Fundamentals & Basics of Maths through Animated Videos -2023

Explore the classification of numbers, including real and imaginary numbers, rational and irrational numbers, and integers, then examine decimals and fractions such as recurring, non-recurring, proper, improper, and mixed.

Classify integers into even and odd, with examples -10, 0, 2, 4 and -3, -1, -5; differentiate natural and whole numbers, primes, composites, twin primes, and perfect numbers like 6.

Explore the Fibonacci sequence, where each number is the sum of the two previous ones, and learn to apply boardman's rule—brackets, division, multiplication, addition, subtraction.

Explore decimal place value from tenths to millions, read numbers before and after the decimal, and determine place value, face value, and rounding to hundreds, tens, and units.

Convert decimals to fractions and recurring decimals by using the 100x minus x method to isolate the fractional part. Work through examples like 3.6868 repeating to find 365/99.

Learn to add and subtract fractions by converting to a common denominator, here 30, then multiply and divide by canceling factors and using reciprocals.

Convert proper fractions to mixed fractions and back, learn to add and subtract mixed fractions by separating whole numbers and fractions, and explore factors and multiples.

Explore lcm and hcf concepts through practical division steps and learn to compute sum and number of factors using prime factorization formulas.

Count trailing zeros in factorials by dividing by five to tally fives, as seen in 20!, 100!, and 1000!, and determine 6^48 in 100! by comparing twos and threes.

Learn divisibility rules for common factors such as 2, 3, 4, 5, 7, 8, 9, 10, 11, and 12, using last digits, digit sums, and subtraction methods to test numbers.

Divide a 24,000-dollar total into 3:4:5 shares for a, b, and c, yielding 6,000, 8,000, and 10,000 dollars. Learn to combine ratios by scaling to equalize values.

Explain proportion as a relation where ratios scale, using 50 cents for 10 chocolates and 70 cents for 14 chocolates, showing the product of extremes equals the product of means.

Explore the types of proportion, including main (mean) and fourth proportions, and learn direct and inverse proportion with practical examples like speed vs distance and heat vs water level.

Explain the concept of percentage as the ratio of part to total, multiplied by a hundred. Demonstrate calculating percentages with examples and comparing scores.

Apply the percentage change formula, (new minus old) over old times 100, using the 350 to 450 marks example, and convert percentages to fractions by dividing by 100.

Explore percent problems by calculating 20 percent of 600 equals 120, interpreting 39 percent as 40 percent minus 1 percent, and solving 250 percent of 300 using a right-to-left approach.

Compute percent off and percent of amounts from 50 percent of 4000, including 30, 20, 40, and 10 percent steps, to determine final price and overall change.

Master fundamentals of math through animated videos by exploring percentage change with practical examples in price, population, and percent adjustments.

Examine how cost price, selling price, and mark price define profit, loss, and discount percentages using the given formulae for selling price, cost price, and mark price.

Explore a graphical example linking cost price, selling price, and market price using a 20 percent discount and a 20 percent profit, with a mark price of 600 dollars.

Explore how to calculate profit or loss percentages using practical price scenarios, including equal cost purchases and combined profit and loss cases for mobile items.

Apply successive discounts of 30% and 40% to a car's price to reach 1,260,000, then reverse them to find the initial price of 3,000,000.

Explore the difference between simple interest and compound interest, define the principal, rate, and time, and apply formulas to calculate amounts under different compounding frequencies.

Learn to compute averages for linear data using first plus last over two, and distinguish nonlinear data by order. Use consecutive and even-number examples to find the second highest.

Explore nonlinear data with no inherent order and learn to compute simple and weighted averages, illustrated by a class example.

Explore solving average problems: deduce a player's score when an entry is counted twice, and determine a new student's weight from a shifting class average.

Explains mixtures as combinations of two or more substances and shows how to combine two vessels with different ratios using common multiples to find total volumes.

Solve a two-resin volume ratio problem by using common multiples to align volumes, compute each part, and derive the final mixture ratio.

Starting with 64 liters of milk and 16 liters of water in a 4:1 milk-to-water mix, add 240 liters of water to reach a 1:4 ratio.

Learn speed, average speed, and relative speed with formulas speed = distance divided by time and average speed = total distance divided by total time, plus opposite- and same-direction examples.

calculate the meeting time of two trains starting at six, one at 60 mph and the other at 80 mph from opposite stations, and determine the distance from station B.

Determine the average speed by dividing the total distance of 1800 miles by the total time of 37 hours across three legs at 40, 50, and 60 mph.

Equate the two travel scenarios—20 m/s six seconds late and 30 m/s four seconds early—to find the normal distance and time between house and office.

Explore lines and angles, including line types, parallel and perpendicular lines, and vertical opposite angles. Know supplementary and complementary angles, and line division on parallel lines with transversals.

Explore triangles basics: the angle sum is 180 degrees, the longest side sits opposite the largest angle, and exterior angles equal the sum of opposite interior angles.

Derive triangle area using base times height, with height from perpendiculars and Pythagoras. For equilateral triangles, compute height as sqrt(3)/2 times the side to obtain area sqrt(3)/4 a^2.

