines)
  • Solving Compound Inequalities — Keep the middle term sandwiched. Perform the same operation on all three parts. · LINEAR INEQUATIONS (Including Number Lines)
  • Graphing Inequalities: Open vs Closed — Learn when to use an open circle and when to use a closed dot on the number line. · LINEAR INEQUATIONS (Including Number Lines)
  • Solve: At Least 80 Marks — Translate 'at least' into a mathematical inequality and solve. · LINEAR INEQUATIONS (Including Number Lines)

Class 9

  • The Hidden Square Root — Simplify surds by hunting for perfect squares. Turn messy roots into clean multiples. · Rational and Irrational Numbers
  • Where does root 2 live? — Use the number line to see why √2 cannot be written as a simple fraction. · Rational and Irrational Numbers
  • Rationalise the Denominator — Multiply by the conjugate to remove the square root from the bottom. · Rational and Irrational Numbers
  • Rationalise 1/(2 + √3) — Multiply by the conjugate to clear the surd from the denominator. · Rational and Irrational Numbers
  • Adding Like Surds — Combine terms with the same root, just like algebraic variables. · Rational and Irrational Numbers
  • Multiply Surds: Root of Product — See why root 2 times root 3 becomes root 6. · Rational and Irrational Numbers
  • Taming the Surd: Simplifying √50 — Break down the number under the root to find perfect squares and simplify. · Rational and Irrational Numbers
  • Watch Money Compound Year by Year — Each year's interest is computed on the previous year's amount, not the original principal. · Compound Interest [Without Using Formula]
  • Interest on Interest: Year by Year — Watch how the principal changes every year in compound interest. · Compound Interest [Without Using Formula]
  • The 2-Year Gap: CI vs SI — Why Compound Interest earns extra rupees in the second year. · Compound Interest [Without Using Formula]
  • The Snowball Effect: Compound Interest — Watch how money grows faster than simple addition. The power of earning interest on interest. · Compound Interest [Using Formula]
  • Compound Interest: The Formula in Action — Watch how P, r, and n combine to calculate the final amount using A = P(1 + r/100)^n. · Compound Interest [Using Formula]
  • Solve CI for Rate: The Cube Root Trick — Isolate the bracket, take the cube root, and find the rate r. · Compound Interest [Using Formula]
  • Depreciation: The Value Drop — Use A = P(1 - r/100)^n to find the value of an item after it loses value. · Compound Interest [Using Formula]
  • The Hidden Recipe of (a+b)^3 — Discover the four secret ingredients inside a cubic expansion. · Expansions
  • Expanding (a + b)³ — Watch how a cube of a binomial expands into four terms using the standard identity. · Expansions
  • Expand (2x + 5)² — Watch the identity (a+b)² = a² + 2ab + b² in action with real coefficients. · Expansions
  • Expand (x + 3)(x + 5) — See how the middle term is the sum of the constants, and the last term is their product. · Expansions
  • Expanding (a + b + c)² — Break the trinomial into a binomial and a single term to expand safely. · Expansions
  • Factor and Find the Roots — Difference of squares unlocks both solutions of x squared minus 9 in one move. · Factorisation
  • Factorise with Substitution — Use a temporary variable u to simplify complex polynomials before factoring. · Factorisation
  • Difference of Cubes: x³ - 8 — Factor x³ - 2³ using the difference of cubes identity. · Factorisation
  • Factorise 2x² + 7x + 3 — Split the middle term to unlock the brackets when the leading coefficient is not 1. · Factorisation
  • The Magic of Elimination — When two equations clash, variables vanish. See how adding equations solves the puzzle. · Simultaneous (Linear) Equations [Including Problems]
  • The Cross-Multiplication Shortcut — Solve two equations without eliminating variables one by one. · Simultaneous (Linear) Equations [Including Problems]
  • Solve Simultaneous Equations: Elimination — Multiply to match coefficients, then subtract to eliminate one variable. · Simultaneous (Linear) Equations [Including Problems]
  • Find the Intersection Point — Plot two lines and see where they meet to solve simultaneous equations. · Simultaneous (Linear) Equations [Including Problems]
  • Substitution Method: Solve the Pair — Swap one variable for its expression. Turn a pair into a single equation. · Simultaneous (Linear) Equations [Including Problems]
  • From Words to Equations — Turn a cricket score story into a simultaneous equation and solve it. · Simultaneous (Linear) Equations [Including Problems]
  • The Power of Negative Exponents — Slide the exponent to discover what happens when powers go below zero. · Indices [Exponents]
