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On this page, you will find Introduction to Graphs Class 8 Notes Maths Chapter 15 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 15 Introduction to Graphs will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 15 Notes Introduction to Graphs

Introduction to Graphs Class 8 Notes Conceptual Facts

• XOX’ and YOY’ taken together are called coordinate axes.
• The plane containing the coordinate axes is called cartesian plane.
• The point of intersection of the coordinate axes is called origin.
• The x-coordinate is always written before y-coordinate e.g., if 2 is x-coordinate and 3 is y-coordinate, then the coordinates are (2, 3).
  
• The x-coordinate of a point lying on y-axis is zero.
• The y-coordinate of a point lying on x-axis is zero.
• The x-coordinate is also called abscissa and y-coordinate ordinate.

On this page, you will find Factorisation Class 8 Notes Maths Chapter 14 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 14 Factorisation will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 14 Notes Factorisation

Factorisation Class 8 Notes Conceptual Facts

• Prime factors of 30 (say) = 2 x 3 x 5
• Factors of algebraic expression 4xy = 4 x x x y
• 1 is a factor of every expression.
• Method of common factors
• 4x + 24 = 4(x + 6)
• Method of factorisation by regrouping terms
  6xy + 3y = 2 x 3 x x x y + xy = 3 xy (2x + 1) = 3y (2x + 1)

Factorisation using identities
a² + 2ab + b²– (a + b)²
a² – 2ab + b²= (a-b)²
a² – b² = (a + b) (a – b)

On this page, you will find Direct and Indirect Proportions Class 8 Notes Maths Chapter 13 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 13 Direct and Indirect Proportions will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 13 Notes Direct and Indirect Proportions

Direct and Indirect Proportions Class 8 Notes Conceptual Facts

1. The two quantities are said to be directly proportional if

• an increase in one leads to a corresponding increase in the other.
• a decrease in one leads to a corresponding decrease in the other.

2. If x varies directly as y then the ratio \(\frac{x}{y}=k\) (constant) symbolically, x α y, where α is symbol of
proportionality or x = ky \(\frac{x_{1}}{y_{1}}=\frac{x_{2}}{y_{2}}=\frac{x_{3}}{y_{3}}=k\)

3. The two quantities are said to be inversely proportional if

• an increase in one leads to a corresponding decrease in the other.
• a decrease in one leads to a corresponding increase in the other.

4. If x varies inversely with y, then x α \(\frac{1}{y}\) ⇒ xy = k(constant) or xy – x₁y₁ = x₂y₂ = k.

5. Speed =\(\frac{\text { Distance }}{\text { Time }} \) or Distance = Speed x time or time =\(\frac{\text { Distance }}{\text { Speed }}\)

On this page, you will find Exponents and Powers Class 8 Notes Maths Chapter 12 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 12 Exponents and Powers will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 12 Notes Exponents and Powers

Exponents and Powers Class 8 Notes Conceptual Facts

• A numeral (a)ⁿ is called an exponential expression where a is called base and n the exponent or power.
  aⁿ = a x a x a x a……… x a (n times)
• A negative rational number raised to an even power is always positive, \(\text { e.g. },\left(-\frac{1}{2}\right)^{4}=\frac{1}{16}\)
• A negative rational number raised to an odd power is always negative, i.e., \(=\left(-\frac{1}{2}\right)^{3}=-\frac{1}{8}\)

Laws of exponents:

On this page, you will find Mensuration Class 8 Notes Maths Chapter 11 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 11 Mensuration will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 11 Notes Mensuration

Mensuration Class 8 Notes Conceptual Facts

1. Area of rectangle
A = Length x Breadth
= a x b sq. units

2. Area of square
A = (side)²
= a² sq. units

3. Area of triangle
A = \(\frac{1}{2}\) x b x h sq.units

4. Area of equilateral triangle
A = \(\frac{\sqrt{3}}{4} a^{2}\) sq.units

5. Area of parallelogram
A = b x h sq. units

6. Area of Circle
A = πr² sq. units

7. Area of trapezium
A = \(\frac{1}{2}\)(a + b) x h sq. units

8. Area of general quadrilateral
A = Area of ΔABC + area of ΔACD
= \(\frac{1}{2}\) (a + b) x AC sq. units

9. Area of rhombus
A = \(\frac{1}{2}\) (d₁ x d₂) sq. units

10. Surface area of cube
A = 6a² sq. units

11. Surface area of cuboid
A = 2 [ab + bc + ca] sq. units

12. Surface area of cylinder
A = 2πrh sq. units

13. Volume of cube V = a³ units

14. Volume of cuboid V = a x b x c cu. units

15. Volume of cylinder V = πr²h