Let’s dive deep into the world of maths, which is a most hyped subject for Indian students. We would check some of the most comprehensive, easy-to-understand NCERT Solutions for Class 8 Maths. Whether you want to be a scientist, entrepreneur, or anything else, maths is key to understanding all. As maths is a compulsory subject till class 10th, let’s try to befriend it to our advantage. And we’re here to make maths fun and simple!
Our detailed solutions will guide you through each textbook exercise. We will break down the challenging concepts and make them easy to grasp. We have added extra practice with a unique mix of easy and difficult questions for Class 8 students.
Unlock the magic of maths with IndiaFolks.com – where learning meets simplicity and fun!
Contents of the NCERT Textbook for Class 8
- Chapter 1 Rational Numbers
- Chapter 2 Linear Equations in One Variable
- Chapter 3 Understanding Quadrilaterals
- Chapter 4 Data Handling
- Chapter 5 Squares and Square Roots
- Chapter 6 Cubes and Cube Roots
- Chapter 7 Comparing Quantities
- Chapter 8 Algebraic Expressions and Identities
- Chapter 9 Mensuration
- Chapter 10 Exponents and Powers
- Chapter 11 Direct and Inverse Proportions
- Chapter 12 Factorisation
- Chapter 13 Introduction to Graphs
1. NCERT Solutions for Chapter 1 Rational Numbers
Solutions
2. NCERT Solutions for Chapter 2 Linear Equations in One Variable
Linear Equations in One Variable
Explanation: A linear equation in one variable is an equation in which the highest power of the variable is one. It generally has the form ax + b = c, where x is the variable.
Example: In the equation 3x + 4 = 10, x is the variable. To find the value of x, rearrange the equation: 3x = 10 – 4, so x = 6 / 3, which means x = 2.
Solutions
3. NCERT Solutions for Chapter 3 Understanding Quadrilaterals
Solutions
4. NCERT Solutions for Chapter 4 Data Handling
Solutions
5. NCERT Solutions for Chapter 5 Squares and Square Roots
Squares of a Number
Explanation: The square of a number is the result of multiplying the number by itself.
Example: The square of 3 is 3² = 3 x 3 = 9.
Square Roots
Explanation: The square root of a number is a value that, when multiplied by itself, gives the original number.
Example: The square root of 25 is √25 = 5, because 5 x 5 = 25.
Solutions
- Exercise 5.1 Squares and Square Roots
- Exercise 5.2 Squares and Square Roots
- Exercise 5.3 Squares and Square Roots
6. NCERT Solutions for Chapter 6 Cubes and Cube Roots
Exploring Cubes and Cube Roots –
1. Cubes
Cubes are numbers obtained by multiplying a number by itself three times. For example, the cube of 2 is 2 × 2 × 2, which equals 8. A cube of side 3 cm is made from 27 small cubes of side 1 cm, as 3 × 3 × 3 equals 27. This is why numbers like 1 (1³), 8 (2³), 27 (3³), … are called perfect cubes. Examples of cubes from 1 to 10 are 1³ = 1, 2³ = 8, 3³ = 27, up to 10³ = 1000.
2. Cube Roots
Cube roots are the inverse operation of cubing a number. For example, if the volume of a cube is 125 cm³, its side length can be found by calculating the cube root of 125. Since 5³ = 125, the cube root of 125 is 5. This means the side of the cube is 5 cm. Similarly, the cube root of 8 is 2, as 2³ = 8. Other examples include the cube root of 27 being 3, as 3³ = 27.
Solutions
7. NCERT Solutions for Chapter 7 Comparing Quantities
Important Formulas and Concepts: Comparing Quantities
1. Ratio
Definition: A ratio shows the relative sizes of two or more values.
Formula: Ratio of ‘a’ to ‘b’ is ‘a : b’ or ‘a/b’.
2. Percentage
Definition: A percentage is a fraction or ratio expressed as a part of 100.
Formula: Percentage = (Value / Total Value) × 100.
3. Converting Fractions to Percentage
Formula: (Fraction) × 100%.
4. Converting Decimals to Percentage
Formula: (Decimal) × 100%.
5. Profit and Loss
Profit: Selling Price (SP) – Cost Price (CP), when SP > CP.
Loss: Cost Price (CP) – Selling Price (SP), when CP > SP.
6. Calculating Profit/Loss Percentage
Profit %: (Profit / CP) × 100%.
Loss %: (Loss / CP) × 100%.
7. Discount
Definition: Reduction given on the marked price.
Formula: Discount = Marked Price – Sale Price.
8. Calculating Discount Percentage
Formula: (Discount / Marked Price) × 100%.
9. Sales Tax/Value Added Tax (VAT)
Definition: Tax added to the selling price of an item.
Formula: Sales Tax = Tax Rate × Selling Price.
10. Compound Interest
Definition: Interest calculated on the initial principal and also on the accumulated interest from previous periods.
Formula for Amount (A): A = P(1 + R/100)ᴺ, where P = Principal, R = Rate per annum, N = Number of years.