  • Solve Exponential Equations — Match the bases to unlock the exponent. · Indices [Exponents]
  • Cracking the Code: 8^(2/3) — Decode fractional exponents by breaking the fraction into a root and a power. · Indices [Exponents]
  • Simplify: Nested Powers — Master the order: expand brackets, multiply, then divide. · Indices [Exponents]
  • The Logarithm Decoder — Logarithms are exponents in disguise. Slide the base and argument to unlock the hidden power. · Logarithms
  • Change of Base Formula — Convert log_b(a) into a ratio of common logs. · Logarithms
  • The Logarithm Decoder — Rewrite exponential equations as logarithms using the definition. · Logarithms
  • Solve log Equations: The Bridge — Convert log form to exponential form to isolate the variable. · Logarithms
  • The Power Rule: Exponents Become Multipliers — log(a^n) = n times log a · Logarithms
  • Splitting log(ab) into log a + log b — A product inside the log becomes a sum outside. · Logarithms
  • The Quotient Rule: A Subtraction in Disguise — log(a/b) is just log a minus log b · Logarithms
  • The Rule of Signs in Inequalities — Why dividing by a negative number flips the inequality sign, unlike equations. · Inequalities
  • Word Problems: Linear Inequalities — Translate a real-world scenario into an inequality and solve it. · Inequalities
  • Inequalities: The Negative Flip — Solve -2x + 5 < 13. Watch what happens when you divide by a negative number. · Inequalities
  • From Inequality to Set-Builder — Solve the inequality, then write the solution in set-builder notation. · Inequalities
  • The Slope and Intercept Dance — Discover how m tilts the line and c lifts it up in y = m*x + c · Co-ordinate Geometry
  • The Zero Trap: Points on Axes — Find the secret coordinate for points that sit exactly on the x or y axis. · Co-ordinate Geometry
  • Plotting Points: The Coordinate Map — Treat coordinates like an address: X is the street, Y is the floor. Plot (3, 4) to see how it works. · Co-ordinate Geometry
  • Quadrant Detective: Where is the Point? — Drag the point to each corner. Watch how the signs of x and y change. · Co-ordinate Geometry
  • The Intersection Point — Find where two lines meet to solve simultaneous equations graphically. · Graphical Solution
  • The Great Railway Mystery — Two parallel tracks never meet. Discover why some equations have no solution. · Graphical Solution
  • Plotting y = 2x + 1 — Calculate three points, check the pattern, and draw the line. · Graphical Solution
  • From Table to Graph: Plotting y = 2x + 1 — Fill the table, plot the points, and draw the line. Watch how the equation becomes a picture. · Graphical Solution
  • The Meeting Point — Find the solution to two equations by seeing where their lines cross. · Graphical Solution
  • The Lighthouse Beam: Finding Distance — How the slope and intercept of a line relate to the distance of points from the origin. · Distance Formula
  • Are they in a straight line? — Use the distance formula to check if three points are collinear without graphing. · Distance Formula
  • Distance from (0,0) to (3,4) — Use the distance formula to find the length of a line segment starting at the origin. · Distance Formula

Class 10

  • The GST Multiplier: Why 18% is 1.18 — Visualise how tax rates stretch prices. Slide the slope to find the magic GST multiplier. · GST [Goods and Services Tax]
  • Discount First, Then GST — Why the order matters: calculating the final price of a ₹5000 phone. · GST [Goods and Services Tax]
  • Cracking the GST Bill — Calculate the total cost including CGST and SGST using algebra. · GST [Goods and Services Tax]
  • Intra vs Inter: The ₹500 Shirt — Watch how CGST and SGST split for local buys, while IGST stays together for cross-state orders. · GST [Goods and Services Tax]
  • The Shape of Saving — Watch how monthly deposits build maturity over time in a Recurring Deposit. · Banking (Recurring Deposit Accounts)
  • RD Interest: The Sum Formula — Derive and apply I = P * n(n+1)/2 * r/(12*100) for recurring deposits. · Banking (Recurring Deposit Accounts)
  • RD Maturity: Total Deposit + Interest — See how total deposits and interest combine to give the maturity value. · Banking (Recurring Deposit Accounts)
  • The Yield Lever: Dividends vs Price — Why does a stock's return change when the price moves, even if the dividend stays the same? · Shares and Dividends
  • Calculate Your Dividend — Find the cash return from shares using rate and nominal value. · Shares and Dividends
  • Face Value vs Market Value — Why a Rs 100 share might cost you Rs 150. Solve for the premium. · Shares and Dividends
  • Calculating Yield of Shares — Use the formula Yield = (Income / Market Price) x 100 to find the return rate. · Shares and Dividends
