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Showing posts with label class9-maths. Show all posts
Showing posts with label class9-maths. Show all posts
Tuesday 28 March 2017
Monday 27 March 2017
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.
Friday 17 February 2017
CBSE Class 8 - Maths - CH3 - Understanding Quadrilaterals (Worksheet) (#cbsenotes)
Understanding Quadrilaterals
(Worksheet)
☛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.
Wednesday 15 February 2017
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)
Tuesday 7 February 2017
Monday 6 February 2017
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)
Sunday 29 January 2017
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.
Friday 27 January 2017
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)
Thursday 26 January 2017
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
Tuesday 24 January 2017
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
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?.
Sunday 22 January 2017
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.
Thursday 5 January 2017
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. | ? | ? | ? | ? |
Friday 30 December 2016
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°
Monday 19 December 2016
Class 9 - Mathematics - Ch10 - Circles (Worksheet) (#CBSENotes)
Circles
CBSE Class 9 - Mathematics - Chapter 10
Worksheet
Fill In the blanks
1. A _____ is a set of points in a plane, each one of which is at a constant distance from a fixed point in the plane.
2. A line segment joining two points on a circle is called the ______ of the circle.
3. A line which meets a circle in two points is called a ________ of the circle.
4. A chord passing through the center of the circle is called a ________ of the circle.
Friday 16 December 2016
CBSE Class 9 - Mathematics - Probability - Problems and Solutions
Probability
Problems and Solutions (NCERT Exemplar Answers)
Problem 1: Two dice are thrown simultaneously 500 times. Each time the sum of numbers appearing on their top is noted and recorded as given in the following table:
Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Frequency | 14 | 30 | 42 | 55 | 72 | 75 | 70 | 53 | 46 | 28 | 15 |
If the dice are thrown once more, what is the probability of getting a sum
(i) 3
(ii) more than 10
(iii) less than 5 or equal to 5
(iv) between 8 and 12
Solution: Click here to see the solution.
Problem 2: Here is an extract from a mortality table:
Age(in years) | 60 | 61 | 62 | 63 | 64 | 65 |
Number of persons surviving out of sample of one million | 16090 | 11490 | 8012 | 5448 | 3607 | 2320 |
(i) Based on this information, what is the probability of a person 'aged 60' of dying within a year?
(ii)What is the probability that a person 'aged 61'will live for 4 years?
Tuesday 13 December 2016
CBSE Open Text Based Assessment (OTBA) for classes IX & XI, 2017 is Available
Open Text Based Assessment (OTBA)
For classes
IX & XI 2017
Available Now
OTBA Material for Class 9 and Class 11 for this session (2016-2017) is available at CBSE website. Here are the links to download the pdfs.
Open Text Material for Class IX
Subject- Hindi
Mathematics - English - Hindi
Science - English - Hindi
Social Science - English - Hindi
Friday 2 December 2016
CBSE Class 9 - Maths - Quadrilaterals (Questions and Answers)
Quadrilaterals
Class 9 NCERT Exemplar Problems and Solutions
Question 1: If angles A,B,C and D of a quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4 then ABCD is a trapezium. Is this statement true? Give reason for your answer.Solution: Since, the angles are in the ratio 3:7:6:4,
Let these angles be 3x,7x,6x and 4x.
∵Since sum of angles of a quadrilateral is 360°,
∴3x+7x+6x+4x=360°
⇒ 20x=360°
⇒x=18°
∴The angles are:
∠A=3×18°=54°,
∠B=7×18°=126°,
∠C=6×18°=108° and
∠D=4×18°=72°
Since ∠A+∠B=54°+126°=180°. Thus, the sum of co-interior angles is 180°formed by lines AD,BC and transversal AB, ∴, AD∥BC.
So,ABCD is a trapezium.
Hence, the given statement is true.
Sunday 20 November 2016
Class 9 - Maths - Quadrilaterals - Important Points to remember (#CBSE-Notes)
Quadrilaterals
Important Points to remember
Based on Class 9 NCERT Chapter on QuadrilateralsSimple Classification of Quadrilaterals. For detailed version check at wikipedia |
① A simple closed figure bounded by four line segments is called quadrilateral.
② The sum of (interior) angles of a quadrilateral is 360°- Angle Sum Property of Quadrilateral
③ A quadrilateral in which one pair of opposite sides is parallel is called trapezium.
④ A quadrilateral in which both pairs of opposite sides are parallel is called parallelogram.
⑤ If one of the angles of a parallelogram is right angle then it is a rectangle.
⑥ If all sides of a quadrilateral are equal then it is called rhombus.
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