9 Green C Math Class

The "Less than" method :

In this 'less than' method, we start with the upper limits of the classes and go on
adding the frequencies. After plotting, the frequencies, we can get a rising curve.

Draw less than ogive curve from the data given below :

Marks 0 – 20 20 – 40 40 – 60 60– 80 80–100 100–120
No. of. students 5 3 2 4 6 7

At first, we need to make frequency distribution table to find c.f (cumulative fre-
quency).

Class f. c.f 30
0 –20 5 5
20 – 40 3 8 27
40 – 60 2 10
60 – 80 4 14 24
80 – 100 6 20
100 – 120 7 27 No. of Students 21 Less than curve

18

15

12

9

6

3

O 40 80
20 60
100
120
140
(Marks)

The "More than" method :

In this 'less than' method we start with the upper limits of the classes and go on
adding the frequencies. After plotting, the frequencies, we can get a falling curve.

Draw more than ogive curve from the data given below

Marks 0 – 20 20 – 40 40 – 60 60– 80 80–100 100–120
No. of. students 5 3 2 4 6 7

(x, y) = {20, 5), (40, 8) (60, 10), (80, 14), (100, 20), (120, 27)}.

More than method

30

Class f. c.f 27
0 – more 5 27
20 – more 3 22 24 More than curve
40 – more 2 19
60 – more 4 17 No. of Students21
80 – more 6 13 40
100 – 120 7 7 6018
100
12015
140
12

9

6

3

O 80
20

(Marks)

GREEN Mathematics Book-9 295

The "less than" and "more than" ogive curve

When we draw 'less than'and more than ogive curve on the same graph paper, two
curves are intersecting at a point, from that point we should draw perpendicular on
x-axis. The intersecting point of perpendicular and x-axis is median of the given data.

Look at the following example :

Draw less than and more than ogive curve from the data given below :

Marks 0 – 20 20 – 40 40 – 60 60– 80 80–100 100–120
No. of. students 5 3 2 4 6 7

At first, we need to make frequency distribution table to find c.f (cumulative fre-
quency).

Class f. Less than c.f More than c.f
0 –20
20 – 40 55 27
40 – 60
60 – 80 38 22
80 – 100
100 – 120 2 10 19

4 14 17

6 20 13

7 27 7

In this figure, two curves are intersecting 30
at point A. The perpendicular is drawn
from point A to the x-axis, the coordinate No. of Students 27 More then curve Less then curve
of point A is (90, 15). 24
21 A
Therefore, median = 90. 18

15

12

9

6

3

O 40 80
20 60
100
120
140
(Marks)

296 GREEN Mathematics Book-9

EXERCISE 17.5

A. Very Short Questions

1. The following line graph shows the average Temperature 35
temperature in every 2 hrs of a day from 6 AM 30
to 6PM. 25
20
a. At what time is the temperature 15
maximum? 10
5
b. At what time is the temperature minimum?
6.AM8.AM10.AM12.Noon2.PM 4.PM 6PM
c. What is the temperature at 12 noon? Times

d. What is the difference of the temperature
between 10AM and 6PM.

2. Observe the cumulative frequency curve and 40
answer the following questions.
No. of Students 35 Less then curve
a. Which axis represents the frequency and 30
marks? 25

b. How many students are there altogether? 20

c. Find the difference between number of 15
students who got 40 and 70 marks.
10

5

O
10 20 30 40 50 60 70

(Marks in math)

3. a. Find the class for "Quartile first" from the given c.f. 25
O-give curve. c.f 20
15
10
5

O
10 20 30 40
(Marks)

b. Find the median class from the given ogive. 20
16
12
8
4

O
10 20 30 40 50 60 70
(Marks)

GREEN Mathematics Book-9 297

Find the class for third quartile from the 16
given ogive curve. 14
c. 12
10
8
C.f. 6
4
4. Observe the histogram and answer the following: 2

O
10 20 30 40 50 60 70

(Marks)

a. How many people got Rs. (180 – 200)? No. of People 96
84
b. Write two wages of group having the same 72 120 140 160 180 200 220 240 260 280
number of people. 60 Daily wage (Rs.)
48
c. What is the difference of no. of people 36
between the wages in the class (160 – 180) and 24
(220 – 240)? 12

C. Short Questions O

5. The monthly income of a family is Rs. 20,000. The monthly expenditure on different

items are shown in the given pie-chart, study the pie-chart and 5% 10%
answer the following. 25%
Rent
a. Find the amount of expenditure on food. EduTcraatniospnort
b. How much money is spent on rent?
c. How much money is spent on medicine and education? Medicine Food
d. How much money is spent on other? 5% 35%
Other

6. A worker's monthly income is Rs. 125000. If he spends the

money as indicated in the pie- chart, answer the questions. Education
50%

a. Monthly expenditure in rent. Rent Other

b. Total expenditure on food and education. 5% 5%
40%

Food

7. Complete the frequency distribution table

a. Class f c.f b. Class f. c.f.

0 – 10 1 5 0 – 20 5 5
10 – 20 2 15
20 – 30 3 – 20 – 40 – 18
30 – 40 4 –
40 – 50 6 12 40 – 60 – –
50 – 60 5
– 60 – 80 7

20 80 – 100 5

–

8. Complete the table below with reference to more than ogive method

298 GREEN Mathematics Book-9

a. Class c.f b. Marks c.f.
More than 10 77 0 – 10 80
More than 20 (.......) – 5 = 72 10 – 20 80 – (.......) = 77
More than 30 72 – (.......) = 58 20 – 30 77 – (.......) = 69
More than 40 (.......) – 25 = 33 30 – 40 69 – 17 = (.......)
More than 50 33 – (.......) = 10 40 – 50 (.......) – 29 = (.......)
50 – 60 23 – (.......) = 28
N = ................ 60 – 70 (.......) – (.......) = 2
N = ...............

9. a. The number of students in different classes of the year 2073 are presented
below. Show the following information in a histogram.

Class III IV V VI VII VIII IX X

No. of. students 75 80 85 90 100 85 115 90

b. Represent the following on a line graph.

Wages (Rs.) 500 600 700 800 900 1000

No. of. workers 20 10 15 8 4 24

c. The following data gives the population of a village of 7 years. Show the
following information in histogram.

Year 2067 2068 2069 2070 2071 2072 2073
Population 2000 1500 3000 4000 3500 4500 5000

d. Show the information on a line graph

Children 123456

No. of family 5 3 8 9 7 4

e. Show the information on a line diagram.

Year 1991 1992 1993 1994 1995 1995
400 800 85
Production (quintal) 200 600 1000

10. Draw a histogram to show the given information.

Wages 100 – 150 150 – 200 200 – 250 250 – 300
No. of workers 5 2 10 9

11. Make a histogram to show the data given below in the table. Also answer the
following questions.

GREEN Mathematics Book-9 299

Age group (ys) 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
No. of people 2 12 22 7 3

a. Which group people are more than other? Others
b. Which group have less people? 750
c. Is the number of people directly proportion to ages of group?
d. Which class have second lowest number of people?

C. Long Questions

12. Show the information in a pie-chat

Expenditure Food Edu. Rent Cloths
Income 1000 1500 500 1250

13. The area of different districts for the production of agriculture are given below.
Show them in a pie-chat.

District Rautahat Bara Parsa Mahotari Sarlahi Chitwan
2000 3000
Production (Q.) 5000 4000 1500 2500

14. Show the given height of different Himalayans range in a pie-chart.

Himalayan Dhwalagiri Annapurna Manaslu Sagarmatha Makalu
Height (M) 8172 8078 8156 8848 8470

15. Collect the details of 5 years SLC result of your school and show them in a
pie-chart.

16. Ask the yearly expenditure details of your family and show them in a pie- chart
on the basis of food, Education, Rent, Medicine and others.

17. The monthly budget of a family on different items are given below:

Food - Rs. 2100 Education - Rs. 3300

Other - Rs. 2250 Saving - Rs. 3150

Represent the information in a pie-chart.

18. Show in a pie-chart:

Year 2010 2011 2012 2013 2014
Students 500 560 700 600 850

19. Show the following information on the histogram.

Daily wages Less Less Less Less Less Less
(Rs.) than 50 than 100 than 150 than 200 than 250 than 300

No. of workers 5 3 6 9 7 5

300 GREEN Mathematics Book-9

20. Draw the histogram representing the data given below:

Age group (yrs) 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
2 4 5 12
No. of people 1 3

21. Draw the histogram to show the data given below:

Class 0 < 10 0 < 20 0 < 30 0 < 40 0 < 50
Frequency 12 18 21 27 32

22. Draw the histogram to represent the data give below:

Class < 100 < 200 < 300 < 400 < 500
Frequency 40 60 70 80 150

23. The given data represents the information about blood pressure of ladies of age
between 20 - 45 years. Draw the cumulative frequency table to show the ogive
curve (Free hand curve).

Diastolic 70 – 75 75 – 80 80 – 85 85 – 90 90 – 95
No .of ladies 2 12 22 7 3

24. Construct less than and more than ogive from the table given below:

Class 0–5 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30
f 2 4 3 1 5 7

25. From the data given below, construct a cumulative frequency curve or ogive to
represent less than method if one of the class is 0 – 10.

0, 3, 20, 7, 11, 10, 18, 21, 13, 15, 25, 30, 39,

40, 50, 52, 47, 48, 12, 23, 31, 27, 59, 47

26. Draw a "less than" ogive from the data given below:

Class 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
f 13 4 5 2 6

27. Draw the 'More than" ogive on the same coordinate axes and find the quartile
second of the distribution.

Class 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
f 2 5 3 4 6

28. Draw the "less than" ogive and find the class for upper quartile.

Class 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100
f 2 1 5 4 3

GREEN Mathematics Book-9 301

18

Probability

Estimated Teaching Periods : 8

The pascal is the SI derived unit of pressure used to quantify internal
pressure, stress, Young's modulus and ultimate tensile strength. It is
defined as one newton per square meter. It is named after the French
polymath Blaise Pascal.

Contents

18.1 Introduction

18.2 Some basic terms used in probability

18.3 Empirical probability

a. Probability (P)= No. of favourable events = n(E)
No. of total events n(S)

Objectives

At the end of this unit, students will be able to:
introduce probability, know the types of probability
know about probability scale
know about the law of probability
solve the problems related to probability

Materials

Coin, dice, playing cards, spinner, different colour balls, bag, thumb pins, number
cards, etc.

302 GREEN Mathematics Book-9

18.1 Introduction

'Probability', 'Likelihood' and 'Chance' are very commonly used words in our day - to
day conversation. These words are used in the same sense. For example, we say that the
probability that I may not be able to come to the party. It is likely to rain today. Similarly
we say that they have little chance of winning the foot ball match. All these events are
not certain. They are probabilistic. Probability theory is a concept which numerically
measures the degree of uncertainty. Probability is the measure of the likelihood or chance
that a particular event will happen.

There are two possibilities – either an event may take place or it may not take place. The
probability of possibilities never exceeds one. If it is sure that an event can never take place
the probability is 0 and if it is sure that something will always happen, its probability is 1.
Chance between absolute certainty and impossibility lies between 0 and 1.

0 1

Impossibility Absolute certainty
(events never take place) (events always take place)

18.2 Some basic terms used in probability

Experiment:
An activity or operation which produces result is called an experiment. For example,
when we toss a coin, either a 'Head' or a 'Tail' appears on the top.

Random experiment:
An experiment whose outcome can not be predicted in advance is called a random
experiment. For example, which event (Head or tail) will appear on the top if a coin
is tossed once.