11. Depreciation
Definition: Decrease in the value of an asset over time.
Formula: Depreciated Value = Original Value – Depreciation.
- Exercise 7.1 Comparing Quantities
- Exercise 7.2 Comparing Quantities
- Exercise 7.3 Comparing Quantities
8. NCERT Solutions for Chapter 8 Algebraic Expressions and Identities
- Class 8 Maths Algebraic Expressions and Identities Exercise 8.1
- Class 8 Maths Algebraic Expressions and Identities Exercise 8.2
- Class 8 Maths Algebraic Expressions and Identities Exercise 8.3
- Class 8 Maths Algebraic Expressions and Identities Exercise 8.4
9. NCERT Solutions for Chapter 9 Mensuration
The important elements of this chapter are –
A. Area of a Polygon (Trapezium, Rhombus)
- Trapezium: A quadrilateral with one pair of parallel sides. Area is calculated by averaging the lengths of the parallel sides (a and b) and multiplying by the height (h).
Formula: Area = (a + b) / 2 * h - Rhombus: A parallelogram with all sides equal. Area is found by multiplying the lengths of the diagonals (d1 and d2) and dividing by two.
Formula: Area = (d1 * d2) / 2
B. Surface Area of Cube, Cuboid, and Cylinder
- Cube: A three-dimensional shape with six equal square faces. Surface area is calculated by multiplying the square of the side length (side) by six.
Formula: Surface Area = 6 * side² - Cuboid: A box-shaped object. Surface area is found by adding the areas of all six faces (length l, width w, height h).
Formula: Surface Area = 2lw + 2lh + 2wh - Cylinder: A solid with circular ends and a curved surface. Surface area is the sum of the areas of the two circles (radius r) and the curved surface (height h).
Formula: Surface Area = 2πr(r + h)
C. Volume of Cube, Cuboid, and Cylinder
- Cube: A solid shape with six equal square faces. Volume is the cube of the side length (side).
Formula: Volume = side³ - Cuboid: A box-shaped solid. Volume is the product of its length (l), width (w), and height (h).
Formula: Volume = lwh - Cylinder: A solid with circular ends. Volume is the product of the area of the base (circle with radius r) and height (h).
Formula: Volume = πr²h
D. Volume and Capacity
- Volume: Measures how much space an object occupies, often calculated in cubic units.
- Capacity: Refers to the amount a container can hold, typically measured in units of liquid capacity (like liters or gallons).
Solutions
10. NCERT Solutions for Chapter 10 Exponents and Powers
Exponents
Explanation: An exponent represents the number of times a base number is multiplied by itself.
Example: In 2³ (read as 2 raised to the power of 3), 2 is the base and 3 is the exponent, meaning 2 x 2 x 2 = 8.
Powers
Explanation: A power is the result of raising a base number to an exponent.
Example: 5² (read as 5 to the power of 2) means 5 is multiplied by itself once, resulting in 25.
Solutions
11. NCERT Solutions for Chapter 11 Direct and Inverse Proportions
Direct Proportions
Explanation: In direct proportions, as one quantity increases, the other quantity increases at the same rate, and vice versa.
Example: If 5 kg of rice cost ₹500, then 10 kg of rice will cost ₹1000 (since the cost increases directly with the quantity of rice).
Inverse Proportions
Explanation: In inverse proportions, as one quantity increases, the other quantity decreases at the same rate, and vice versa.
Example: If a car takes 6 hours to cover 300 km at a certain speed, it will take 3 hours to cover the same distance at double the speed (since time taken decreases as speed increases).
Solutions
12. NCERT Solutions for Chapter 12 Factorisation
A. Factors of Natural Numbers
Factors of a natural number are the numbers that divide it exactly without leaving a remainder. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, as 30 can be expressed as 2 × 15, 3 × 10, and 5 × 6.
B. Factors of Algebraic Expressions
An algebraic expression like 5xy is factored into its irreducible factors. Here, 5xy = 5 × x × y. The factors 5, x, and y cannot be further simplified, making them irreducible. Unlike in arithmetic, in algebra, we use ‘irreducible’ instead of ‘prime’ to describe such factors.
C. What is Factorisation?
Factorisation is the process of breaking down a complex number or expression into a product of simpler factors. It refers to finding the numbers that multiply to give the original number. In algebra, it involves breaking down expressions into irreducible factors.
D. Factorisation by Regrouping Terms
This method involves rearranging and grouping terms in an expression to simplify factorization. For example, in the expression 4x + 8y + 6x, we can regroup it as (4x + 6x) + 8y, which simplifies to 10x + 8y, making the factorization process easier.
5. Factorisation Using Identities
Some algebraic expressions can be factored using standard identities like (a+b)² = a² + 2ab + b². For example, x² + 10x + 25 can be factored as (x + 5)², using the identity of a perfect square.
Solutions
1 Comment
Thank you. The solutions helped me by breaking down complex algebraic expressions into simpler, understandable steps.