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?

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- English
Subject- Hindi
Mathematics - English - Hindi
Science - English - Hindi
Social Science - English - Hindi

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.

Class 9 - Maths - Quadrilaterals - Important Points to remember (#CBSE-Notes)

Quadrilaterals 

Important Points to remember

Based on Class 9 NCERT Chapter on Quadrilaterals

Simple 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.

CBSE Class 9, 10, 11, 12 - Mathematics - Know about Special Constants

Know about Special Constants

Change is the only constant in our lives. However, there are constants or constant numbers that are frequently used in the domains of Science, Mathematics, Economics etc.

Do you know what is golden ratio?

What is the value of Pi?

What are transcendental numbers?

What's the value of cube root of 2?

CBSE - Class 6-12 - Mathematics - Important Formulas

Mathematics - Important  Formulas 

eduvictors.com has added a new section "Mathematics" and has compiled important formulas on different topics.

Here is the list of Mathematics formulas:

1. Algebra Formulas

⓵ Polynomials
⓶ Fractions
⓷ Algebraic Identities
⓸ Exponents
⓹ Roots

CBSE Class 9 - Mathematics- SA1- Sample Question Paper (2016)

CBSE Class 9 - Mathematics- SA1- Sample Question Paper (2016) 

CBSE Class 9 - SA1 - Maths - Lines and Angles (Questions and Answers)

Lines and Angles 

(Questions and Answers)

 

Here follows few questions that have asked in previous examination papers.

CBSE Class 9 - Maths - SA1 - Polynomials (Problems Usually Asked)

Polynomials 

Problems Asked in SA1 Papers

You may download this post as pdf.
Q1: Solve the following question using factor theorem.



Q2:

CBSE Class 9 - Lines and Angles (Worksheet-2)

Lines and Angles (Worksheet-2)

Question: Fill in the blanks

1. Three or more points said to be __________ if there is a line which contains all these points.


2. Two lines are called ___________ lines, if they have common point.


3. Three or more lines intersecting at the same point are called as ____________ lines.


4. An angle whose measure is less than 90° is called _________ angle.


5. An angle whose measure is 90° is called _________ angle.


6. An angle whose measure is more than 90° but less than 180°, is called _______ angle.

CBSE Class 9 - Maths- SA2- Sample Question Paper (2016)

CBSE Class 9 - Maths- SA2- Sample Question Paper (2016) 

CBSE Class 9 Maths - SA2 - Sample Question Paper (2012)

CBSE Class IX - Maths- SA2- Sample Question Paper (2012) 
The sample paper is based on old pattern, still it is good for practice.

CBSE Class 9 - Maths - SA1 -Sample Question Paper (2015-16)

CBSE Class 9 - Maths - Sample Question Paper
Paper sent by one of the reader. Good for practice.

CBSE Class 9 - Maths SA1 - Sample Question Paper (2010-11)

CBSE Class 9 - Maths - Sample Question Paper
The paper is based on old pattern MCQs have been replaced by Very Short Questions. Still helpful.

CBSE Class 9 - Maths - Number Systems (Very Short Questions and Answers)

NUMBER SYSTEMS 

Very Short Q & A

Q1: Categorize the following numbers as
(i) Natural Numbers
(ii) Whole Numbers
(iii) Integers

(iv) Rational Numbers

7, 3/2, 0, 2, -9/5, 1/4, -8

Answer:
(i) Natural Numbers {2, 7}

(ii) Whole Numbers {0, 2, 7}

(iii) Integers {-8, 0, 2, 7} 

(iv) Rational Numbers {-8, -9/5, 0, 1/4, 3/2, 2, 7}

Q2: What is the rational number which does not have reciprocal?

Answer: 0 (zero)

Q3: Write the greatest negative integer.

Answer: -1

Q4: Name the smallest natural number.