Trial and outcome (event) :
Performing a random experiment is a trial and result of it is an event or outcome.
Rolling a dice is a trial and getting 1, 2, 3, 4, 5, or 6 is an event.

GREEN Mathematics Book-9 303

Equally likely events:
Events of an random experiment which have equal chance of occurence when we
throw a die the out comes 1, 2, 3, 4, 5 and 6 are equally likely to appear.

Sample space:
The set of all possible outcomes of a random experiment is called a sample space. The
sample space is generally denoted by 'S'.
For example:
a. When an unbiased coin is tossed once, sample space (S) = {H, T}
b. When a coin is tossed two times in succession, S = {HH, HT, TH, TT}

Exhaustive event:
The total number of all possible outcomes of a random experiment is called the
exhaustive event.
Example : In a deck of playing cards, the total possible outcomes= 52.

Favourable events:
The events (out comes) of a random experiment which are expected are called
favourable events.
For example : While rolling a die, S = {1, 2, 3, 4, 5, 6} and the number of favourable
events getting prime number, are 2, 3, and 5.

18.3 Empirical probability

Number of events
Empirical probability is defined as :

Total numbers of experiement

304 GREEN Mathematics Book-9

Worked Out EXAMPLES

EXAMPLE 1 A box contains 5 red, 6 black and 7 blue balls. If a ball is drawn at

random, find the probability of getting a black ball.

Solution : Here, total balls, n(S) = 5 + 6 + 7 = 18
Let E be the event getting black ball.
Thus n(E) = 6

Now, P(E) = n(E) = 6 = 1
n(S) 18 3

EXAMPLE 2 From the cards numbered from 5 to 20, a card is drawn at random.
Find the probability of getting a card which is a prime number.
Solution :
Here,
Total cards, n(S) = 16 [20 – 4 = 16]
Let E be the favourable event.
Thus, E = {5, 7, 11, 13, 17, 19}

Now, P(E) = n(E) = 6 = 3
n(S) 16 8

EXAMPLE 3 A natural number is chosen at random from the first 100 natural
numbers, what is the probability that the number is exactly divis-
Solution : ible by 7?

Here,

n(S) = 100

Let E be the fovourable event

Thus, E = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]

n (E) = 14 100 = 14 2 = n(E) =
Now, p(E) = n(E) = 14 = 7 7 7
14
n(S) 100 50

∴ The probability that the number is exactly divisible by 7 = 7 .
50

GREEN Mathematics Book-9 305

EXAMPLE 4 From a pack of 52 playing cards, a card is drawn. Find the probabil-

ity that it is a face card of heart.

Solution : Total cards, n(S) = 52 Face cards Jack, Queen, King
Thus, n(E) = 3

Now, P(E) = n(E) = 3
n(S) 52

∴ Probability of getting a face card of heart = 3 .
52

EXAMPLE 5 An unbiased dice is thrown. What is the probability of not getting
3 or 6.
Solution :
Here,
n(S) = 6 [s= {1, 2, 3, 4, 5, 6}] P(not getting 3 or 6) = P(E)
Let E be the event getting 3 or 6
Thus, n(E) = 2

Now, p(E) = n(E) = 2 = 1
n(S) 6 3

p(E) = 1 – P (E) = 1 – 1 = 2
3 3

∴ The probability of not getting 3 or 6 = 2 .
3

EXAMPLE 6 If one of the letters of the word 'PROBABILITY' is touched by clos-
ing the eyes, find the probability of touching 'B'.
Solution :
Total letters in the word PROBABILITY, n(S) = 11
No. of favourable event, n(E) = 2 [no of B]

Now, p(E) = n(E) = 2
n(S) 11

EXAMPLE 7 Find the probability of giving birth to a child by a pregnant woman

on Monday.

Solution : n(S) = 7 [Sun, Mon ....... Sat]

Let E be the favourable event

Thus n(E) = 1 [Monday]

Now, p(E) = n(E) = 1
n(S) 7

∴ The required probability = 1 .
7

306 GREEN Mathematics Book-9

EXAMPLE 8 In a class of 25 student if the probability of selecting a girl as a
monitor is 0.6, find the number of boys.
Solution :
Total students, n(S) = 25
Let E be the event selecting a girl as a monitor.

Now, p(E) = n(E)
n(S)

P(E) = 0.6 = 6 = 3 i.e. 3 × 5 = 15
10 5 5 5 25
∴ n(E) = 15

∴ Number of boys = Total number of students – Number of girls
= 25 – 15 = 10

EXAMPLE 9 In a lottery there are 10 prizes and 20 blanks. What is the chance of
getting a prize?
Solution :
n(S) = 10 + 20 = 30

Let E be the event of getting a prize

Thus, n(E) = 10

Now, P(E) = = n(E) = 10 = 1
n(S) 30 3

∴ The chance of getting a prize = 1
3

EXAMPLE 10 Head occures 10 times when a coin is tossed 25 times. Find the em-

pirical probability of tail.

Solution : n(S) = 25 ( total number of experiments)
n(E) = n(T) = 25 – 10 = 15
Now,

n(E) = n(E) = 15 = 3
n(S) 25 5

∴ The empirical probability of tail = 3
5

GREEN Mathematics Book-9 307

EXERCISE 18.1

A. Very Short Questions

1. a. What do you mean by sample space in probability?

b. Write the sample space of the following random experiments.

i. tossing a coin. ii. rolling a die

iii. tossing of two coins simultaneously iv. tossing a coin twice.

c. Define empirical probability.

d. What are the probabilities of impossible events and certain events?

e. What do you mean by equally likely event? Write with examples.

f. If the number of favourable events and possible outcomes are n(E) and n(S)
respectively, write the probability of occuring the event E.

g. A is the event that Ram wins a game and B is the event that Ram doesn't win a
game. (i) find the value of p(A) + p(B). (ii) if p (A) 2 , find p(B).
3

B. Short Questions

2. a A box contains 5 red and 10 white marbles. If a marble is taken out randomly,
find the probability that the marble is red.

b. A bag contains 1 red, 1 green and 1 white identical balls. If a ball is drawn ran-
domly from the bag, find the probability that (i) the ball is red. (ii) the ball is not
red. ?

c. There are 3 red, 3 blue and 5 white balls in a box. A ball is taken out randomly.
What is the probability of a ball being blue?

d. A box contains 4 red, 5 black and 6 white balls. If a ball is drawn at random, find
the probability of not getting a black ball.

3. a From the number cards numbered from 1 to 15 a card is drawn at random. Find
the probability of getting a card having a prime number. .

b. From the number card numbered from 1 to 30, a card is drawn at random. Find
the probability of getting a number which is divisible by 5 or 7?

c. A number card numbered from 1 to 30 is drawn randomly. What is the proba-
bility of getting a card having the number which is the multiple of 5 or 6?

d. A natural number is chosen at random from the first 100 natural numbers. What
is the probability that the number so chosen is divisible by 3?

e. A number card is drawn at random from the group of number cards numbered
from 1 to 20. Find the probability of getting a square or cube numbered card.

308 GREEN Mathematics Book-9

f. Find the probability that a number chosen at random from the integers between
10 and 20 inclusive is a multiple of 5 or a multiple of 2.

4. a. A card is drawn from a well shuffled pack of 52 cards. Find the probability of (i)
getting a king (ii) not getting a king .

b. A card is drawn from a well shuffled pack of 52 cards. Find the probability of
getting a spade or a diamond.

c. Find the probability of getting a face card when a card is pulled out from a deck
of 52 playing cards.

d. A card is drawn out from a well shuffled pack of 52 cards. Find the probability
of getting (i) an ace (ii) a card from ace to 10 (iii) a black card or face card.
(iv) a red queen .

C. Long Questions

5. a. A coin is tossed once. Find the probability of getting (i) head (ii) tail

b. Two coins are tossed simultaneously.
i. Write the sample space.
ii. Find the probability of getting head in both coin.
iii. Find the probability of getting at least one head.
iv. Find the probability of getting no head.
v. Find the probability of getting one head and another tail.

6. a. What is the probability of getting 4 when a die is rolled once?

b. When a die is thrown, find the probability that the face turned up may be odd
number only.

c. If a die is thrown once, what is the probability of getting a number which is the
multiple of 2?

d. Find the probability of getting a prime number when a die is rolled once.
e. If a die is rolled once, find the probability of :
i. getting multiple of 2 or 3.
ii. not getting six
iii. getting prime number or even number.
iv. getting a number greater than 5 or less than 2.
v. getting a number less than 1.
vi. getting a number that is not 1.

GREEN Mathematics Book-9 309

2

7. a. While rotating the needle on the given spinner as in the figure, 1 3
write down the probability of the needle stopping at 1.

4

b. In a class of 40 students, 3 boys and 5 girls wear the spectacles.

If one of the students needs to be selected for debate competi-

tion, find the probability of selecting the students wearing the spectacles.

c. The probability of winning a prize in a raffle is 1 . Find the probability of not
5
winning the prize in the raffle.

d. A letter is chosen at random from the world "MISSISSIPPI". Find the probability
that the chosen letter is i. a vowel ii. a consonant.

e. What is the probability of giving birth to a child by a pregnant woman on
Saturday?

f. If the probability of germinating a seed of a flower is 0.8, how many seeds out
of 100 will germinate?

g. There are numbers of three digits 1, 3 and 5. If a number is selected, what is the
probability that the number is divisible by 5?

h. Out of 30 students of a class, there are 10 boys. Find the probability of selecting

a girl student as a monitor.

8. a. An unbiased coin is tossed 100 times and the outcome is in the table.

Face Head Tail

Frequency 60 40

i. Find the empirical probability of getting a head

ii. Find the empirical probability a tail.

iii. Find the sum of two probabilities.

b. A die is thrown 100 times and the outcomes are recorded in the table.

Out comes 1 2 3 4 5 6

Frequency 10 15 30 12 18 15

Calculate the empirical probability of getting a number.

i. less than 3 ii. 3

iii. 4 or 5 iv. 4 or getter than 4.

310 GREEN Mathematics Book-9

Revision for Examination

Sets

1 Marks Questions

1. Write down the formula of U having two sets A and B.

2. What is the cardinal number of set A which is the set of number of boys student
studying on their own school.

3. What is the formula of A∪B ?

4. Give one example of set having cardinal number zero.

5. If A = {2, 4, 6, 8, 10} and B = {8, 10, 12} then A – B {...............}.

2 Marks s

1. If P = {8, 9, 11, 12, 15} and Q = {10, 11, 12, 14, 16, 18} find Q – P and P∩Q.

2. If U = {7, 8, 9, 10, 11, 12, 13}, M = {7, 9, 11} and N = {8, 9, 11, 12}, Find N – M .

3. If A = { – 5, – 3, – 2, 3, 6} and B = {2, 3, 6, 7, 12}, find (A – B)∪ (B – A).

4. Using the given venn - diagram prepare a list of the elements of following sets.

U

H 68 T
4

5 79

3

(T – H) UH

5. If U = {4, 5, 6, 7, 8, 9}, A = {4, 6, 8, 9} and B = {5, 6, 7}, find A∪B.

4 Marks Questions
1. If n(U) = 100, n(A) = 50, n(B) = 48 and n(A∩B) = 11 then.

(i) Find the value of n(A∪B)
(ii) Show it in a venn-diagram.

2. In a survey of 60 students, 30 drink milk, 25 drink curd and 10 students drink milk
as well as curd then,

(i) Draw a Venn-diagram to illustrate the fact.
(ii) Find the number of students who drink neither of them.

3. In a class of 50 students, 25 students like to play football, 35 like to play cricket and
15, like to play both the games. How many students do not like to play any games?
Illustrate the above information by a venn-diagram.

