Chapter 1: Rational Numbers
Q1. Add: 3/4 + (-5/6).
SolutionLCM of 4 and 6 = 12
= (9/12) + (-10/12) = -1/12
Q2. Find the additive inverse of -7/9.
SolutionAdditive inverse = 7/9
Chapter 2: Linear Equations in One Variable
Q1. Solve: 3x + 5 = 17.
Solution3x = 17 - 5 = 12
x = 4
Q2. Solve: (x/2) + (x/3) = 7.
SolutionLCM = 6
(3x + 2x)/6 = 7
5x = 42
x = 42/5 = 8.4
Chapter 3: Understanding Quadrilaterals
Q1. Find the sum of interior angles of a hexagon.
SolutionSum = (n-2) × 180°
= (6-2) × 180° = 720°
Q2. What is the property of a parallelogram regarding opposite angles?
SolutionOpposite angles of a parallelogram are equal.
Chapter 6: Squares and Square Roots
Q1. Find the square root of 144.
Q2. Is 225 a perfect square?
Chapter 7: Cubes and Cube Roots
Q1. Find the cube root of 216.
Q2. Is 1000 a perfect cube?
Chapter 8: Comparing Quantities
Q1. Find 12% of 850.
Solution12/100 × 850 = 102
Q2. A shirt costs Rs. 800 after 20% discount. Find the marked price.
Solution80% of MP = 800
MP = 800 × 100/80 = Rs. 1000
Q3. Find the compound interest on Rs. 5000 at 10% per annum for 2 years.
SolutionA = P(1 + r/100)² = 5000(1.1)² = 6050
CI = 6050 - 5000 = Rs. 1050
Chapter 9: Algebraic Expressions and Identities
Key Identities:
• (a+b)² = a² + 2ab + b²
• (a-b)² = a² - 2ab + b²
• (a+b)(a-b) = a² - b²
Q1. Expand: (2x + 3y)².
Solution= (2x)² + 2(2x)(3y) + (3y)²
= 4x² + 12xy + 9y²
Q2. Evaluate 99 × 101 using identities.
Solution= (100-1)(100+1) = 100² - 1² = 10000 - 1 = 9999
Chapter 11: Mensuration
Q1. Find the area of a rectangle with length 12 cm and breadth 5 cm.
SolutionArea = l × b = 12 × 5 = 60 cm²
Q2. Find the volume of a cube with side 4 cm.
SolutionV = a³ = 4³ = 64 cm³
Chapter 12: Exponents and Powers
Q1. Simplify: 2³ × 2².
Solution2³ × 2² = 2¹ = 32
Q2. Write 0.00045 in scientific notation.
Chapter 14: Factorisation
Q1. Factorise: 12x² + 18x.
Q2. Factorise: x² - 9.