  • The Flip Switch: Solving Linear Inequations — Master the sign flip when multiplying or dividing by a negative number. · Linear Inequations (In one variable)
  • Brackets on the Number Line — Square brackets [ ] mean 'include this number'. Curly { } mean 'integers only'. · Linear Inequations (In one variable)
  • Solving Inequalities: Integer Solutions — Solve the inequality, then pick only the whole numbers that fit. · Linear Inequations (In one variable)
  • Find the Max Integer Solution — Solve an inequality from a word problem, then pick the largest valid integer. · Linear Inequations (In one variable)
  • The Shape of a Quadratic — Slide the sliders to see how a, b, and c sculpt the parabola. Find the hidden roots. · Quadratic Equations
  • Completing the Square: Perfect Fit — Turn x^2 + 4x into a perfect square by adding just the right number. · Quadratic Equations
  • The Discriminant: A Crystal Ball for Roots — Calculate b² - 4ac to predict if roots are real, equal, or imaginary without solving. · Quadratic Equations
  • The Discriminant Detective — Use the discriminant to predict if roots are real, equal, or imaginary. · Quadratic Equations
  • The Discriminant: A Crystal Ball — Calculate D to predict if roots are real, equal, or imaginary without solving. · Quadratic Equations
  • The U-Shape: Parabolas — Explore how a, b, and c shape the graph of a quadratic equation. · Quadratic Equations
  • Spot the Quadratic: Standard Form — Rearrange terms to find a, b, and c in ax² + bx + c = 0. · Quadratic Equations
  • The Quadratic Formula in Action — Plug in a, b, and c. Watch the formula simplify to the roots. · Quadratic Equations
  • Solve by Factoring: The Zero Trick — Split the middle term, factorise, and use the Zero Product Property to find roots. · Quadratic Equations
  • Secrets Hidden in the Coefficients — Find the sum and product of roots without actually solving the quadratic equation. · Quadratic Equations
  • The Rectangle's Hidden Quadratic — How area and perimeter constraints create a quadratic equation to solve for sides. · Solving (simple) Problems (Based on Quadratic Equations)
  • Age Problem: Son and Father — Translate a word problem into a quadratic. Solve, then check if the answer makes sense. · Solving (simple) Problems (Based on Quadratic Equations)
  • Area Problem: Garden Pathway — Translate a real-world garden problem into a quadratic equation and solve it. · Solving (simple) Problems (Based on Quadratic Equations)
  • Consecutive Odd Integers — Translate a word problem into a quadratic. Solve for the number. · Solving (simple) Problems (Based on Quadratic Equations)
  • Train Speed: The Quadratic Model — Translate a speed-time word problem into a quadratic equation and solve it. · Solving (simple) Problems (Based on Quadratic Equations)
  • The Cross-Multiplication Bridge — Turn a tricky fraction equation into a simple linear one. · Ratio and Proportion (Including Properties and Uses)
  • Alternendo and Invertendo — Rearrange a proportion to swap places or flip fractions. · Ratio and Proportion (Including Properties and Uses)
  • Componendo & Dividendo Shortcut — Solve (x+2)/(x-2) = 7/3 using the ratio shortcut. · Ratio and Proportion (Including Properties and Uses)
  • The Middle Term Trick — When a:b = b:c, the middle term is the geometric mean. · Ratio and Proportion (Including Properties and Uses)
  • The Zero Test: Seeing Factors in Plain Sight — If plugging in a number makes the polynomial vanish, you've found a factor. Here is the proof. · Factorization of Polynomials (Remainder and Factor Theorems)
  • Cracking a Cubic with One Root — Use the Factor Theorem to split a cubic into a linear factor and a quadratic. · Factorization of Polynomials (Remainder and Factor Theorems)
  • The Zero Test: Factor Theorem — If p(a) = 0, then (x - a) is a factor. Verify it by expanding. · Factorization of Polynomials (Remainder and Factor Theorems)
  • Find a root by trial — Test divisors of the constant term to find an integer root. · Factorization of Polynomials (Remainder and Factor Theorems)
  • Polynomial Division: The Reverse Process — If (x-2) is a factor, multiplying by the quotient must give back the original polynomial. · Factorization of Polynomials (Remainder and Factor Theorems)
  • The Remainder Theorem Shortcut — Skip long division. Plug in the number to find the remainder instantly. · Factorization of Polynomials (Remainder and Factor Theorems)
  • The Matrix Cell: It's Just Addition — Matrices aren't magic. They are just numbers in boxes, obeying the same rules you already know. · Matrices
  • Matrix Addition is Element-by-Element — Add same-order matrices by summing the cells that share an address. · Matrices