GREEN Mathematics Book-9 311

4. Out of 100 students in the examination of class V, 70 passed in Maths, 60 passed in
Science and 20 failed in both subjects, find the number of students who passed in
both by using a venn-diagram.

5. In a survey of a community 45% of the people like Dashain festival, 65% like Tihar
festival and 20% like both festivals

(i) Show it in a Venn-digram.

(ii) What percent of them don't like both?

5 Marks Questions

1. In a school, 80 students of class X were asked what they would like milk or tea
60 said, they would like tea. 50 said they would like milk and 10 said they would
like neither milk nor tea. By drawing a Venn-diagram, find the following number of
students:

(i) Who like both tea and milk.

(ii) Who like milk only?

(iii) Who like tea only?

2. In a survey of a community, it was found that 85% of the people like winter season
and 65% like summer season. If there were none who did not like both seasons.

(i) Present the above information in a venn-diagram.

(ii) What percent were there who liked both the seasons?

(iii) What percent liked winter season only?

3. Out of 90 civil servants, 65 were working in the office, 50 were working in both the
premises, if 70 were working in the field.

(i) How many civil servants were absent?

(ii) How many civil servants were working in the field only?

(iii) Represent the above information in a venn-diagram.

4. 32 teachers in a school like either milk or curd or both. The ratio of number of teachers
who like milk to the number of teachers who like curd is 3:2 and 8 teachers like both
milk and curd. Find how many like only milk by using a Venn-diagram.

5. In a group of 150 people, 85 like grapes and 43 1 like grapes but not the raspberry. If
every people like at least one of them: 3

(i) find the number of people who like both raspberry and grapes.

(ii) find the number of people who like raspberry but not the grapes.

Profit and Loss

1 Mark Questions
1. Write down the formulae for loss percent.

312 GREEN Mathematics Book-9

2. A shopkeeper purchased an electric fan for Rs. 1,560 and sold it at 5% profit. Find his
actual profit amount.

3. If profit is P% and cost price is C.P. what will be the selling price?

4. If loss is L% and S.P. is selling price then what will be the cost price?

5. A man sells a mobile set for Rs. 5,994 at a loss of Rs. 500. What is the cost price of that
mobile set?

2 Marks Questions

1. A watch bought for Rs. 100 is sold at Rs. 120. What will be the gain in percent?

2. 4 lemons are bought for Re. 1 and sold at 3 for Re 1. Find the profit or less percent.

3. A CFL bulb is sold for Rs. 226 at a profit of 13%. At what price was the bulb purchased?

4. An article is bought and sold at a profit of 25% of selling price. Find the profit percent.

5. A person bought 9 oranges for Rs. 45 and he sold each of them at Rs. 7. What
percentage did the make profit?

4 Marks Questions
1. The marked price of a article was Rs. 6000. What will be the price of that article if 15%

VAT was levied after allowing 15% discount on it?

2. Allowing 20% discount on the MP of a watch, If the value of the watch will be Rs.
2376 when a VAT of 10% is added, find its marked price.

3. After allowing 10% discount on the marked price of television and 5% VAT is charged
on it, then its price becomes Rs. 20720. How much amount was given in discount?

4. A shopkeeper marks the price of an article 40% above the cost price. After allowing a
discount of 15% on its marked price, it was sold at a gain of Rs. 950. Find the marked
price of the article.

5. A shopkeeper fixed the marked price of his radio to make a profit of 30%. Allowing
15% discount on the marked price, the radio was sold, what percent profit will be
made?

5 Marks Questions
1. A shopkeeper marks the price of an article Rs. 550 and gives the customer a discount

of 10%. In this way there will be gains Rs. 75 on the article. How much percent will
the marked price be more than cost price?

2. A tourist buys an article at 10% discount on the marked price and he pays 5% VAT.
If the VAT is Rs. 720, find the selling price including VAT.

3. The marked price of a digital camera is Rs. 24000. x% discount is given and 2x% VAT
is levied in the camera. If the price with VAT is 8% more than the marked price, find
the rate of VAT.

4. The list price of an electric iron is Rs. 750. A customer is given two successive
discounts. He pays Rs. 634.50 for it. If the rate of 1st discount is 10%, find the second
discount.

GREEN Mathematics Book-9 313

5. Sita has some sugar of worth Rs. 3000. She sells 1 of it with 10% loss. By how much
3
percentage must the selling price be increased for making 10% profit on the outlay.

If 20% discount is allowed in the selling price, find the profit or loss.

Commission and Taxation

1 Marks Question
1. What is the formula of commission percent?

2. The monthly salary of a civil servant is Rs. 7500. If Rs. 60,000 is tax free amount in
year, how much tax should he pay?

3. A broker receives Rs. 7500 as commission on the total sales Rs. 150000, find the rate
of commission.

4. Find the rate of sales tax if amount of payment is Rs. 5750 when the price if Rs. 5000.

5. If an agent receives Rs. 4500 commission by selling an article at commission rate 5%.
What is the price of the article?

2 Marks Question
1. The annual income of a man is Rs. 90000. He pays a tax of Rs. 4500 at the rate of 15%

of taxable income. Find the tax free amount.

2. A sales agent is paid as salary Rs. 1000 every month and a commission of 0.8% on
total sales. If he receives Rs. 1192 at the end of the month, find the total sales.

3. A company gains Rs. 40,0000 in a year. If 5% profit is divided among 10 employees
as bonus, how much will each employee get?

4. An agent sold some carpet at the rate of Rs. 4500 each and received Rs. 9000 as
commission at 5%. Find the number of carpets sold.

5. Find the rates of sales tax if amount of payment is Rs. 12978 when price is Rs. 12360.

4 Marks Question
1. The monthly salary of an employee in a electric shop is Rs. 16,500 and 1.25%

commission is provided when the monthly sales is more then 5 lakh rupees. If the
sales of the shop in a month is Rs. 7,50,000, find the income of the employee in the
month.

2. A man working in a NGO pays 30% on taxable income upto Rs. 146000 and 40%
on taxable income from 1460001 to 172000. He earns Rs. 189500 and his allowances
income is Rs. 34500. He earns Rs. 189500 and his allowances income is Rs. 34500.
How much tax does he pay?

3. An employee draws Rs. 12,750 as monthly salary in a wholesale stationary shop. A
certain commission is given as per the monthly sales. If the sales of a month is Rs.
10,00,000 and the total income of the employee of the month including commission
is Rs. 25,250, find the rate of commission.

4. An insurance company offered 1% commission for the first 10 lakh and 1.5% for the

314 GREEN Mathematics Book-9

rest of the sum of money collected from new clients by its agents. If an agent is able
to collect a sum of Rs. 12,60,000 from his new clients, find his total commission.

5. A man allowed 10% discount to the buyer and offered 5% commission to the broker
in the price of land. If he received Rs. 256500, what was the fixed price of the land?

5 Marks Questions
1. The monthly income of a man is Rs. 80,000 and 10% of monthly salary is deducted

and deposited as provident fund. If 1% social security tax is levied upto the annual
income of Rs. 3,00,000, 15% tax is levied on Rs. 3,00,000 to Rs. 4,00,000 and 25% tax is
levied above Rs. 4,00,000, how much income tax should he pay in a year?

2. A business company made a profit of Rs. 24,00,000 the last year. The management
decided to distribute 20% bonus from the profit to its 30 employees,

(i) find the bonus received by each employee .

(ii) by what percent should the bonus be increased so that each employee can

receive Rs. 20,000?

(iii) what should be the profit of the company so that it can provide Rs. 20,000 to

each employee at 20% bonus?

Home Arithmetic

1 Marks Questions
1. A meter reader said to the house owner, the unit in Baishakh was 1214 and in Jestha

it is 1620. Find the consumption of units.

2. If the cost of electricity consumption per unit is Rs. 7.30. Find the cost for 11.3 units
consumption.

3. A person paid Rs. 190 to taxi driver. If initial value was Rs. 10 and for each kilometer
was Rs. 9, find how many km did a person travel?

2 Marks Questions

1. The minimum cost upto 20 units is Rs. 80 and the cost per unit from 21 units to 250
units is Rs. 8. Find the total cost from 170 units.

2. A meter reading for the consumption of electricity of a house hold was 1050 units on
30th Chaitra and 1250 units on 30th Baishakh. The minimum charge upto 20 units is
Rs. 80 and above 20 unit is Rs. 7.30. Calculate total charge paid by house holder.

3. The change of ISD call for the USA from Ktm is Rs. 45 per minute. If a man calls for
10 minutes, calculate the cost paid by him with 10%. Telecom service charge (TSC).

4. The minimum charge for the first 250 telephone call is Rs. 425. If the charge for each
additional call is Rs. 3.25, how much will be charged for 439 telephone calls.

5. The number shown by a meter in previous month was 1234 and the current reading
is 1634. The charge upto 100 units = Rs. 150 and each extra unit = Rs.3, VAT = 10%.
Find the bill amount.

GREEN Mathematics Book-9 315

4 Marks Questions

1. The meter reading of a household was 1250 units on Jestha 1st and 1470 units on Asar
1st. The charge upto 20 units is Rs. 80, Rs. 7.30 per units from 21-50 units, Rs. 8.60 per
unit from 51-150 units and Rs. 9.50 per unit from 151 - 250 units. If the payment of
the bill was made on 2n­­d Shrawan, how much money paid by household?

2. The minimum charge of telephone calls upto 175 calls is Rs. 200. The charge for each
extra call is Re 1. If house hold paid Rs. 633 with 10% TSC and 13% VAT to clear the
bill of a month, find the total number of calls made in the month.

3. A man travelled 7.5km by a meter taxi. The minimum fare of Rs. 14 appeared
immediately after the meter was flagged down, then the fare went on at the rate of
Rs. 7.20 per 200 meters. An additional waiting charge of Rs. 720 per 2 minutes and
the taxi needs to wait for 6 minutes during the journey. Calculate the total fare paid
by the man.

4. The meter reading for the consumption of water of a house hold was 1230 units on
the 1st Shrawan and 1275 units on the 1st Bhadra. Calculate the charge to be paid
including 50% sewerage service charge, if the payment of the bill is made in the
following schedule:

i. within the second month after the bill issued.

ii. within fourth month after the bill issued

iii. within sixth month after the bill issued.

[Within 2nd month 3% rebate, with in 3rd month no rebate/no fine, with in 4th month
10 % fine, within 5th month 20% fine and 5 months after 50% fine. ]

5. The charge for the consumption of electricity of a house-hold in a month was
Rs. 2,83,24 with 3%. rebate. If the charge from 0 to 50 units is Rs. 730 per unit, how
many units of electricity was consumed?

Mensuration

1 Mark Questions
1. What is the formulae of area of equilateral triangle?
2. Mention the area of a path running inside a rectangle.
3. What is the formulae for the area of 4 walls of the room?
4. Write down the formulae for the area of trapezium?
5. What is the formulae for the area of path running outside a circular field.
2 Marks Questions

1. Calculate the area of the shaded regions. 10cm

4cm
12cm

316 GREEN Mathematics Book-9

2. Find the perimeter of the rectangle whose length is thrice of its breadth and area is
27m².
12cm
3. Calculate the area of the shaded regions, whose 2cm

l = 12cm = b and d = 2cm. 2cm 12cm

4. Calculate the area of path crossing each other having its l = 18cm, 4cm 16cm
b = 16cm and d = 4.
4cm

18cm

5. If the cost of plastering 4 walls of a room at Rs. 45 per sq. meter is Rs. 8100, find area
of the 4 walls of the room.