Explore the Pythagorean theorem: the hypotenuse is opposite 90-degree angle and c squared equals a squared plus b squared, with 3-4-5 triplets and multiples illustrating ratios and congruent triangles.

Explore types of triangles—scalene, isosceles, equilateral; learn acute, obtuse, and right triangles, plus centers like the incenter, circumcenter, excenter, and centroid; and the midpoint theorem with area relations.

Explore special triangles, including 30-60-90 and 45-45-90, and learn how altitude in an equilateral triangle reveals key side ratios and hypotenuse relations.

Discover quadrilaterals as four-sided figures with 360-degree angle sums and various types: square, rectangle, rhombus, parallelogram, trapezium, highlighting diagonals, opposite sides, and area formulas.

Explore polygons by adding sides from quadrilateral to shapes, relate interior angle sums to triangles, apply exterior angle sums of 360 degrees, and compute diagonals with n(n-3)/2 for regular polygons.

Explore circle basics: radius, diameter, center, segments, arc, and tangent; distinguish major and minor segments, and learn arc length and sector area calculations.

Explore circle properties: semicircle theorem yields right triangles, equal angles in the same segment, and center angle doubling the angle at circle; cyclic quadrilaterals sum opposite angles to 180 degrees.

Explore three dimensional geometry by analyzing cuboids and cubes, deriving lateral and total surface areas, calculating volume, and finding the maximum rod length that fits inside each figure.

Cover cylinders, cones, spheres, hemispheres, prisms and pyramids, deriving lateral and total surface areas and volumes from base circles and polygons, with radius and height as key parameters.

Explore coordinate geometry by locating points in four quadrants, calculating distances, slopes, midpoints, and line equations, including intercepts and forms like slope-intercept, point-slope, and two-point forms.

Explore algebra by examining algebraic expressions with operations, variables, and constants, such as 3x + 4y + 3, and identify forms like binomial and trinomial.

factor the quadratic x^2+3x-2x-6 to get roots 2 and -3, and learn the quadratic formula with discriminant and the sum and product of roots.

Learn the basics of exponents and key formulas, including product and power rules, and expand binomial expressions like (x+y)^2 and (x+y)^3.

Explore how functions and algebraic expressions define operations, solve simple equations using coefficient elimination, and analyze line intersections to identify zero, infinite, or unique solutions.

Explore inequalities, solving for x in examples like 3x+4 ≥ x+7 and 3x+4 ≤ 2x+7, with number-line visuals; learn how addition, subtraction, and multiplying or dividing affect signs, with negatives.

Explore how absolute values and the modulus function transform inequalities into ranges for x, such as |x|≥5 yielding x≤−5 or x≥5, and |x−3|<3 yielding −3<x<3.

Factor the quadratic x^2-4x+3 to get roots 1 and 3, then apply zero-product reasoning to find x≤1 or x≥3 for ≥0, and 1<x<3 for >0.

Represent x^2 - 4x + 3 as (x-1)(x-3); zeros at 1 and 3; solve >0 with x<1 or x>3, and <0 between 1 and 3, illustrated by the graph.

Solve a spring-mass problem by substituting l = 73 into the linear relation l = 24 + 3.5 m, yielding m = 14.

Demonstrates solving simple linear equations with addition and division, using examples like 4x + 12 = 8 and 2x + 7, guiding steps to reach 2x + 7 = 5.

Learn how to find a parabola's x-intercepts by setting y to zero, factoring x^2-6x+8 to (x-4)(x-2), and identifying intercepts (2,0) and (4,0).

Solve a linear equation about a game score: starting with k points, losing two points per failed task, for 100 failures yielding a final score of 200.

Explore the basics of algebra by using letters to represent numbers and unknown quantities, learn about variables, and apply algebraic expressions and operations to solve puzzles and everyday problems.

Multiply the apples in a box (30) by the number of boxes (n) to obtain the total number of apples. The resulting expression is 30n.

Explore classification of expressions as monomials, binomials, and trinomials with examples like 3x+5y, x+y-7xy, and z^2-3z+5, and distinguish like versus unlike terms.

Explore permutations and combinations through examples, showing how order matters in permutations and how selection ignores order, with two-at-a-time and three-person scenarios.

Learn how to arrange versus select three people from ten, using a slot method and factorial formulas (nPr and nCr) to reveal 720 permutations and 120 combinations.

Adopt a four-step approach to permutations and combinations: identify the target, decide order, draw slots, and use division for combinations; illustrated with choosing 2 from 30 for handshakes.

Explore conditional slots in combinatorial counting by selecting two vertices of an octagon to form diagonals.

Explore counting techniques for selection using slots, solving examples of choosing three boys and two girls from separate groups, and counting rectangles and squares in a five-by-five chessboard.

Explains probability as the ratio of favorable outcomes to total outcomes, shows bounds between zero and one, and demonstrates calculating at least one event using coin toss and rain examples.

Explore independent and dependent events in probability, using with and without replacement examples, and apply multiplication and addition rules to red, blue, and green ball outcomes.

Explore probability question types using coin tosses and dice, counting outcomes and denominators, and see how outcomes grow with powers of two and six.

Explore progression types—arithmetic, geometric, and harmonic—alongside sums of natural numbers, squares, and cubes, and learn core formulas and relationships, including the harmonic link to reciprocals.