CBSE Class 9 - Maths - CH 13 - Surface Area and Volume (Study Points)

Surface Area & Volume

Key Concepts

S.no.	Name	Figure	Lateral/ Curved Surface Area	Total Surface Area(TSA)	Volume(V)	Symbols use for
1	cuboid		2(l + b)xh	2(lb + bh + hl)	lbh	l=length b=breadth h=height
2	cube		4s2	6s2	s3	s = side
3	Right circular cylinder		2Πrh	2Πr(h + r)	Πr2h	h = height r = radius of base
4	Right circular cone		Πrl	Πr(l + r)	1 3 Πr2h	r = radius of base h = heightl = Slant height
5	Sphere		4Πr2	4Πr2	4 3 Πr3	r = OA = radius

CBSE Class 9 - Maths - Ch 14 - Statistics (NCERT Ex 14.3)

Statistics

Exercise 14.3

Question 1:

A survey conducted by an organisation far the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures(in %):

S.no.	Causes	Female fatality rate(%)
1	Reproductive health conditions	31.8
2	Neuropsychiatric conditions	25.4
3	Injuries	12.4
4	Cardivasculor conditions	4.3
5	Respiratory conditions	4.1
6	Other Causes	22.0

(i) Represent the information given above graphically.

(ii)Which condition is the major cause of women's ill health and death worldwide?

(iii) Try to find out, with the help of your teacher, any two factors which play a major role ill the cause in (ii) above being the major causes.

Answer:

(i) By representing causes on x-axis and family fatality rate on y-axis and choosing an appropriate scale (1 unit 5% far y axis), the graph of the information given above can be constructed as follows:

In the graph, the rectangle bars are of the same width and have equal spacing among them.

(ii) As shown, Reproductive health condition is the major cause of women's ill health and death worldwide.

(iii) The factors are as follows.

1. Lack of medical facilities

2. Lack of awareness of  right medical treatment

Question 2:

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.

CBSE Class 9 Maths - CH14 - Statistics (NCERT Ex 14.1 and 14.2)

Statistics (NCERT Ex 14.1 and 14.2)

NCERT Exercise 14.1

Question:1

Give five examples of data that you can collect from day to day life.

Answer:

In our day to day life,we can collect the following data.

1. Numbers of girl students per class in a school.

2. Number of cars of different models in our colony.

3. Production of rice in last 20 years in our country.

4. Rainfall in our city in the last 10 years.
5. Scores made by a team in Indian Premier League tournament.

Question:2

Classify the data in Q1 above as primary or secondary data.

Answer:

The information which is collected by the investigator himself with defined objectives is called as primary data whereas when the information is gathered from a source which already had stored, is called as secondary data.
Item 1 and 2 are the primary data where as the data in 3, 4 and 5 is secondary data.

Exercise 14.2

Question:1

The blood groups of 30 students of class VIII are recorded as follows:

A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O

A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O.

CBSE Class 9 - Maths - Quadrilaterals (NCERT Ex 8.2)

Quadrilaterals

NCERT Ex 8.2


Q1: ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see the given figure). AC is a diagonal. Show that:



(i) SR || AC and SR = AC

(ii)PQ = SR

(iii)PQRS is a parallelogram.

Answer:

(i) In ▲ADC, S and R are the mid-points of sides AD and CD respectively.

In a triangle, the line segment joining the mid-points of any two sides of the triangle is parallel to the third side and is half of it.

∴ SR || AC and SR = AC ... (1)

(ii) In ▲ABC, P and Q are mid-points of sides AB and BC respectively. Therefore, by using mid-point theorem,

PQ || AC and PQ = AC ... (2)

Using equations (1) and (2), we obtain

PQ || SR and PQ = SR ... (3)

⇒ PQ = SR

(iii) From equation (3), we obtained

PQ || SR and PQ = SR

Clearly, one pair of opposite sides of quadrilateral PQRS is parallel and equal.

Hence, PQRS is a parallelogram.


Q2: ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Answer:

In ▲ABC, P and Q are the mid-points of sides AB and BC respectively.

∴ PQ || AC and PQ = AC (Using mid-point theorem) ... (1)

CBSE Class 9 - DAV Panvel - SA 1 Practice Test Papers (2014)

Class 9 SA 1 Practice Test Papers

Credits: The SA1 Practice Test Papers designed by DAV (Panvel) teachers.

SA1 English Sample Question Paper (2014)

SA1 Hindi Sample Question Paper (2014)

SA1 Mathematics Sample Question Paper (2014)