4 Marks Questions

1. A rectangular garden is 52m long and 34m broad. A path of 2m wide is running
inside the garden.

i. Calculate the cost of gravelling the path at Rs. 40 per sq. meter.

ii. Calculate the cost of covering the empty space with turfs at Rs. 18 per sq. meter.

2. The cost of carpeting a square room at the rate of Rs. 75 per sq. metre is Rs. 10,800. If
the cost of plastering its walls at Rs. 25 per sq. meter is Rs. 6000, find the height of the
room.

3. Calculate 4cm
4cm
(i) the area of cross section (ii) lateral surface area 3cm
3cm 8cm

(iii) total surface area 9cm

4. The adjoining figure is a rectangular glass vessel of length

40cm, breadth 30cm and height 20cm. If it contains some 20cm

water upto the height of 12cm, how many liters of water is to

be poured into it to fill the vessel completely? [ 1l = 1000cm³] 12cm

5. A wall is 20m long, 3m high and 20cm wide. How many 20cm 30cm
bricks each of 15cm × 10cm × 5cm are required to build
the wall? Also find the cost of bricks at Rs. 8500 per
1000 bricks.

5 Marks Questions

1. The cost of carpeting the floor of a room, whose breadth is twice the height and the
length is twice its breadth, at the rate of Rs. 80 per sq. meter is Rs. 10,240. What will
be the cost of plastering its wall at Rs. 30 per sq. meter?

2. A wall is 40m long. 5m high ad 25cm wide. It contains two windows each of 2m ×
1.5m and a door each of size 1.5m × 4m.

(i) Find the number of bricks each of 25cm × 20cm × 4cm required to construct
the wall .

(ii) Find the cost of bricks at the rate of Rs. 9000 per 1000 bricks.

GREEN Mathematics Book-9 317

3. The dimensions of a wall is 30m × 5m × 20cm. It contains three windows each of 2m
× 1.5m. How many bricks of size 20cm × 10 cm × 5cm are required to build the wall
leaving 10% of the space for the cement work? Also find the cost of bricks at the rate
of Rs. 9000 per 1000 bricks.

4. The area of a square pond is 5625m² and a of 2m wide path is made around the pond.

(i) Find the area of the path.

(ii) Calculate the number of tile each of 40cm × 20cm required to pave the path.

(iii) If the cost of a tile is Rs. 35, find the cost of paving the path.

Algebraic Expressions

1 Mark Questions 2. Factorise: 9a² – 1
1. Factorise: 4x² y + 6xy². 4c²
3. Factorise: a4 + b4 + a²b²
4. Factorise: x³y – 64y4

2 Marks Questions

1. Simplify: a² 2a² – 4a 2 2. Factorise : 81ax5 – 16ax
+ a – 2a – 4. Find the H.C.F. of x² – 25 and x² + 2x – 15

3. Resolve into factors: a² – 3 + 2b²
b² a²
5. Simplify: 1 + 1
a+1 a–1

4 Marks Questions

1. Find the L.C.M. of a² – 4, a³ – 8 and a² – 7a + 10.
2. Simplify: x² + 3x + 2 × x² – 9

x² + x – 6 x² – x – 6
3. Simplify: (a – b)² – c² + (b – c)² – a² + (c – a)² – b²

a² –(b + c)² b² – (c + a)² c² – (a + b)²

4. Find the H.C.F.: 2x³ – x² – x, 4x³ – x, 8x4 + x

5. Simplify : x² + ax + a² + x² – ax + a²
a+x x–a

5 Marks Questions

1. Simplify: x – y + x + y + 2y³

x² – xy + y² x² + xy + y² x4 + x²y² + y4

2. Simplify: a² a–1 2 + a–2 + a² a–5 15
– 3a + a² – 5a + 6 – 8a +

3. Find the H.C.F. of : a³ + b³, a4 + a²b² + b4, a³ – a²b + ab²

318 GREEN Mathematics Book-9

Indices

1 Mark Questions 2. Simplify : 0.25 3. Solve : 2x = 8

3

1. Evaluate: (9)2

4. Simplify : 48 ÷ 8² 5. Solve cdx – 4 = dcx – 4

2 Marks Questions

1. Simplify: o 8 3 27 2 o 32 –1 2

p ×o p× p 2. Simplify: 3 (x + y)– 8 × (x + y)3
9 16 81 4. Solve: 1 = 27– x

3. Solve : 3x + 1 – 3x = 162 9 × 32x

5. Solve: 3x + 2 × 2x – 1 = 162

4 Marks Questions

1. a+b xa² b+c xb² c+a xc²

Simplify : × × xa²
xb² xc²

2. If 2 – –2 show that x³ + 3x = a – 1.
a
a3 a3,

3. Solve : 9x + 1 = 32x + 1 + 54.

4. If a = bc, b = ca and c = ab, prove that abc = 1.

5. Simplify: oxxa²a+bb² a + b oxxb²b+cc² p b + c × o xc² + a² c + a
xca
p × p

5 Marks Questions 2
2 3
1. If m2 + 2 = + 5– , prove that 5m3 + 15m – 24 = 0.
53

2. Simplify : a+b xa2–b2 × b+c xb2–c2 × c+a xc2–a2

3. Simplify: o xp r xq p xr q
xq xr xp
p× o p ×o p

4. If a³ + b³ + c³ = 1, prove that : o xa a² – ab + b²× xb b² – bc + c² × xc c² – ca + a² = x²
x–b ox–cp ox–ap
p

Ratio and Proportion

1 Mark Questions

1. Find the ratio of 5 years and 5 month.
2. Divide 455 into the 6:7 ratio.
3. Find the triplicate ratio of 7:9.

GREEN Mathematics Book-9 319

2 Marks Questions
1. If (5a – 3b) : (7a – 4b) = 9:13, then find the value of a : b.

2. The sum of two numbers is 80, if their ratio is 7:9, find the numbers.

3. If a = c = c , then prove that a + c + e = e .
bd f b+d+f f

4. If a = c , then verify that a+b = c+d
b d a–b c–d

5. Find the mean proportional between 4 and 16.

4 Marks Question

1. If x : y = 8 : 9, find the ratio of (7x – 4y) and (3x + 2y)

2. Divide 780 in the ratio 1 : 2 : 3.
3. What must be added to each term of the ratio 83 : 237 to make the ratio 1 : 2?
4. What must be subtracted from each term of the ratio 15 : 17 to make the ratio 5 : 6.

5 Marks Question

1. If a = b , then prove that a(a + b) = a3
bc c(b + c) c3

2. If a = c , then verify that (c + a)3 = b(a – c)4
bd (b + d)3 a(b – d)4

3. If a, b, c, d, e, and f are in continued proportion, then prove that a = a5 .
f b5

3. If a, b, c, d, are continued proportion, prove that a3 + b3 + c3 = a .
b3 + c3 + d3 d

5. If (7p + 5q) (7r – 5s) = (7r + 5s) (7p – 5q), then prove that p = r .
q s

Simultaneous and Linear Equations

2 Marks Question

1. Solve:

a. x + y = 7 b. 2x + y = 18 c. 3x + 2y = 11
4x – 3y = 9
x – y = 3 x – y = 2

4 Marks Question

1. Solve the following equations by graphically:

a. x – y = 1 b. x–8 = 3x – 3 c. x + y = 3 and x – y = –1
2x + 3y = 12 4 5 5 4 2 10 2 2

320 GREEN Mathematics Book-9

2. Solve each pair of simultaneous each by elimination method.
2x – 3y – 12 = 0
3x – 2y – 13 = 0
3. Solve the equation by substitution method
x=3–y
x – y = 3.
5 Marks Question

1. The cost of 4kg of apples and 6kg of oranges is Rs. 620. If the cost of 8kg of oranges
is the same as the cost of 5kg of apples, find the cost of apples and oranges per kg.

2. The difference of the present ages of a father and his daughter is 30 years. Four years
ago father was seven times as old as his daughter was. Find their present ages.

3. The sum of the digits of a two digit number is 14. If 36 is subtracted from the number,
the places of the digits are reversed. Find the number.

4. The ages of two girls are in the ratio of 5:7 . Eight years ago their ages were in the
ratio of 7:13. Find their present ages.

5. Three years ago the sum of the age of a father and his son was 48 years and three
years hence father's age will be three times that of this son. Find their present ages.

Quadratic Equation

1 Marks Question

1. Solve : x² – 16 = 0

2. What are the two roots of equation ax² + bx + c = 0

3. If a = 3, b = –10 and c = – 8 in quadric equation ax² + bx + c + 0 then find the value of x.

4. If square of a number is 1 more than 15, find the number.

5. Solve : x (5x – 1) = 0

2 Marks Question

1. Solve : 3x² – 5x + 2 = 0
2. Solve : x² – 6x + 5 = 0 by completing square.
3. Solve : 5x² + 8x – 21 = 0 by factorization method.
4. The sum of square of two number is 260. If one of numbers is 2 find other.
5. Solve the equation 2x² – 6x = 0 by using formulae.
4 Marks Question

1. Solve: x+3 – 2x – 3 = x–3
x+2 x–1 2–x

GREEN Mathematics Book-9 321

2. Solve the following equation by completing square 4 – 5 – 3
x–1 x+2 x

3. Solve these equations by factorisation method x – 2 + x + 2 = 2x + 6
x+2 x–2 x–3

4. Solve: 2x + 2x – 5 = 8 1 by completing square.
x–4 x–3 x

5 Marks Question

1. The perimeter of a rectangle is 32cm and its area is 60cm². Find its length and breadth.

2. The sum of the ages of a father and his son is 36 years and the product of their ages
is 180. Find their ages.

3. The difference of two numbers is 4 and their product is 165. Find the numbers.

4. In a two digit number, the product of the digits is 18 and their sum is 9. Find the
numbers.

5. The sides of a right angled triangle are (x – 2)cm, x cm and (x + 2)cm. Find the length
of each side.

Triangle

1 Mark Questions

1. Define a triangle. 3x D
40° C
2. Find the value of x in the adjoining figure. 55°
2x 5x

3. In the given figure, if AB = AC then can you write AB>AD? A

2 Marks Questions A 55°
1. Find the unknown angles of given figure. B
x 30°

y Z

YW

2. In a right-angled triangle ABC, if two sides are 2 and 3 then find the remaining side.

A

3. In adjoining figure, if AB = AC = 25cm and AD⊥BC, BC = 14cm,

find the length of AD. B DC

4. Explain 'S' in terms of x of 40° 55°
x
S
ba
5. Find the values of 'a' and 'b'.

60°

4 Marks Questions A

1. In the figure alongside ∠ABC = ∠EAD, AB = AE and BC = DE

then verify that ∆ACD is an isosceles triangle. B CD E

322 GREEN Mathematics Book-9

M

2. In the given figure, MN = MP, PB⊥MN, NA⊥MP then verify B A

that OB = OA. O P
N

3. In the figure alongside ABCDis a trapezium AB||CD||XY A B

and XY is the median, then prove that 2XY = (AB + CD). X Y

D C
M
4. In the given figure, ∠BAC = 76° and OB and OC are bisector A
of ∠ABC and ∠ACB respectively, then prove that ∆OBC is an 76°
O
isosceles triangle. B
C
N
C
5. In the given figure alongside ∆ANC and ∆BCM are the

equilateral triangles then verify that BN = AM.

