CBSE Class 9 - Maths - Half Yearly Examination Paper - (2017-18) (#cbsePapers)

CBSE Class 9 - Maths - Half Yearly
Examination Paper - (2017-18)

CBSE Class 9 - Maths - Mid Term Examination Paper - (2017-18) (#cbseNotes)

CBSE Class 9 - Maths - Mid Term
Examination Paper - (2017-18)

CBSE Class 9 - Maths - Chapter 10 - CIRCLES - NCERT Exercise 10.1 (#cbseNotes)

Chapter 10 - CIRCLES -
NCERT Exercise 10.1

Question 1: Fill in the blanks

(i) The centre of a circle lies in __________ of the circle. (exterior/ interior)

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

(iii) The longest chord of a circle is a __________ of the circle.

(iv) An arc is a __________ when its ends are the ends of a diameter.

(v) Segment of a circle is the region between an arc and __________ of the circle.

(vi) A circle divides the plane, on which it lies, in __________ parts.


Answer:
(i) The centre of a circle lies in interior of the circle.

Maths Pearls - What is so special about Srinivasa Ramanujan's Magic Square? (#cbseNotes)

What is so special about Srinivasa Ramanujan's Magic Square?

You may be familiar with magic squares. Srinivasa Ramanujan also designed his own magic square.

This magic square looks similar to any other square. What is so special about it?


Sum of any rows is 139

CBSE Class 9 - Maths- Periodic Test Paper - (2016-17) (#cbsePapers)

CBSE Class 9 - Maths- Periodic Test Paper - (2016-17) 

Topics covered are:
1. Euclid Geometry
2. Co-ordinate Geometry
3. Lines and Angles

CBSE CLASS 9 - Maths - Heron's Formula - Assignment Sheet (#cbseNotes)

Heron's Formula

Assignment Sheet

CLASS 9 - Maths

⒈ The sides of a triangular field are 41 m,40 m and 9 m. Find the number of rose beds that can be prepared in the field, if each rose bed ,on an average needs 900 cm² space.


⒉ Find the cost of lying grass in a triangular field of sides 50m ,65 m, and 65 m at the rate of ₹ 7 per m²


⒊ From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10cm and 6 cm. Find the area of the triangle.


⒋ The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.

CBSE Class 9 - Maths - Co-Ordinate Geometry (Questions and Answers) (#cbseNotes)

Coordinate Geometry

Q & A

Q1: Write the name of the point where both axes intersect?

Answer: Origin

Q2: In which quadrant(s), ordinate of a point is negative?

Answer: III and IV

Q3: If the cooridnates of of two points P(-2,3) and Q(-3, 5), then find (abscissa of P) - (abscissa of Q) 

Answer: = (-2) - (-3) = -2 + 3 = 1

CBSE Class 9 - Maths - Number Systems - Important Points To Remember (#cbsenotes)

Number Systems

CBSE Class 9 Maths 

Important Points To Remember

① Counting numbers 1, 2, 3, 4... are called Natural Numbers (N)


② Whole Numbers (W): Natural numbers 1, 2, 3... together with number 0 (zero) are called Whole Numbers


③ All natural numbers, zero and negative numbers together i.e. ...., –4, –3, –2, –1, 0, 1, 2, 3, 4, ... are known as Integers (Z).


④ Rational Numbers (Q): Numbers of the form p/q where p, q both are integers and q ≠ 0.

CBSE Class 9 - Maths - Chapter 2 - Polynomials (Important Points) (#cbsenotes)

Polynomials

(Important Points)

CBSE Class 9 - Maths Chapter 2

① A combination of constants and variables which are connected by basic mathematical operations, is known as Algebraic Expression. For e.g. x² – 7x + 2, xy² – 3 etc.

② A Polynomials p(x) in one variable x is an algebric expression in x of the form
p(x) = a_nxⁿ + a_n–1x^n–1 + ... + a₁ x + a₀ , where a₀ , a₁ , a₂ ..... a_n are constant and a n ≠ 0 are called coefficients and n is a positive integer.

③ The highest power of variable x in a polynomial p(x) is called the degree of the polynomial.

④ A polynomial of degree 1 is called a linear polynomial. For e.g. 4x + 9 is a linear polynomial in x.

CBSE Class 9 - SA2 Mathematics Sample Question Paper (2016-17) (set-2) (#cbsepapers)

CBSE Class 9 - SA2 Mathematics Sample Question Paper (2016-17)

CBSE Class 9 - SA2 Mathematics Sample Question Paper (2016-17)(#cbsepapers)

CBSE Class 9 - SA2 Mathematics Sample Question Paper (2016-17)

CBSE Class 9 - Mathematics - CH 14: Statistics - Important Points

Statistics - Important Points

CBSE Class 9 - Mathematics 

① In statistics we study collection, presentation analysis and interpretation of data.

② Facts or figures collected with a definite purpose are called data.

③ Data are fundamental. Statistical tests are performed on raw not manipulated data.

④ The number of times an observation occurs in the given data is called frequency of the observation.

⑤ Class intervals are the groups in which all observations are divided.

