Complete Mathematics/Math Course through Animated videos2023

Use the square root technique for numbers 1 to 200. Split two-digit groups, consult a table of squares and last digits, and determine the correct root by between-square checks.

Master the cube root technique for numbers 1 to 200 using a two-part method that splits the number and uses cube range plus last-digit rules to find the root quickly.

Practice questions on square roots and cube roots with quick, timed drills, solving example problems to sharpen speed and accuracy for each question day.

Master two multiplication techniques: technique 1 builds products from digit-based parts, while technique 2 uses complements to a hundred, demonstrated with near-hundred examples.

Explore technique three for multiplying numbers near a hundred by decomposing them into parts above a hundred, computing sums and products, and concatenating results as shown in 103×109 and 103×102.

Master the 100-based mental math technique by expressing numbers as deviations from 100, adding those deviations, and regrouping to final results with examples.

Learn to simplify products using the difference of squares identity a^2 - b^2 to compute nearby numbers quickly, with examples like 53×47, 98×82, 23×37, and 71×69.

technique 6 presents an easy two-digit multiplication method using cross products of digits, with step-by-step examples such as 38 into 292, 54 and 268, and 79 into 83.

Learn technique 7, a pictographic line method to multiply by drawing lines for each digit and counting intersections. Add carries to previous parts to get the final product quickly.

practice questions on multiplication technique guide you through solving example questions, using a 15-second timer to improve speed and accuracy.

Learn a universal multiplication technique for double-digit numbers, using straight lines, cross marks, and carries to compute products like 23×71 and 84×296 step by step.

Technique 9 teaches a cross-mark, straight-line approach for three-digit multiplication, splitting numbers into four parts, summing partial products, and carrying extras to the previous part.

Master eleven's rule for quick multiplication by eleven and the square technique for numbers containing ones, using ascending-then-descending digit arrangement and edge-sum carries.

Learn the nine's rule technique to multiply numbers by 99, 9999, and 999999 by reducing the other factor by one and subtracting from all nines, with worked examples.

Master the 9's rule technique 2 to multiply by nines when digit counts differ, by reducing the first part by one, padding zeros to align digits, and subtracting from nine.

Explore the 9's rule technique 3 for multiplying by 99, learning how to split numbers, increment the first part, and perform quick subtractions for two-digit and three-digit cases.

Practice with example questions on 11's rule and 9's rule, solving each question within a fifteen-second time limit to build speed and accuracy.

Classify numbers into real and imaginary, and distinguish rational from irrational numbers, integers as negative, zero, or positive, and decimals and fractions including recurring, non-recurring, proper, improper, and mixed forms.

Explore how integers are classified into even and odd. Also distinguish natural and whole numbers, primes, composites, numbers that are neither prime nor composite, twin primes, and perfect numbers.

Explore the Fibonacci sequence, where each number is the sum of the two preceding ones, and apply Boardman's rule for order of operations—brackets, division, multiplication, addition, and subtraction.

explore decimals and place value from before the decimal to millions, including place and face value of digits, and rounding to nearest hundreds, tens, units, and thousands.

Convert decimals to fractions and recurring decimals by setting x equal to the number, using bar notation to identify repeats, multiplying to shift decimals, subtracting to isolate x, and solving.

Master adding and subtracting fractions by finding a common denominator, using 30 as the target, and applying cancellation and reciprocals in multiplication and division.

Convert proper fractions to mixed fractions and back, using division and remainders. Add and subtract mixed fractions, and explore factors, multiples, and vectors.

Explore lcm and hcf concepts by listing multiples and factors, solving examples like lcm of 4, 6, 8 as 24 and hcf as 2, and using factorization methods.

Explore how to compute lcm and hcf of numbers using prime factorization, and apply formulas to find the sum and number of factors with step-by-step examples.

Learn how to find the maximum power of primes in factorials by counting twos and fives to determine trailing zeros, and compute the highest power of six in a factorial.

Explore divisibility rules for numbers 2 through 12, using last digits, digit sums, and alternating sums, with practical example to determine divisibility quickly.

Introduce ratio and proportion, differentiating ratio from fraction, and illustrate with class examples. Demonstrate how ratios express relationships and how combining classes affects boy-to-girl ratios.

divide twenty-four thousand dollars by the ratio 3:4:5 to allot shares for a, b, and c (6k, 8k, 10k). learn to scale ratios to a common basis for x:y:z:w.

Explore proportion as a relation where price scales with quantity: 50 cents for 10 chocolates and 70 cents for 14, with product of extremes equal to product of means.

Explore the main (mean) proportion, the fourth proportion, and direct and inverse proportions with examples like speed, distance, heat, and water levels.

Learn the concept of percentage (per cent) defined as by a hundred, and master calculating percentages using the formula opt-in value divided by total value multiplied by hundred for comparison.

Learn to compute percentage change using the formula change over original value times 100, with an example from 350 to 450, and convert percentages to fractions by dividing by 100.

Practice solving percent problems by computing various percentages, such as 20 percent of 600, 39 percent as 40 percent minus 1 percent, and 50 percent of 300, using step-by-step calculations.

Explore percent-based price calculations with step-by-step examples, including discounts, increases, and percentages of amounts, to determine final prices for shirts and televisions.