5 Marks Question AB
PQ

1. In the adjoining figure PQ||RS, QT = TR and PU = UR, V UT
prove that PV = VS.

S R

P

2. In the given ∆PQR, PE is angle bisector of ∠QPR, QM⊥PE

and QU = UR prove that 2MU = (PR – PQ). M

Q EU R

3. In the given figure, SA bisects ∠MSK and AB||SC, M

AC||BS then verify that AC = AB = SC = BS. BA

4. Prove that the bisector of vertical angle of an isosceles S CK

triangle bisects its base. A

5. In the adjoining figure, AD⊥BC, CA⊥AB and ∠BAD = 45°,
45°
then prove that ∆ABC is an isosceles triangles.

BD C

Trigonometry

1 Mark Questions

1. Define trigonometry.

3 A
2
2. If Sinθ = , find Tanθ.

3. In the given figure, if AB = 6cm, BC = 8cm, then find length of AC. B C

GREEN Mathematics Book-9 323

2 Marks Questions

1. Express SinA in terms of CosA.

2. If Cosθ = 2 3 and P = 2 then find (i) h (ii) b and θ.
4

3. Find the value of 2Tan30° .
1 – Tan230°

4. Solve for θ, Cosθ = 3
2

5. Prove that : Tan2θ – Sin2θ = Tan2θ . Sin2θ
4 Marks Questions

1. If A = 60°, B = 30° then verify that Cos (A – B) – Cos(A + B) = 2SinA . sinB.

2. Find the value of : Cosec30° + Sec245° + Cosec90°. A
Sec0° + Sec60° + Cosec245°

3. In ∆ABC, ∠A = θ, ∠B = 90°, AB = 0.9cm BC = 4cm, then find θ

AC, Sinθ, Cosθ and Tanθ. B C
D
4. Verify that : 1 – Cot260° = Cos230° – Sin230° A
1 + Tan230° 60° C

5. In the figure ABCD is a rectangle if ∠AED = 60° AD = 2 3 cm E

and ∠CED = 90°, find the value of CD. B

5 Marks Questions

1. Prove that : (1 + tan2A) + o1+ 1 p = 1.
tan2A Sin2A – Sin4A

2. Prove that : (SinA – SinB) + (CosA – CosB) = 0
(CosA + CosB) (SinA + SinB)

3. Show that : 1 + Cosθ = Cosecθ + Cotθ.
1 – Cosθ

4. Prove that : Sinθ + 1 Cosθ 1 + Sinθ
=
Cosθ + Sinθ Cosθ

Statistics

1 Mark Questions
1. Explain the meaning of statistics.

324 GREEN Mathematics Book-9

2. Construct cumulative frequency table of:
x 10 20 30 40 50 60 70 80 90 100
f 2 4 6 8 10 12 14 16 18 20

3. Find the Q1 of : 3, 7, 9, 5 and 10
4. Find the mean of factors of 40.

5. If the mean of 32, x, 43, 55, 11 and 26 is 31, find the value of x.

2 Marks Questions
1. The mean of 8 observations was found to be 17 but later on, it was found 23 was

measured as 32, find the correct mean.

2. Find the model data of :
x 5 6 7 8 9 10
f 123456

3. Draw an ogive for the given data:

Years 067 068 069 070 071 072

Students 4 6 12 10 14 20

4. Find the median class of :

No. of students 60
50
40
30
20
10

O
10 20 30 40 50 60
Marks obtained

5. Draw a pie diagram of 070 071 072 073
Year 2000 4000 3000 5000

Production (Kg)

4 Marks Questions

1. Find the value of Q1 and Q3 of:
x 16 24 30 38 45

f 2 3 10 9 5

2. Calculate the value of 'x' that the mean is = 35.

Age 25 30 35 40 15

Students 5 7 8 x 4

3. The average age of 20 men and 10 women is 14 years. But the average age of the men

only is 16 years, what is the average age of the women only?

GREEN Mathematics Book-9 325

4. Find the missing frequency in the given data, if the mean of the data is 21.
x 10 15 20 25 35
f 3 10 ? 7 5

5. Draw a line graph of
Month Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec
Students 17° 15° 19° 22° 20° 18° 19° 17° 23° 20° 16° 15°

5 Marks Questions

1. Construct a frequency polygon from the following data:

CI 51-75 76-100 101-125 126-150 151-175 176-200
6 4
f 8 12 14 9

2. Given data are the monthly expenditure of Sabin's family, represent this data in a
pie-chart.

Particulars Food Clothes Education Health Others

Expenditure 4000 1500 6000 5000 3500

3. Find the Q3 of: 10 11 12 13 14
x9

f 237431

4. Find the mean of :

x 0-10 0-20 0-30 0-40 0-50

f 5 15 18 27 40

5. Find the model class of: 20-30 30-40 40-50
x 10-20 20 30 40
f 10

Probability

2 Marks Questions

1. A ball is taken out from a bag containing 5 red and 6 yellow. Find the probability of
getting red ball.

2. A card is taken out from a well suffled of playing card. Find the probability of getting
king or black.

3. A die rolled once and same times a coin toced. Find the probability of getting 5 on die
and tail on coin.

4. Two children are born in family. Find the probability of getting son.
5. A card is taken out from a set of numbered cards having number from 5 to 30. Find

the probability of getting M3 or M5.

326 GREEN Mathematics Book-9

Answers

Unit 1 Sets

Ex. : 1.1

1. Show to your subject teacher.

2. a. {3, 6} b. {0} c. Infinite set d. Finite set e. {3, 4, 5, 7}

f. {1, 3, 5, 7, 9} g. {w, x y, z} h. Discription method i. {5, 9} j. {5}

3. a. Empty b. Single 4. Equivalent; n(A) = n(B)

5. a. {2, 4, 6}, {2, 4}, {2, 6}, {4, 6}, {2}, {4}, {6}, { } b. {a} {b} {a, b} { }

6. a. D = {days in a week} b. B = {Vowels of English alphabet}

7. (A ∪ B) = {6, 7, 9} 8. (M ∩ N) = { 6 } 9. A' = {2, 4, 6, 8} and Bc = {1, 3, 5, 7, 9}

10. a. A' = {7, 9} b. (A ∩ B) = {4, 6, 8} c. (A – B) = {1, 2, 3, 5} (B – A) = {7, 9}

d. (A ∪ B) = {1, 2, ......., 9} e. (A ∪ B) = { }

11. Show to your subject teacher. 12. (A ∪ B) = {a, b, x, y, z}

13. a. A ∪ (B – C) = {1, 3, 5, 7, 9, 4, 8} b. A ∪ (B – C) = {2, 6}

c. (A ∩ B ∩ C) = { 3 } d. (A – B) ∩ C = {9} e. (A ∪ B ) = {1, 2, 4, 5, 6, 7, 8, 9, 10}

14. a. (A∪ B) = {1, 2, 3, 4, 5, 6, 8} and (A ∪ B ) = {1, 3, 5, 6, 7, 8, 9, 10, 11, 12}

b. (A ∩B ) ={7,9,10,11, 12} c. (B – A) = {6, 8} d. (A – B)={2, 4, 6, 7, 8, 9, 10, 11, 12}

e. (A ∩ B) = {1, 3, 5, 6, 7, 8, 9, 10, 11, 12}

15. i. a. A ∩ B = { } b. (B – A) = {1, 2, .....6} c. (B – A) = {7, 8, 9} d. (A – B) = {1, 3, 5}

e. {1, 3, 5, 7, 8, 9}

ii. a. (A ∩ B ∩ C) = {1, 2, 5, 6, 7, 8, 9} b. (A ∪ B ∪ C) = { }

c. (A ∩ B ∩ C) = {3, 4} d. (A ∪ B) ∩ C) = {3, 4, 6, 7} e. (A∪C)U(B∩C) = (1, 2, .......9}

16. a. {1, 2, 3, 5, 7, 9} b. {1, 2, 4, 6, 8, 9, 10} c. {3, 5, 7} d. {4, 6, 8, 10} e. {1, 2, 9}

17. a. {1, 2, 4, 6} b. {3} c. {1, 5} d. {2, 3, 4, 5, 6, 7} e. {5, 7}

Ex. : 1.2

1. 2. Show to your subject teacher.

3. a. ii. 15 b. 5 c. 10 d. 17
5.a. 30 b. i. 52
4. a. 25 b. 19 b. i. 190 ii. 140 ii. 58
e. 68 f. ii. 50% iii. 440
6 a. ii. 20 iii. 55 h. i. 40 ii. 25 iii. 35%
iii. 1 iv. 8
c. ii. 15% d. ii. 50 viii 2 ix. 6 v. 13
x. 2 xi 6
g. i. 20% ii. 45%

7. i. 12 ii. 14

vi. 6 vii 1

8. a. 100 b. 1600

GREEN Mathematics Book-9 327

Unit 2 Profit and Loss

Ex. : 2.1

A. Show to your subject teacher.

B. 3.a. P = 20% b. L% = 5% 4. a. P = 33.33% b. P = 25% c. P=25%

5.a. P = Rs. 75 b. Rs. 350 c. C.P. = Rs. 7000 d. C.P. = Rs. 240

e. Rs. 300 f. C.P. = Rs. 900 6. a. 20% b. Rs. 5,35,000 c. Rs. 247

7.a. C.P. = Rs. 400 b. S.P. = Rs 1100 c. Rs. 9095

C. 8.a. C.P. = Rs. 6000 b. C.P. = Rs. 200 c. C.P. = Rs. 5000

9.a. L = 0.25% b. L = 4% c. L = 0.82%

10.a.C.P. = Rs. 200 b. L = 1% c. P = Rs. 72, P = 5% d. Rs. 19.5

11.a.Rs. 19.20 b. Rs.40000 12. a. Rs. 76 b. Rs. 192.30

Ex. : 2.2

A. Show to your subject teacher.

B. 5.a. Rs. 1710 b. Rs. 247 c. Rs. 495
c. Rs. 1650
6.a. Rs. 17500 b. Rs. 3051 c. Rs. 2700 d. Rs. 5000
c. Rs. 1525.50 d. Rs. 80
C. 7.a. Rs. 4675 b. Rs. 1,52,550 10.a. Rs. 26000, Rs. 20000 b. Rs. 625, Rs. 500

8.a. Rs. 160 b. Rs. 4000

9.a. Rs. 2357.14 b. Rs. 4000

11.a. Rs. 3000 b. Rs. 4000

12.a. Rs. 1200 b. Rs. 1200 13.a. Rs. 600 b. Rs. 4841

14. a. Rs. 10,000 b. Rs. 18,000 15.a. Rs. 20,000 b. Rs. 1352.66 c. Rs. 24,000

Unit 3 Commission and Taxation

Ex. : 3.1

1. Show to your subject teacher.

2. Rs. 433333.33/month 3. Rs. 10,000 4. Rs. 5850000
Rs. 444444.44
5. Rs. 234.37/teacher 6. Rs. 101500 7. 8. Rs. 935672.5
Rs. 1638
9. a. Rs.1930750 Rs. 1000 c. Rs. 56000
Rs. 28,000 c. Rs. 1,00,000
10. a. Rs. 30 b. Rs. 175 c. Rs. 2,05,000

11. a. Rs. 16,000 b. Rs. 14,000 c.

12. Rs. 72,500 13.a. Rs. 10,500 b.

d. Rs. 84,000 14.a. 262500 c.

