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)

CBSE Class 9 Maths - Surface Areas and Volumes - NCERT Exercise 13.2 (#cbseclass9Notes)

Surface Areas and Volumes

NCERT Exercise 13.2

Q1: The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.

Answer: Given, h = 14 cm,
curved, surface area (CSA) = 88 cm², r = ?
CSA  = 2πrh
⇒ 88 = 2 × (22/7) × r × 14
⇒ 88 = 44 × 2 × r
⇒ r = 88/88 = 1
∴ diameter = 2r = 2 cm


Q2: It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?.

CBSE Class 9 Maths - SURFACE AREAS AND VOLUMES (NCERT EXERCISE 13.1) (#cbsenotes) (#ncertsolutions)

SURFACE AREAS AND VOLUMES

Class 9 Maths 

NCERT EXERCISE 13.1

Q1: A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine :
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 m2 costs Rs 20.

Answer: Given,
l = 1.5 m,
b = 1.25 m,
h = 65 cm = 0.65 m

(i) ∵ the box is open at the top, it has only five faces.

Surface Area (SA) for five faces = lb + 2(bh + hl)

= 1.5 × 1.25 m² + 2 (1.25 × 0.65 + 0.65 × 1.5) m²
= 1.875 + 2 (1.7875) m² = 1.875 + 3.575
= 5.45 m²

(ii) Cost of 1 m² of the sheet = ₹ 20
∴ cost of 5.45 m² of the sheet = 20 × 5.45 m² = ₹ 109 (Answer)


Q2: The length, breadth and height of a room are 5m, 4m and 3m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m².

Class 8/ Class 9 - Properties Of Quadrilateral Figures (Worksheet) (#CBSEClass8Maths) (#CBSEClass9Maths)

Properties Of Quadrilateral Figures

(Worksheet)

Question. Fill in the blanks (True or False) for the properties of the following figures:

Property	Parallelogram	Rhombus	Rectangle	Square
1. Both pairs of opposite sides are parallel and equal.	?	?	?	?
2. Both pairs of opposite angles are equal.	?	?	?	?
3. Diagonals bisect each other.	?	?	?	?
4. Diagonals are equal.	?	?	?	?
5. Each angle is 90°	?	?	?	?
6. Diagonals intersect at right angles.	?	?	?	?
7. All sides are equal.	?	?	?	?

CBSE Class 9 - Mathematics - CH 11 - Constructions - Very Short Questions and Answers (#CBSEClass9Notes)

Constructions

Very Short Questions and Answers
Based NCERT Class 9 Mathematics Chapter


Q1: With the help of ruler and compass, which of the following angles can be constructed?

(a) 35°
(b) 40°
(c) 37.5°
(d) 15°


Answer:  37.5° and 15° angles can be constructed using a ruler and a compass.


Q2(NCERT Exemplar): With the help of a ruler and a compass it is not possible to construct an angle of :

(A) 37.5°
(B) 40°
(C) 22.5°
(D) 67.5°