Apply percent-change calculations from an initial value of 100, using change divided by the original value times 100, to solve price and population increases and decreases.

Explore profit and loss concepts by relating cost price, selling price, and mark price (MRP), and apply formulas for profit, loss, and discount percentages.

Graphically analyze pricing by applying a 20 percent discount and a 20 percent profit against a 600 mark price to find cost and selling prices.

Learn to calculate profit or loss percentage from cost price and selling price through mobile price examples and scenarios where equal selling prices or equal cost prices yield overall results.

Learn to compute an initial car price from successive discounts of 30% and 40%, by equating 42x to 1,026,000 and then setting initial price as 100x.

Learn the difference between simple and compound interest, define principal, time, rate, and amount, and apply the simple and compound formulas to calculate interest and totals.

Explore averages by distinguishing linear data from nonlinear data and applying the first plus last divided by two rule, with examples of consecutive numbers and even-number sequences.

Explore nonlinear data sets with no inherent order, learn to compute simple and weighted averages, and apply the class example to obtain a weighted mean of 14.4.

Explore average problems by deriving missing scores and totals from partial averages, including cricket team scoring and how a new student shifts class averages and totals.

The lecture introduces mixtures and allegations, showing how to equalize two vessels with different water-to-resin ratios using a common multiple of five and seven, then combine scaled amounts.

Explore calculating mixing ratios for two resins by using common multiples to equalize volumes, and derive a final mixture ratio of 5:12.

Analyze a milk-to-water mixture problem, convert a 4:1 ratio to 1:4 by adding water; compute initial volumes and solve using cross-multiplication to determine 40 liters of water to add.

Define speed as distance divided by time, and show average speed as distance divided by total time, with relative speed as the speed difference in motion.

two trains start at six am from opposite stations, traveling at 60 mph and 80 mph; they meet after 5.5 hours, 440 miles from station b.

Compute a three-leg journey between X and Y, each leg 600 miles, at 40, 50, and 60 mph; derive the average speed as 1800/37 mph.

Solving the house-to-office distance from two speeds, 20 m/s and 30 m/s, with six and four seconds difference, yields 600 meters and 24 seconds as the normal travel time.

Set up a proportion to scale a 7-in-400 inspection rate to 20,000 bulbs and compute 7 times 20,000 divided by 400 to find 350 inspected.

Calculate the profit from a $120 performance by subtracting 43% costs, leaving about $68.40 in profit when eight attendees attend.

Estimate the unknown element's atomic weight by subtracting 20% of calcium's 40 amu, yielding about 32 amu.

Explore geometry fundamentals by studying lines and angles, including parallel and perpendicular lines, supplementary and complementary angles, vertical opposite angles, and the role of transversals in proportional divisions.

Explore triangles by examining angle-side relationships: interior angles sum to 180 degrees, exterior angles equal the sum of opposite interior angles, and any two sides exceed the third.

Learn triangle area formulas by using base and height, derive height in equilateral triangles via Pythagoras, and find area equals sqrt(3)/4 a^2.

Explore the pythagorean theorem, the hypotenuse concept, and classic triplets such as 3-4-5 and 5-12-13, then compare similar and congruent triangles through proportionality.

Identify triangle types—scalene, acute, right, obtuse, isosceles, equilateral—and study centers like incenter, circumcenter, excenter, centroid, orthocenter, plus the midpoint theorem showing area is one fourth.

Explore special triangles, including 30–60–90 and 45–45–90. Learn how equilateral splits produce these right triangles and derive their side ratios using Pythagoras.

Explore quadrilaterals, four-sided figures with interior angles totaling 360 degrees. Identify square, rectangle, rhombus, parallelogram, and trapezius, and note that opposite sides and angles are equal, with diagonals bisect.

Explore how polygons form by adding sides—from quadrilateral to pentagon and beyond—and learn that interior angles sum to (n-2) times 180 degrees and exterior angles sum to 360 degrees.

Explore circle basics by examining radius, diameter, center, chord, arc, and tangent, and learn major and minor arcs and segments, circumference, arc length, and sector area.

An angle in a semicircle is 90 degrees, so any triangle is right. Angles in the same segments are equal; opposite angles in a cyclic quadrilateral sum to 180 degrees.

We explore three-dimensional geometry with cuboids and cubes, learning about lateral surface area, total surface area, volume, and the space diagonal.

Explore 3-d geometry by deriving cylinders, cones, spheres, hemispheres, prisms, and pyramids, with lateral and total surface areas and volumes.

Explore coordinate geometry basics: four quadrants, distance between points, slope, midpoint, x-intercept and y-intercept, and line equations including intercept forms and y = mx + c.

Explore algebra basics through algebraic expressions with variables and constants, such as 3x+4y+3, and learn about monomials, binomials, and trinomials in simple equations.

Learn to solve quadratics by the ac factoring method, factor x^2+x-6 to (x+3)(x-2), find roots 2 and -3, and apply the quadratic formula and discriminant.

Demonstrates exponent rules and basic power formulas, including (x+y)^2, (x−y)^2, (x+y)^3, and the expansion of x^2+y^2+z^2 with cross terms.

Explore functions and algebraic expressions, and learn to solve simple linear equations with two variables using elimination, revealing unique, infinite, or no solutions as lines intersect or run parallel.