Ex. : 3.2

1. Show to your subject teacher.

2. Rs. 528 3. 100 employees 4. Rs. 150 5. Rs. 234.37
9. Rs. 45,000 10. 400 shares
6. Rs. 4320 7. 12% 8. Rs. 312500

Ex. : 3.3 c. Rs. 64,000 d. Rs. 7,000 7. Rs. 12,80,000
5. Rs. 80,000 6. 15%
1. Show to your subject teacher. 10. Rs. 2,970
2. a. Rs. 49,000 b. Rs. 71,500
3. Rs. 19,200 4. Rs. 75,000
8. Rs. 45,000 9. Rs. 8,000

328 GREEN Mathematics Book-9

Unit 4 Household Arithmatics

Ex. : 4.1

A. 1. 2. Show to your subject teacher.

3. a. 1 unit b. 2.5 unit c. 0.7 unit d. 1.35 units e. 76.5 units

4. a. 5 b. 7.5 c. 15 d. Rs. 1176.48 e. Rs. 3999
b. Rs. 1524 13. Rs. 7211.95
B. 5. Rs. 470 6. Rs. 808 7. Rs. 1087.25 12. Rs. 574
c. Rs. 8.80
8. a. Rs. 25.80 b. Rs. 25.80 c. Rs. 1161

C. 9. a. 68 units b. 93 units 10.a. Rs. 849

11. a. Rs. 1543 b. Rs. 102.6 c. Rs. 2221

14. Rs. 810.30 15. a. Rs. 3875.7 b. Rs. 2355.54

Ex. : 4.2

A. 1. 2. Show to your subject teacher.

B. 3. Rs. 285 4. Rs. 808 5. Rs. 473 6. Rs. 744.56 7. Rs. 1131.13
b. Rs. 416.40
C. 8. a. Rs. 679 b. Rs. 727.15 9.a. Rs. 553.13

10. 240 11. Rs. 2268.47

Ex. : 4.3

A. Sho to your subject teacher.

B. 4. Rs. 93 5. Rs. 370 6. Rs. 487.50 7. Rs. 335.40
10.a. Rs. 737.39 b. Rs. 760.20
C. 8. a. Rs. 625 b. 60 units c. Rs. 836.22

Ex. : 4.4 4. Rs. 259 5. Rs. 266 6. Rs. 362
8.a. 26.44km b. Rs. 295 9. 5km
A. Show to your subject teacher.
B. 2. Rs. 156.60 3. Rs. 277
C. 7. a. Rs. 18.22 b. 178

Unit 5 Mensuration c. 12cm² d. 42cm² e. 10 3m2

Ex. : 5.1 4.a. 72m b. 54m 5. a. 9 3cm2 b. 24m
8. a. 204m²
A. Show to your teacher. 7. a. 17775m² b. 594m² f. 42cm²
B.2. a. 42cm² b. 84cm²
f. 24cm² g. 60cm² d. 400m² e. 16.94m² 13. Rs. 16000
3. a. 225cm b. 148m 18. 1.8m
6. a. 426m² b. 384m² i. 225cm2
b. 228m² c. 252m²
g. 112.03cm² h. 25.62cm2 11. Rs. 4800 12. Rs. 2000
9. 11.69m, 9.6m 10. Rs. 2000
14. Rs. 1200000 15. Rs. 273780 16. Rs. 9564.80 17. 21m

GREEN Mathematics Book-9 329

Unit 5 Mensuration

Ex. : 5.2

1. a. 112m2 b. 3.5m 2. a. 88m2 b. 8.8m
3. a. 180m b. 7.5m2 4. a. Rs. 18000 b. 192m2
5. a. 110 b. 88m² 6. a. Rs. 18000 b. 24m
7. a. 3.75m b. 6m 8. a. Rs. 1530 b. Rs. 663000
9. a. Rs. 7200 b. Rs. 3840 c. Rs. 3600 10. a. 6cm b. 5m

Unit 5 Mensuration

Ex. : 5.3
1. a. 540cm3 b. 540cm2 c. 567cm2
2. a. 392cm2 b. 368cm2 c. 132cm2
3. a. 3080cm2 b. 10cm 4. a. 140cm2, 236cm2 b. 4cm
5. a. 300cm3 b. 8000 liters
6. a. 56.cm2, 252cm2, 364cm2, 392cm3 b. 56cm2, 352cm2, 464cm2, 448cm3
c. 24cm2, 140cm2, 188cm2, 120cm3 d. 76cm2, 362cm2, 514cm2, 760cm3
7. a. i. 2.32m2 ii. Rs. 1624 iii. 6000 liters b. 32,225m3
8. a. 6cm b. 38400cm2 9. a. 1:16 b. 4320cm3

Ex. : 5.4 b. 150m3 2. a. 10000 b. 20000 3. a. 750000 b. 60m3
b. 783cm³
1. a. 240m3 b. 26.4m³ 5. a. 26400
4. a. 2 3 m
6. a. 9m³ b. Rs. 1,60,000 c. 7520cm³
7. Rs. 1903.20
12. Rs. 1600 8. Rs. 208593.75 9. 5m 10. Rs. 10080 11. Rs. 1056
15. 5m
13. Rs. 6000 14. 4.5m

Unit 6 Algebraic Expression

Ex. : 6.1

1. a. 2(x + 2y) b. 3a(x – y) c. xy (x + y)
2. a. (x – y) (a + b) b. (3a – b) (x – y) c. (xy + z) (zx – y) d. o5x – 1 p o5x – 1 p
6y 6y
e. ox – 1 p ox – 1 p ox² – 1 p
xx x²

3. a. (8b – 3c) (8b + 3c) b. (2p – 3q) (2p + 3q) (4p² + 9q²) c. 3x (x – y)²

d. (3x – 2y) (2a² – 5b²) e. (x + 4) (x – a) f. x² (a² + x²) g. 9(xa – 2)(xa + 2)

h. (a + 9) (3a – 2) i. 3xy(x + 9y) (x – 9y) j. 2a² (a³ – 3b) (a³ + 3b)

4. a. 24ab b. (5x + y) ( 1 + 5x – y) c. (a – b + c) (a – b – c)

d. p² (p + q)² e. (x – 2) (x + y) f. 2o 1 – 6p o 1 + 6p
7x 7x

g. 1 oa2b + 1 p oa² b – 1 p h. o 21 – x p o 21 + x p i. 1 o 5a – 3bp o 5a + 3bp
a2 2 ab yz ab yz b 4 4

5. a. (m – p) (mn2 + 1) b. (a – b + 1) (a + b + 1) c. (a + b + 3)(a – b – 3)

d. (2x – 4y + 5)(2x + 4y + 5) e. (x – 1)² (x + 1) f. 12a(6a – 1) (1–2a) g. (21m + 19n) (19m + 21n)

6. a. b(2a + b) (2a - b) (4a2 + 2ab + b2) (4a2 – 2ab + b2) b. (2x + 3y - 4z) (2x + 3y + 4z)

c. (x + y – 9) (x – y + 1) d. (p + q) (p – q) (p4 + q4) e. oyx22 + x2 – 4p oyx22 – x2 – 4p
y2 y2

330 GREEN Mathematics Book-9

Unit 6 Algebraic Expression

Ex. : 6.2

1. a. (a + b – c) (a – b + c) b. (a – b + c) (a – b – c) c. (a2 + b2) (a + b) (a – b)

2. a. (x + 1) b. (x – 1) c. (x + 1)

3. a. (x2 – 2xy + 2y2) (x2 + 2xy + 2y2) b. (2a2 – 2ab + b2) (2a2 + 2ab + b2)

c. (x2 + 2x + 2) (x2 – 2x + 2) d. (a – 1 + b) (a – b + 1)

e. (a + b + 1) (a – b + 1) f. (a + 3 + b) (a – b – 3) g. 4(3m + 2n) (2m + 3n)

h. (a – b + c) (a – b – c)

4. a. –4bc (b2 + c2) b. (x + a – 1) (x – a + 9) c. (x + y + 1) (x – y – 7)

d. (pr + ps + qs – qr) (pr + qs – ps + qr) e. (1 + xy + x – y) (1 + xy – x + y)

f. (2x + 3y – 4z) (2x + 3y –4z)

5. a. (a + b + c) b. x – y – z c. a2 (+aa+bb+) b2 d. (1 – xy + x + y)
x + y – z

6. a. 18 b. 23 c. 45 d. 20 e. 4 f. 5 g. 5

Ex. : 6.3

1. a. (2x + 3y) (4x² – 6xy + 9y²) b. oa – bp o a² + b² + 1p c. 2x(x² + 6x + 12)
b a b² a² (1 – x) (x² + 4x + 7)

2. a. xy²(x – y) (x² + xy + y²) b. m(m² + mn + 3n² + 2m) c.

d. 2a(3b2 + a2) 1
x
3. a. (a + 3b)³ b. ox + p³ c. (2a + 3b)³

4. a. (3a + 5) (9a² – 15 ab + 25b²) b. o p – q po p² + q² + 1p
q p q² p²

c. o 2nm + 2nmpo 4m² + n² – 1p d. (a – b + 5) (a² – 2ab + 5a – 5b + b² + 25)
n² 4m²

e. 2(2x + y) (7x2 + 16xy + 13y2) f. x o 1 + 8po 1 – 8 + 64p
x x² x
g. 2(x + y – 2) (x² + 2xy + y² – 2x – 2y + 4) h. (x² + 2xy + y² – 4x – 4y + 16) (x + y + 4)
(x + y)³

i. (a – 2x) (a2 + 2ax + 4x2 + 2y) j. (a + 3b) (7a² + 6ab + 3b²)

k. (2a – b) (4a² + b²) l. (a – b + 2) (a² – 2ab + b² – 2a + 2b + 4)

5. a. 2xy(3x + 2y) (9x² – 6xy + 4y²) b. (x – y) (x² + x + xy + y + y²)

c. (p + 3q) (7p² + 6pq) + 3q² d. (x – 4) (x² + 7x + 31) e. (a – 2) (a² – a + 1)

f. 2x(x – 2y) (x² + 2xy + 4y²)

g. 2o2a – 1 po4a² + a + 1 p h. ab o 1 + 5po 1 – 5 + 25p
4b 2b 16b² c c² c

i. (a 1 b)³ (x – 9) (x² + 9x + 81)
–

6. a. (m + 3n)3 b. (2a – 5)³ c. (m – n) (m² + m + mn – n + n²) 1
2x
d. (a – b) (a² + ab – a – b + b²) e. (5 – 2x)³ f. o2x + p³
h. 1 (ab – 5) 25)
g. (x + y) (x² – xy + y² + 1) ab (a²b² + 5ab +

i. (x – 2y) (x² + 2xy + 4y²) (x6 + 8x³y³ + 64y6) j. (m –2n) ( m² + 2mn + 4n² + 2p)

7. a. 90 b. 756 c. 198

GREEN Mathematics Book-9 331

Unit 6 Algebraic Expression

Ex. : 6.4

1. a. x(x – 7y) (x + 7y) b. 3(x² – 1)² c. (2a + b)(a + 4b) d. (a + 4b)(3a – 5b)

e. (p² – 7)(p³ – 6) f. (a2 – a – 2) (a2 + a –2) g. (x2 + y2) (x + y) (x – y)

2. a. a(a² + 2ab + 2b²) (a² – 2ab + 2b²) b. (x² + 2xy + 2y²) (x² – 2xy + 2y²)

c. (x² + x + 1) (x² – x + 1) d. o x² – 3x + 1po x² + 3x + 1p
y² y y² y

e. (a + b – 14) (a – b + 2) f. (x² – 3) (x² + 3) g. (2 – m² – n²) (2 + m² + n² )

h. (p² + 2pq – q²) (p² – 2pq – q²) i. (m² + 2n) (m² – 2n – 6)

j. (b² – c² – 6)(b² – c² + 6) k. 3(x – y + 2z) (x – y – 2z)

l. (2x² + 3xy – 2y²)(2x² – 3xy – 2y²)