  • The Two Special Matrices: O and I — Zero matrix annihilates; identity matrix preserves. · Matrices
  • Matrix Multiplication: Row meets Column — Watch how a single cell in the product matrix is built from a dot product. · Matrices
  • Matrix Multiplication is NOT Commutative — AB and BA can give different matrices — even when both products exist. · Matrices
  • Reading a Matrix: Rows, Columns, Cell Names — A 2x3 matrix has 2 rows and 3 columns. The element a_23 lives in row 2, column 3. · Matrices
  • Scalar Times Matrix: Every Cell Scales — Multiply a matrix by a number — every entry gets multiplied. · Matrices
  • Spotting Matrix Types — Use algebra to verify if a matrix is square, diagonal, or identity. · Matrices
  • The Steady Step: Building Arithmetic Progressions — Slide 'a' and 'd' to see how a constant difference creates a predictable pattern. · Arithmetic Progression
  • Two Terms, One Sequence — Given two non-consecutive AP terms, solve a 2x2 system to find a and d. · Arithmetic Progression
  • The Nth Term Formula: Why (n-1)? — Unpack the formula a_n = a + (n-1)d to find the 20th term of an AP. · Arithmetic Progression
  • Is it an AP? — Use the formula to check if the difference between terms is constant. · Arithmetic Progression
  • Sum of n Terms: Pair Them Up — S_n = n/2 * (2a + (n-1)d) — the formula falls out of pairing first and last terms. · Arithmetic Progression
  • The Saving Plan: AP in Daily Life — Every month you save Rs 100 more than the previous month. After 12 months, how much total? · Arithmetic Progression
  • The Power of the Ratio — See how a single multiplier shapes the entire curve of a Geometric Progression. · Geometric Progression
  • The nth Term Formula: a * r^(n-1) — Find any term in a GP without listing them all. · Geometric Progression
  • Spot the Geometric Pattern — Divide each term by the previous one. If you get the same ratio every time, it is a GP. · Geometric Progression
  • Sum of n GP Terms: The Compact Formula — S_n = a(r^n - 1)/(r - 1). One line replaces adding ten terms by hand. · Geometric Progression
  • AP vs GP: Add or Multiply? — AP: each term is previous + d. GP: each term is previous * r. Different DNA. · Geometric Progression
  • The Lighthouse Principle: Finding the Middle — Visualise how the midpoint formula dictates the path of a line through two points. · Section Formula and Mid-Point Formula
  • The Midpoint: Average the Coordinates — The midpoint of (x1,y1) and (x2,y2) is just their coordinate-wise average. · Section Formula and Mid-Point Formula
  • External Division: A Point Beyond the Segment — Same formula with a minus: a point dividing PQ externally in ratio m:n lies OUTSIDE the segment. · Section Formula and Mid-Point Formula
  • Internal Division: Cutting a Line in a Ratio — A point dividing PQ internally in ratio m:n has coords ((mx2+nx1)/(m+n), (my2+ny1)/(m+n)). · Section Formula and Mid-Point Formula
  • Slope-intercept form: y = mx + c — Move the m and c sliders. Watch the equation, graph, and table change together. · Equation of a Line
  • Drop a Perpendicular — The distance from a point to a line is measured along the perpendicular. Slide to feel it shrink to zero when the point lies on the line. · Equation of a Line
  • x-Intercept Meets y-Intercept — When a line is described by where it cuts the axes, the intercept form is the cleanest way to write it. · Equation of a Line
  • Parallel Lines Share a Slope — Two non-vertical lines are parallel iff they have the SAME slope (and different intercepts). · Equation of a Line
  • Negative Reciprocal Slopes — Two non-vertical lines are perpendicular exactly when the product of their slopes is -1. · Equation of a Line
  • Anchor Any Point — Use the point-slope form to write the equation of a line through any specific point. · Equation of a Line
  • Slope from Two Points: Rise Over Run — Given (x1,y1) and (x2,y2), slope m = (y2-y1)/(x2-x1). · Equation of a Line
  • Two Points Make a Line — Given any two points, you can find the slope and write the line's equation. · Equation of a Line
  • The Unshakable Identity — Why sin²x + cos²x is always 1, no matter how x changes. · Trigonometrical Identities
  • Proving an Identity: Show LHS Equals RHS — Prove (1 - sin)(1 + sin) = cos^2 using the Pythagorean identity. · Trigonometrical Identities
  • The Pythagorean Identity: sin Squared Plus cos Squared — For every angle, sin^2 + cos^2 = 1 — the unit circle in algebraic form. · Trigonometrical Identities
  • The Quotient Identity: tan as sin Over cos — tan(theta) is defined as sin(theta) / cos(theta) — every identity proof starts here. · Trigonometrical Identities
Chat with us

Subscription Status