CBSE Class 8 - Maths - CH3 - Understanding Quadrilaterals (Worksheet) (#cbsenotes)

Understanding Quadrilaterals

(Worksheet)

The worksheet helps you identify a specific quadrilateral based on its properties.

☛Directions: Fill in the blanks

① A simple closed curve made up of only line segments is called a ________.
 


② A _________ of a polygon is a line segment connecting two non- consecutive vertices.
 


③ A _______ _______ is a polygon in which no portion of its any diagonal is in its exterior.
 


④ A quadrilateral is a polygon having only ________ sides.
 

CBSE Class 9- Maths - Surface Areas and Volumes - NCERT EXERCISE 13.8 (#ncertsolutions) (#cbsenotes)

Surface Areas and Volumes - Spheres

Class 9 - Maths - NCERT EXERCISE 13.8

Q1: Find the volume of a sphere whose radius is

(i) 7 cm

(ii) 0.63 m


Answer:
(i) Given, r = 7 cm
Volume of sphere = (4/3)πr³
= (4/3) × (22/7) × (7)³
= 1437⅓ cm³

(ii) Given,  r = 0.63 m
Volume of sphere = (4/3)πr³
= (4/3) × (22/7) × (0.63)³
= 1.05 m³ (approx)

CBSE Class 9 - Mathematics Pre-SA2 Sample Question Paper (2016-17)

CBSE Class 9  - Mathematics Pre-SA2 Sample Question Paper (2016-17)

CBSE Class 9- Maths - Surface Areas and Volumes -NCERT EXERCISE 13.7 (#cbsenotes)

Surface Areas and Volumes 
NCERT EXERCISE 13.7

Q1: Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm
(ii) radius 3.5 cm, height 12 cm

Answer:
(i) Given, r = 6 cm, h = 7 cm

 Volume of the cone = ⅓πr²h
= (1/3) × (22/7) × 6² × 7
= 264 cm³ (Answer)

(ii) Given, r = 3.5 cm, h = 12cm
 Volume of the cone = ⅓πr²h
  = (1/3) × (22/7) × 3.5² × 12
  = 154 cm³ (Answer)

CBSE Class 9 Maths - Surface Areas and Volumes - NCERT Exercise 13.6 (#cbsenotes) (#NCERTAnswers)

Surface Areas and Volumes (Cylinder)

EXERCISE 13.6

Q1: The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm³ = 1l)

Answer: Given, h = 25 cm, 2πr = 132 cm.
⇒ 2πr = 132
⇒ 2 × (22/7) × r = 132
⇒ r = (132 × 7)/ (2 × 22) = 21cm

Volume = πr²h = (22/7) × 21 × 21 × 25
= 34650 cm³
= 34650/1000
= 34.65 litres  (Answer)


Q2: The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm³ of wood has a mass of 0.6 g.

CBSE Class 9 Maths - Surface Areas and Volumes - NCERT Exercise 13.5 (#cbsenotes) (#ncertsolutions)

Surface Areas and Volumes 

NCERT Exercise 13.5

Q1: A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Answer: Given, l = 4 cm, b = 2.5 cm, h = 1.5 cm
Volume of 1 matchbox = lbh
= 4 × 2.5 × 1.5 cm3 = 15 cm³
Volume of 12 matchboxes = 15 × 12  = 180 cm³ (Answer)


Q2: A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m³ = 1000 l)

Answer: Given,  l = 6 m, b = 5 m, h = 4.5 m
Volume of the tank = lbh
= 6 × 5 × 4.5 = 135 m³
= 135 × 1000 litres = 1,35,000 litres (Answer)

CBSE Class 9 - Maths - Surface Areas and Volumes (NCERT Ex 13.4) (#cbseclass9notes)

Surface Areas and Volumes - Spheres

(NCERT Ex 13.4)

Q1: Find the surface area of a sphere of radius 
(i) 10.5 cm
(ii) 5.6 cm
(iii) 14 cm

Answer:
(i) r = 10.5 cm
Surface area of the sphere = 4πr²
= 4 × (22/7) × (10.5)²
  = 1386 cm² (Answer)

(ii) r = 5.6 cm
Surface area of the sphere = 4πr²
= 4 × (22/7) × (5.6)²
= 394.24 cm² (Answer)

(iii) r = 14 cm
Surface area of the sphere = 4πr²
= 4 × (22/7) × 14 × 14
= 2464 cm² (Answer)


Q2: Find the surface area of sphere of a diameter :
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m

CBSE Class 9 - Maths - Surface Areas and Volumes - NCERT Ex 13.3 (#cbsenotes)

Surface Areas and Volumes

EXERCISE 13.3

Q1: Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Answer: Given r = 10.5/2 = 5.25 cm, l = 10 cm.

Curved surface area (CSA) of the cone = πrl
= (22/7) × 5.25 × 10  = 165 cm² (Answer)



Q2: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

Answer: Given, l = 21m, r = 24/2 = 12 m
TSA (cone) = πr(l + r)
= (22/7) × 12 (21 + 12)
= 1244.57 m² (Answer)