Get comprehensive solutions to all NCERT Class 8 Maths questions with detailed explanations. Master advanced mathematical concepts and prepare confidently for Class 9 and board examinations.
Q1. Solve: 3(x + 2) = 2(x - 1) + 7
Answer:
3(x + 2) = 2(x - 1) + 7
3x + 6 = 2x - 2 + 7
3x + 6 = 2x + 5
3x - 2x = 5 - 6
x = -1
Q2. The sum of two consecutive even numbers is 54. Find the numbers.
Answer:
Let the numbers be x and x + 2
x + (x + 2) = 54
2x + 2 = 54
2x = 52, x = 26
The numbers are 26 and 28
Q1. Find the square root of 144 by prime factorization.
Answer:
144 = 2⁴ × 3²
√144 = 2² × 3 = 4 × 3 = 12
Q2. Find the smallest number by which 1800 must be multiplied to make it a perfect square.
Answer:
1800 = 2³ × 3² × 5²
To make it perfect square, multiply by 2
1800 × 2 = 3600 = 60²
Q1. Find the compound interest on ₹8000 for 2 years at 10% per annum.
Answer:
A = P(1 + R/100)ⁿ
A = 8000(1 + 10/100)²
A = 8000(1.1)² = 8000 × 1.21 = ₹9680
CI = A - P = 9680 - 8000 = ₹1680
Q2. A shopkeeper marks his goods 20% above cost price and gives 10% discount. Find his profit percent.
Answer:
Let CP = ₹100
Marked price = ₹120
SP = 120 - 10% of 120 = 120 - 12 = ₹108
Profit% = (108-100)/100 × 100 = 8%
Q1. Expand: (x + 5)(x - 3)
Answer:
(x + 5)(x - 3) = x² - 3x + 5x - 15 = x² + 2x - 15
Q2. Use identity to find: (97)²
Answer:
(97)² = (100 - 3)²
= 100² - 2(100)(3) + 3²
= 10000 - 600 + 9 = 9409
Q3. Factorize: x² - 9
Answer: x² - 9 = x² - 3² = (x + 3)(x - 3)
Q1. Find the area of a trapezium with parallel sides 12 cm and 8 cm, and height 5 cm.
Answer:
Area = (1/2) × (sum of parallel sides) × height
Area = (1/2) × (12 + 8) × 5 = (1/2) × 20 × 5 = 50 sq cm
Q2. Find the volume of a cube with side 6 cm.
Answer: Volume = side³ = 6³ = 216 cu cm
Q3. Find the curved surface area of a cylinder with radius 7 cm and height 10 cm.
Answer:
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 sq cm
Q: How many chapters are there in Class 8 Maths?
A: There are 16 chapters in NCERT Class 8 Maths covering advanced mathematical topics.
Q: Which are the most challenging topics in Class 8 Maths?
A: Algebraic expressions, linear equations, mensuration, and factorization are considered challenging topics.
Q: How important is Class 8 Maths for board exams?
A: Very important! Class 8 Maths builds the foundation for Classes 9 and 10 board examinations.
