Mathematics for Class 8 students

Learn to solve linear equations in one variable by moving x terms to the left and constants to the right, balancing with addition, subtraction, multiplication, and division.

Identify a variable, set up linear equations, and solve examples: sum of three consecutive multiples of 11 equals 363, and a currency note problem with 50, 20, 10 rupees.

Identify the variable and form a linear equation in one variable from the given data, then solve using techniques like a common denominator, cross multiplication, and moving terms across sides.

Learn how simple versus not simple curves behave on a surface, distinguishing open and closed paths by continuity, start and end points, and crossings.

Explore closed curves, interior and exterior regions, and determine convex versus concave shapes by examining line segments between two points.

Explore polygons by examining straight, closed shapes with non-intersecting sides. Learn to identify vertices and interior and exterior angles, and count diagonals in triangles, quadrilaterals, and pentagons.

Learn how to count diagonals in any polygon using n(n-3)/2, illustrated by a pentagon with five diagonals, and understand regular polygons as those with equal sides and equal interior angles.

Explain how the sum of interior angles in a triangle is 180 degrees and extend to polygons by dividing into triangles, giving the formula (n-2) times 180 degrees.

Learn how exterior angles of polygons relate to interior angles, with a pentagon example, and prove that the sum of exterior angles equals 360 degrees regardless of n.

Analyze how interior and exterior angles determine polygon sides, using the 360-degree exterior angle sum and examples like 45°, 20°, and 15°, and note that 22° is not possible.

Explore quadrilaterals, four-sided polygons, and learn their key features: vertices, sides, interior and exterior angles, and diagonals, and study special types like trapezium, parallelogram, kite, rhombus, rectangle, and square.

Review congruence of triangles, noting that three elements with at least one side establish congruence, while all angles alone yield similarity; examine parallel line angle relations for parallelograms.

Explore how parallelograms have opposite sides and angles that are equal, and how adjacent angles are supplementary, using diagonals to demonstrate congruent triangles in practice.

Discover how the diagonals of a parallelogram bisect each other and cut into two equal parts, proving that opposite sides are equal.

Solve parallelogram angle problems by using opposite angles equal, supplementary angles, and triangle angle sums; find angles when adjacent angles are in a 3:2 ratio, yielding 108°, 72°, and 100°.

Analyze data from ten customer purchases to build a frequency table and tally chart, identifying which items (potatoes, tomatoes, onions, or capsicum) are most popular and guiding decision making.

Learn to build a frequency table for marks data using class intervals, tally charts, and boundary conventions to count scores across ranges like 50–60, 60–70, 70–80, 80–90, and 90–100.

Draw a bar chart from a frequency table of vegetables, using the x-axis for items and the y-axis for frequency, to compare purchases and identify onions as maximum.

Learn to construct a histogram from grouped scores using class intervals and frequencies, create a bar chart with touching bars, and answer questions like how many students scored above 90.

Learn how to create and read a two-source bar chart that compares monthly incomes from a fruit stall and a snack bar, with axis scaling and interpretation of differences.

Interpret pie charts to compare parts of the whole; Rohit spends one third of his income on food, Mohan one fourth, illustrating how angles show expense ratios.

Plot time on the x-axis and distance on the y-axis with appropriate scales. Connecting the data points yields a straight line that shows the time-distance relationship.

Explore time vs distance graphs: a line parallel to the x-axis fixes distance at 100 meters, while a line parallel to the y-axis fixes time at 55 seconds.

change handling shows how varying cycling speed alters the time-distance graph: acceleration rotates the line anticlockwise, deceleration rotates clockwise, with speed changes affecting slope rather than mere translation.

Plot time on the x axis and distance on the y axis to study distance–time graphs; observe positive, zero, and negative slopes that reflect outward speed, pause, and return.

Explore random experiments with equally likely outcomes and how to compute probability as favorable over total outcomes, using park selection, a fair die, and red, white, and black balls.

Learn to construct triangles from two sides and an angle or all three angles, and understand why four sides alone don’t fix a quadrilateral without extra data.

Explore how to form algebraic expressions from real-life scenarios, using variables for length and width to compute area changes, and model costs and savings with two-variable and one-variable expressions.

Learn to identify like terms and unlike terms in algebraic expressions, recognizing variables, powers, and coefficients while performing addition and subtraction.

Learn to add and subtract algebraic expressions by combining like terms and aligning terms with the same variables, then apply the additive inverse approach to subtraction using examples.

Learn how to multiply monomials, understand terms like binomials and polynomials, and apply the rule of adding exponents while multiplying coefficients and variables.

