Aligned with NCERT Chapters.
Chapter 1: Integers
Key Concepts:
- Negative & positive numbers
- Addition/subtraction rules
- Multiplication & division rules
Easy Rules:
- (+) + (+) = +
- (–) + (–) = –
- (+) + (–) → subtract, keep sign of bigger number
- (+) × (–) = –
- (–) × (–) = +
Example:
Q: –7 + 12 = ?
→ 12 – 7 = 5
Q: –4 × –3 = ?
→ Positive result → 12
Chapter 2: Fractions and Decimals
Fractions:
- Like fractions → add/subtract numerators
- Unlike fractions → make denominators same
- Multiplication → numerator × numerator
- Division → multiply by reciprocal
Example:
Q: 3/5 × 2/3 = ?
→ (3×2)/(5×3) = 6/15 = 2/5
Decimals:
- Align decimal points for +/–
- Multiply normally, count decimal places
- For division → move decimal to make divisor whole
Chapter 3: Data Handling
Topics:
- Mean = sum ÷ number of values
- Median = middle value
- Mode = most frequent value
- Bar graphs & pictographs
Example:
Numbers: 2, 5, 7, 7, 10
Mode = 7
Mean = (2+5+7+7+10)/5 = 6.2
Chapter 4: Simple Equations
Steps to solve:
- Remove bracket if any
- Move variables to one side
- Move numbers to other side
- Keep sign change rule in mind
Example:
Q: x + 7 = 15
→ x = 15 – 7
→ x = 8
Q: 3x = 21
→ x = 21 ÷ 3 = 7
Chapter 5: Lines and Angles
Important Angles:
- Complementary → sum = 90°
- Supplementary → sum = 180°
- Vertically opposite angles → equal
- Linear pair → 180°
Example:
Q: One angle is 50°. Its complementary = 40°.
Chapter 6: The Triangle and Its Properties
Concepts:
- Types: scalene, isosceles, equilateral
- Sum of angles = 180°
- Exterior angle = sum of opposite interior angles
- Pythagoras theorem for right triangle
Example:
A triangle has 40° and 50°. Third angle = 180 – 90 = 90°
Chapter 7: Congruence of Triangles
Congruence rules:
- SSS
- SAS
- ASA
- RHS
Congruent triangles → same size and shape.
Chapter 8: Comparing Quantities
Percentages:
Percentage = (value/total) × 100
Profit/Loss:
Profit = SP – CP
Loss = CP – SP
Profit% = (Profit/CP) × 100
Simple Interest (SI):
SI = (P × R × T)/100
Chapter 9: Rational Numbers
Concepts:
- Form: p/q where q ≠ 0
- Equivalent rational numbers
- Comparing rational numbers
- Number line representation
Example:
Is 6/9 = 2/3?
→ Simplify 6/9 → 2/3 → Yes
Chapter 10: Practical Geometry
Topics include:
- Constructing angles
- Constructing triangles (SSS, SAS, ASA)
- Using compass, ruler
Step-by-step construction can be provided if needed.
Chapter 11: Perimeter and Area
Formulas:
- Rectangle perimeter = 2(L + B)
- Area = L × B
- Triangle area = ½ × base × height
- Parallelogram area = base × height
Example:
Rectangle 10 × 4 →
Area = 40 cm²
Perimeter = 28 cm
Chapter 12: Algebraic Expressions
Terms:
- Coefficient
- Variable
- Constant
- Like terms
Example:
3x + 5x = 8x
7a – 2a = 5a
Chapter 13: Exponents and Powers
Rules:
- aⁿ × aᵐ = aⁿ⁺ᵐ
- aⁿ ÷ aᵐ = aⁿ⁻ᵐ
- (aⁿ)ᵐ = aⁿᵐ
- a⁰ = 1
Example:
2³ × 2² = 2⁵ = 32
Chapter 14: Symmetry
Concepts:
- Line symmetry
- Rotational symmetry
- Patterns
Figures like square, circle have multiple lines of symmetry.
Chapter 15: Visualising Solid Shapes
Concepts:
- 2D vs 3D shapes
- Nets of 3D shapes
- Top/side/front views
- Cuboid, cube, cylinder, sphere