3. a. (2p² + 3pq + 11q²) (2p² – 3pq + 11q²) b. oa + 1 + 1poa + 1 – 1p
a a

c. o mn²² + 6m – 4po m² – 6m – 4p d. (13m + 14n)(13m – 14n – 4)
n n² n

e. (t + 3r – 6)(t – 3r – 4) f. x² (x – 1) (x + 1) (x² + 1) (x² – 3) (x² + 3)

g. (x² + y² + 3) (x² – y² – 11) h. (x² + 3xz + y²) (x² – 3xz + y²)

i. (a² – ax + y²) (a² + ax + y²) j. (a + 3b – 6) (a – 3b – 4)

k. oa² + 3 + 1 p oa² – 3 + 1 p l. x² (x² + x + 1) (x² – x + 1)
a² a² y4

m. (x + 1) (x – 4) (x2 – 3x – 7) n. (a2-5a+4) (a2-5a+6) o. o a² + 2a + 6p o a² – 2a + 6p
b² b b² b

Unit 7 Laws of Indices

Ex. : 7.1

1. a. 3 b. 1 c. 13 d. 1 e. 732493 f. 729
6 7
25
b. 3a 5 a3 c. 1
2. a. x21 13

3. a. 91 b. 1 a 2x d. 1
c. xn–2 xb

4. a. 8 b. 287 c. 3 d. xy² e. 4 a²b² f. 1
9 4 9 3
g. 2301 h. 125 i. 9

31 b. 3 c. o ba p2x d. a(a – 1) e. a– 1 1 –2
a f. m²
5. a. 2a 24 x4

g. 4x h. 81 i. n j. a k. 1 l. 1 m. 1 n. 1
9 xb 3
x a + b
y
6. a. 1 b. o p c. 1 d. 1 e. 1 f. 1 g. 1

a–1 i. p 2m x m + n k. 1 l. 1
o q p j. o y p
h. x a

7. Show answers to your teacher.

332 GREEN Mathematics Book-9

Unit 7 Laws of Indices

Ex. : 7.2 b. –4 c. – 3 d. – 3 e. 1 f. 1 g. 4 h. –2 i. 5
2 4 16 g. 2 h. 1 i. –1
1. a. –1 1 1 f. 12 g. 4 h. 1 i. 3
2. a. 23 b. 2 c. 0 d.– 11 e. 3 2
3. a. 23 9. 10 10. 5
j. 2 b. 2 c. 3 d. 2 e. 0 f. – 1
2
4. a. 3
k. 2 l. 0

b. 3 c. 1 d. –2 e. 0 f. 1
2 3 2

Unit 8 Ration and Proportion

Ex. : 8.1

1. a. 614 b. 1 c. 1 d. 1
512 22 2
2. a. 9 : 16
3. a. –31 b. 3b c. 3:10
4
ii. 7 9 2 17
b. i. 4 : 5 4. a. 5 c. 3 d. 43

5. a. –7 b. 13 c. 25 d. – 3 e. 13
8 5 9 1 14
6. a. 114453 b. 5398 c. 52 217
d. 300

7. a. 38,57 b. 55,45 c. 11 d. 12 e. 35 and 45

f. 20 yrs and 25 yrs g. 12 yrs and 16 yrs h. 18 and 27 i. 30 and 40

Ex. : 8.2 c. a = b d. w– x = y–z e. b = d
c d x z a c
1. a. 34
d. 10 e. 4 f. 30
2. b. 10
2 c. 5 9. b. 0 c. 0 d. 0
3. a. 3 b.

Unit 9 Simultaneous Linear Equations

Ex. : 9.1 b. 2, 2 c. 5, 15 2. a. 2 b. 5
b. – 4 , 8 c. 2, 7 d. 5, 1
1. a. 1, 1 i. –1, 2 j. –1, –2 k. 4, 3 e. 2, 2 f. 3, 1 g. 4, – 5
3. a. 1, 0 m. 2, –3 n. 12, –50
h. 5, –1 l. 5, 6 f. 2, 3 g. 2, 3
m. 4, 5 n. 4, 1
4. a. 4, 1 b. – 2, 1 c. –2, – 5 d. 2, – 2 e. 5 , – 1 f. 2, 1 g. 3, 2
2

h. 2, – 3 i. 5, 1 j. 1, 2 k. 6, 7 l. 1, 1

5. a. 5, 3 b. 1, 1 c. 2, 2 d. 6, 2 e. 1, 1

h. b, 19a i. a + b, a – b

j. o b2 – a2 , b2 – a2

p
bn – am bm – an

GREEN Mathematics Book-9 333

Unit 9 Simultaneous Linear Equations

Ex. : 9.2 b. x = 1, y = 1 c. x = 7 d. 1, 4 e. x = 6
b. 2, 3 c. –1, 3 i. 4, – 5 j. 5, – 1
1. a. x = 2, y = 7 g. 3, 2 h. 6, 8
2. a. 2, 2 l. 1, 1
f. (1, 3)
k. 5, 3

Unit 10 Quadratic Equation

Ex. : 10.1

1. a. 31 or – 4 b. 2 or – 3 c. 8 or 2 d. 0, 5 e. 0, 3 f. 0, 2 g. ± a
7 7 9 2

2. a. – 2 or – 4 b. – 1 , 2 c. 3 , – 3
3 2 4
b
3. a. 0, a b. ± 5 c. ± 5
2
4. a. – 3, b. 3, c. 5, – 3 d. – 5, 3 e. 1 , – 1
2 3

5. a. ± 3 b. 0, 3 c. 7, – 9 d. 1, 6 e. 2, 3
2

f. ± 6 b. 3a, –2b c. 4, –1, d. 5 , 8 e. 0, 4
6. a. 0, –1 g. 4, 3 2 3

f. –3, 2 h. 3, – 1 i. 1 , 1 j. 5, 6
2 2 4 5

Ex. : 10.2 b. 2, –3 c. 9, 1 d. 9 , -1
c. –2, –4 5 5
1. a. 3, 0 c. 3, 12
2. a. 1, –5 b. 1, 4 d. 3, –6
3. a. 1, –6 c. 1, –4
f. –3, –4 b. 1, 1 d. –1, – 1 e. –2, 3
4. a. 5, –1 4 2 4

b. 1, -2 d. 2, 4 6
7 13

Ex. : 10.3 b. 2, -31

1. a. –1, ± 5

2. a. 4, 5 b. –2, –3 c. 18, 2 d. –1, -21 e. 2, -1 f. –3, 4
3 3

–m ± m2 – 4nl 2b c. ±15 d. 24, 42 e. 2, –3 f. –2, 1
3. a. 2l b. 1, a–b 5 2
g. 8, –7
h. 1 , -3 i. -2 , 1 j. a + b, a+b k. 1 ± –3
7 7 7 2

334 GREEN Mathematics Book-9

Unit 11 Triangle b. QR, PQ c. BC, AB d. BC, AB

Ex. : 11.1 b. ∠D, ∠E c. ∠Q, ∠R

1. a. AB, BC
2. a. ∠A, ∠C
4. AB

Ex. : 11.2

1. a. ∠C = 30° b. ∠Q = 25° c. ∠P = 60°, ∠Q = 60°, ∠R = 60°

d. ∠C = 46°, ∠ADB = 68°, ∠BDC = 112° e. x = 70°, y = 40°

2. a. 18° b. 15° c. 60° d. 28° e. x = 20° f. 25°

3. a. 100° b. 50° c. 105° d. 130° e. 80° f. 50° g. 150°

h. 20°

4. 55° 5. 30° 6. 40°

7. - 23. Show to your subject teacher. 8. 72.5°

Unit 12 Parallelogram

Ex. : 12.1 c. 3.5cm d. 25°, 80° e. 115° f. 7cm
b. 80° c. a = 50­ , b = 130° g. 58°, 103­°­ h. 50­°, 90°
1. b. 10cm, 10cm e. 70°, 70° f. 110°­­ , 75° d. 55°, 35° e. 60°,120°
2. a. 30°
d. 60° b. 140° c. 92°
i. 130°, 70° g. 30°, 60°
3. a. 130°
f. 90°

Ex. : 12.2

1. a. AB = 2MN b. 10cm c. 10cm d. EQ = QF

2. a. 40° b. 60°, 75°, 75° c. 70°, 50°, 60° d. 20°, 30°, 30°

3. a. 11.4cm b. 5.3cm c. 5.1cm, 4.2cm, 9.4cm d. 4.8cm, 1.8cm

e. 1.9cm, 1.5cm, 2.3cm

Ex. : 12.3

1. 2. Show to your subject teacher.

3. a. 41cm b. 8cm c. 5cm
12cm, 95 cm c. 10cm, 8.5cm, 13.15cm
4. a. 2 6 cm b.

GREEN Mathematics Book-9 335

Unit 13 Construction
Ex. : 13.1

Show to your subject teacher.

Unit 14 Similar triangles

Ex. : 14.1

1. Show to your subject teacher.

2. Show to your subject teacher.

3. a. 10cm b. 5cm, 2cm c. 3cm d. 2cm e. 3.2

4. a. 10cm b. 3cm, 7.2cm , 3cm

Unit 15 Circle

Ex. : 15.1

1. a. AB = CD b. 5cm c. AX = XB d. OP⊥AB e. OX = OY
ii. 6cm2 b. 16cm
2. a. (i) an isosceles Triangle 4. a. 14cm b. 3 3 cm

3. a. (48cm²) b. 24cm²
5. a. 6 2cm b. 6cm

Unit 16 Trigonometry
Ex. : 16.1

Show to your subject teacher.

Ex. : 16.2

1.. i. a. AB b. AC c. AC d. AB e. BC

ii. Show to your subject teacher.

2. a. Cos q = 24 Cot q = 24 b. Cos A = 5 , Tan A = 12 and 12
25 7 13 5 13
11
c. Cos q = 2 , Sin q = 2 d. Tan q = 4
3

3. a. AC b. AC d. Cotθ
AB

4.5. Show to your subject teacher.
6. a. Show to your subject teacher.

b. 5 , 3.3 c. Sin q = 3 , Cosec b = 13 , Tan q = 3 , Sec b = 13
6 6 5 5 4 12

7. a. 99 b. 112
65 65

f. PR = 24cm, Sin q = 24 , Cos q = 275, Tan q = 24 , Cos q = 1254, Sec q = 275, Cot q = 7
25 7 24



336 GREEN Mathematics Book-9

Unit 16 Trigonometry

Ex. : 16.3

1. Show to your teacher. 1
2
2. a. 30° b. 1 c. d. 1 e. 30°

f. 45° g. 0 h. 1 1 e.
3 3 j.
3 b. 21 c. 14 d. 1
3. a. 1 o. 2
5
2 d. a = 45°, y = 3

f. 2 g. 1 h. 1 i. 2– 3
1
k. 1 l. 3 m. – 1 n. 4 4

p. –2 q. 0 r. 1 3 s.
5. a. α = 60° 4

b. α = 45°, b = 45° c. a = 60°, 5 3 2, z = 3

e. x = 2 2, y = 1 f. b = 30°, x = 6

6. a. 12cm b. 80cm, 160cm c. 10cm d. 40cm. e. 60°

f. Sin B = 12 , Cos B = 5 , Tan B = 12 , Cos C = 12 , Tan B = 5 g. 5cm
13 13 5 13 12

h. 2cm i. AB = 3, AC = 4.24cm j. AB = BC = 7cm

k. 60° l. 4 , 4 , 4 and 4
5 3 5 3

7. a. 45° b. 30° c. 60° d. 30°

8. a. 3 b. 4 3 – 1 c. 0 d. 3–2 2
2 4 4

e. 4 – 2 3 f. 46

Unit 17 Statistics

Ex. : 17.1

1. a. |||| |||| b. |||| |||| || c. |||| || d. |||| |||| e. |||

2. a. Mar ks f cf b. W ages f cf c. Marks f cf
0-300 5 5
20 2 2 300 2 2 300-600 4 9
600-900 7 16
25 6 8 550 7 9 900-1200 2 18
N = 18
30 3 11 660 11 20