Learn to simplify algebra by expanding binomials and combining like terms. Expand (a+b)(c-d) and (a-b)(c+d) to obtain 4ac, and simplify (a+b+c)(a+b-c) to a^2+2ab+b^2-c^2.

Learn how identities like (a+b)(a-b)=a^2-b^2 simplify area and multiplication. For example, a 100 by 100 square with length up by 10 and width down by 10 yields 9900 square meters.

Apply algebraic identities to simplify expressions using difference of squares and to multiply linear factors, illustrated by (a-b)(a+b) and (4x+5)(4x+1) and (200-6)(200+6).

This lecture defines factors and irreducible factors and explains prime factorization. It shows how to break numbers like 45 into 5, 3, and 3, noting irreducibles cannot be reduced further.

Learn the regrouping method to factor polynomials by extracting common factors from term pairs. Examples show how (3x-2)(2y-3) emerges and how (a-b)^2 = a^2 - 2ab + b^2.

factorization using identities shows how to rewrite expressions as squares and use a^2+2ab+b^2=(a+b)^2 and a^2-2ab+b^2=(a-b)^2 and a^2-b^2=(a+b)(a-b) to obtain factors, e.g., (3x+2)^2-(5y)^2=(3x+2+5y)(3x+2-5y).

learn to factor polynomials using the factor-sum identity by selecting factors of the constant term that sum to the x-coefficient, with examples like x^2-7x+12 and x^2+6x-16.

Master factorization of quadratics by the product-sum method, splitting the middle term to rewrite and factor expressions like 5x^2+12x+4, 5x^2-12x+4, and 5x^2-8x-4.

Divide algebraic expressions by monomials using factorization, cancel common factors, and subtract exponents to simplify polynomials term-by-term.

Learn to divide polynomials by factoring and cancel common factors to simplify results. Practice includes factoring 8y^2+7y+10 as (y+2)(y+5) and factoring x^4-5x^3-24x^2 as x^2(x-8)(x+3) to cancel with the divisor 11x(x-8).

Divide algebraic expressions using a long-division style method without preparation, and identify the dividend, divisor, quotient, and remainder in the example 5x^2+12x+4 divided by x+2.

Learn to find the perimeter of shapes by tracing their boundary and adding side lengths, and apply circle formulas P = 2 pi r and P = pi D.

This lecture defines area as region inside a shape, shows rectangle area, explains perimeter as distance around, and demonstrates that for a fixed perimeter, the square yields the largest area.

Use area and perimeter to price garden and fencing for a land plot. Garden is 600 m² at 200 rupees/m², fencing 90 m at 100 rupees/m, then tile 1100 m².

Learn to compute the perimeter and area of composite shapes formed by a rectangle with semicircular ends, using diameters, radii, and pi (22/7) from given dimensions.

Learn to find polygon areas by triangulation, dividing shapes like parallelograms, rhombuses, and trapeziums into triangles and applying base-height or diagonal-based formulas.

Learn to apply triangulation to find areas of trapeziums and irregular plots by dividing them into triangles and rectangles, then sum areas using base-height formulas.

learn to find the surface area of cuboid, cube, and cylinder by summing face areas, including six faces for cuboid and cube, and curved plus base areas for cylinder.

Compute application problems on surface area by calculating wall and floor areas for whitewashing and polishing costs. Determine the cylinder’s rolling distance and the curved-surface area for repairs.

Compute volumes for cuboids, cubes, and cylinders by multiplying base area by height, using formulas l×w×h, l^3, and base area times height; compare volumes for practical pouring problems.

Apply surface area and volume to real problems: flatten a hollow cylinder to a rectangle to get a perimeter, then compute volume; compare cube containers by surface area cost scaling.

Learn percentage concepts using direct proportion and the unitary method, with examples on marks, earnings, and profit scenarios including selling price and purchase price.

Learn to use percentage and ratio together to solve real-world problems by converting percentages to numbers and applying them to surveys, class sizes, and travel cost calculations.

Explore how percent changes affect prices, including increases and decreases, and how multiple discounts yield an effective discount on MRP.

Understand four major components of interest rate: principal, rate, time, and compounding frequency, and how simple and compound interest differ under yearly, half-yearly, and monthly compounding.

Examines how changing compounding frequency from yearly to half yearly affects the accumulated amount on an 80000 loan at 10 percent over 2.5 years, and the resulting interest difference.

Explore compounding concepts by applying a 4% yearly salary increment and a 10% annual cost reduction, revealing salaries grow with 1.04^3 and costs drop by 27.1% over three years.