40 4 15 890 15 35

N = 15 N = 35

d. Class f cf

9.5 - 14.5 55

14.5 - 19.5 6 11

19.5 - 24.5 7 18

24.5 - 29.5 8 26

N = 26

GREEN Mathematics Book-9 337

Unit 17 Statistics

Ex. : 17.1 Cont. b. X Tally bars Frequency
Frequency 100 |||| 4
3. a. 103 |||| | 6
X Tally bars 4 105 |||| 5
14 |||| 7 200 |||| 5
16 |||| || 6 20
20 |||| | 5
28 |||| N = 22 Frequency
b. 4
4. a. Frequency Class Tally bars 2
Class Tally bars 6 0-10 |||| 2
10-20 2 10-20 || 4
20-30 |||| | 3 20-30 || 2
30-40 || 2 30-40 ||| 3
40-50 ||| 3 40-50 || 3
50-60 || 3 50-60 |||
60-70 ||| 3 60-70 ||| N = 20
70-80 ||| N = 22
|||

Ex. : 17.2 b. 6 6 c. 60 d. 26.5 2. a. 25 b. 125
7
1. a. 35 b. 117
b. 47 c. 7 4. a. 175 b. 12 2
3. a. 8
5. a. 35 1 b. 338 8 c. 188 3 6. a. 62 6 15
94 7 a. 114 2
3
7. 65 8. a. 21 2 b. 78 22 9. a. 6 3 7
3 29 7
10 a. 77.2
b. 12 c. 62 d. 150 1m
4

Ex. : 17.3

1. a. Md = 12, Q1 = 6, Q2 = 12, Q3 = 16 b. Md = 34, Q1 = 22, Q2 = 34, Q3 = 38

c. Md = 41, Q1 = 31.5, Q2 = 41, Q3 = 49 d. Md = 28, Q1 = 23.5, Q2 = 28, Q3 = 50.5

2. a. Md = 33 b. 7 3. a. 16 b. 14 c. 12 d. 16

4. a. Q2 = 12, Q1 = 8, Q3 = 16 b. Q2 = 50, Q1 = 30, Q3 = 60
b. Md = 400, Q1 = 200, Q3 = 500
5. a. Md = 40, Q1 = 30, Q3 = 50 d. Md = 40, Q1 = 20, Q3 = 50

c. Md = 200, Q1 = 175, Q3 = 215

e. Md = 2000, Q1 = 1000, Q3 = 300

6. a. Q1 = 8, Q2 = 12, Q3 = 18 b. Q1 = 44, Q2 = 55, Q3 = 66 c. Q1 = 200, Q2 = 300, Q3 = 400

338 GREEN Mathematics Book-9

Unit 17 Statistics b. Mo = 40kg, R = 40kg c. Mo = 8, R = 10 d. Mo = 10, R = 9
Ex. : 17.4
b. 60, 50 3. 2 d. 3, 4
1. a. Mo = 1, R = 6 b. 6.55 c. 2, 4
e. Mo = 34, R = 27
2. a. 14, 10 b. 8, 10 c. 3000, 4000

4. a. 10, 13

e. 2, 8

5. a. 100, 55

Ex. : 17.5

1. a. 2 P.M. b. 6 A.M. c. 25°C d. 0°
c. 15
2. a. y-axis frequency and x-marks b. 180
d. Rs. 4000
3. a. (10 – 20) b. (30 - 40) c. (40 – 50)
d. 50 - 60
4. a. 12 b. (140 - 160) and (200 - 220) c. 12

5. a. Rs. 7000 b. Rs. 2000 c. Rs. 2000

6. a. Rs. 6250 b. Rs. 1,12,500

7. 8. 9. 10. Show to your subject teacher.

11. a. 30 - 40 b. 10 - 20 c. No.

12 to 28 Show to your subject teacher.

Unit 18 Probability

Ex. : 18.1 b. 1 , 2 c. 3 d. 2 e. 1 f. 5
33 11 3 4 9
2. a. 1
3 b. 1 c. 1 d. 33
3 3 100
3. a. 2
5 b. 1 c. 3 d. i. 1 ii. 10 iii. 8 iv. 1
2 13 13 3 13 26
4. a. 1 , 12
13 13 ii. 1 b. ii. 1 iii. 3 iv. 1 v. 1
2 44 42
5. a. i. 1
2 b. 1 c. 1 d. 1
2 22
6. a. 1
6 ii. 5 iii. 5 iv. 1 v. 0 vi. 5
6 6 3 6
e. i. 2
3 b. 1 c. 4 d. 4 , 7 e. 1 f. 80
5 5 11 11 7
7. a. 1
4 h. 2 iii. 1 b. i. 1 ii. 3 iii. 3 iv. 9
3 4 10 10 20
g. 1
3 ii. 2
5
8. i. 3
5

GREEN Mathematics Book-9 339

Revision for Examination

Sets

1 Marks:

1. n(U) = n0(A) + n(A∩B) + n0(B) + n(AUB) 2. n(A) 3. U–(AUB)
4. The set of cows which can fly 5. {2, 4, 6}

2 Marks:

1. {10, 14, 16, 18} and {11, 12} 2. {8, 9, 10, 11, 12, 13} 3. {–5, –3, –2, 2, 7, 12}

4. {4, 5} and {4, 5, 6, 7} 5. ∅
4 Marks:
A B M C

1. i. 13 ii. 39 11 37 2. i. 10 15 ii. 15

F C 13 20 15
3. 15 20 and 5 4. 50 5. 10%

10 5 iii. 20 2. ii. 50% iii. 35%
4. 16 5. i. 125 ii. 195
5 Marks: ii. 10
1. i. 40 ii. 20 3 3
3. i. 5

Profit and Loss

1 Marks: 3. CP(100 + P%) 4. SP × 100 5. Rs. 6494
100 100 – l%
1. l% = l ×100 2. P = Rs. 78
CP

2 Marks:

1. 20% 2. 33.33% 3. 200 4. 33.33% 5. 40%
4 Marks:

1. Rs. 5865 2. 2699.18% 3. Rs. 2192.59 4. Rs. 4030.30 5. 10.38%

5 Marks:

1. 30.9% 2. Rs. 15120 3. ................. 4. 6% 5. 30%, loss = 12%

Comission and Taxation

1 Marks:
Comission
1. Sell Price × 100% 2. Rs. 4530 3. 5% 4. 15% 5. Rs. 4736.84

2 Marks: 2. Rs. 24,000 3. Rs. 2000 4. 38 pieces 5. 5%
1. Rs. 60,000 2. Rs. 61200 3. 1.25% 4. Rs. 13900 5. Rs. 3,00,000
4 Marks: 2. i. Rs. 16000 each ii. 25% iii. Rs. 3000000
1. 25375
5 Marks:
1. Rs. 134000

340 GREEN Mathematics Book-9

Home Arithmetic

1 Mark:

1. 406 units 2. Rs. 824.9 3. 20km
3. Rs. 495
2 Marks: 3. Rs. 2444

1. Rs. 1280 2. Rs. 1394 4. Rs. 1039.25 5. Rs. 1155

4 Marks:

1. Rs. 1824 2. 484 calls 4. Rs. ......... 5. 36.66 units

Mensuration

1 Mark: 2. 2d(l + b – 2d) 3. 2h(l + b) 4. 1 × (Sum of || sides) × h 5. πR2–πr2
1. 3 a2 2

4

2 Marks:

1. 69.73cm2­ 2. 24cm 3. 112cm2 4. 120cm2 5. 180cm2

4 Marks:

1. i. Rs. 13120 ii. Rs. 25820 2. 20.83m 3. i. 384cm2 4. 14.4 fit. 5. Rs. 136000

5 Marks:

1. Rs. 5760 2. i. 23500 ii. Rs. 211500 3. Rs. 25380pcs/Rs. 223420

4. i. 616m2 ii. 7700pcs iii. Rs. 269500

Algebraic Expressions

1 Mark: 2. (3a – 21c) (3a + 21c) 3. (a2 + b2 – ab) (a2 + b2 + ab) 4. y(x – 4y) (x2 + 4xy + 16y2)
1. 2xy (2x + 3y)

2 Marks:

1. 2a 2. ax (9x2 – 4) (a2 + 4) 3. (a2-2b2)(b12 – a12) 4. (x + 5) 5. 2a
a+1 a2–1

4 Marks: x+1 – 2a3
x–2 (a+x) (a–x)
1. (a3 – 8) (a – 5) 2. 3. 1 4. 2x + 1 5.

5 Marks:

1. – 2(a + y) 2. 3(aa3-1-)2(a5-a22)(+a-537)(aa--53)5 3. (a2 - ab + b2)
x2 + xy + y2

Indices

1 Mark:

1. 27 2. 0.5 3. 3 4. 1024 5. 5
5. 2
2 Marks:

1. 81 2. (x+1y)2 3. 4 4. 2
16

4 Marks:

1. 1 3. 1 5. x2(a3+b3+c3)

5 Marks: 3. 1
2. 1

GREEN Mathematics Book-9 341

Ratio and Proportion

1 Mark:

1. 12:1 2. 210, 245 3. 343, 729
2 Marks:

1. 3:2 2. a = 35, b = 45 5. 8
4 Marks:

1. 10 : 21 2. 130, 260, 390 3. 71 each 4. 5
5 Marks:

Show to your subject teacher.

Simultaneous & Linear equation

2 Marks: c. 3, 1
1. a. 5, 2 b. 230 , 134

4 Marks:

1. a. 3, 2 b. –4, 0 c. 5, 2 2. 3, –2 3. 3, 0

5 Marks:

1. Rs. 80, Rs. 50 2. 39 years, 9 years 3. 14 4. 15years, 2 years 5. 42 years, 12 years

Quadratic Equation

1 Mark: 2. -b ± b2 – 4ac 3. 4 or 2 4. 4 5. 1 or 0
1. 4 2a 3 4. 16 5

2 Marks: 2 7 4. 36 or 63
3 5
1. 1 or 2. 5 or 1 3. or –3 5. 0 or 3

4 Marks: –1 4
2 3
1. 4 or 0 2. 3 or 3. 0 or

5 Marks:

1. 10cm, 6cm 2. 30years, 6 years 3. 11, 15 5. 6cm and 8cm

Triangle

1 Mark:

1. A plane figure bounded by 3 sides 2. 18° 3. Yes
2 Marks: 4. (40 + x)

1. 30°, 60° 2. 5cm 3. 24cm 5. 65°, 115°

4 Marks:

Show to your subject teacher.

5 Marks:

Show to your subject teacher.

342 GREEN Mathematics Book-9

Trigonometry

1 Mark:

1. Show to your subject teacher.

2 Marks: 2. i. h = 4, ii. θ = 30°, b = 2 3 3. 3 4. 30°
1. 1 – Cos2A

4 Marks: 3. 4.1cm, 4 , 0.9 , 4.9 5. 4cm
1. Show to your subject teacher. 2. 1 4.1 4.1 0.9
5 Mark:

Show to your subject teacher.

Statistics

1 Mark:

1. 2. Show to your subject teacher. 3. 7 4. 11.25 5. 19
4. 20 - 30 5. 40 - 50
2 Marks: 3. 10 years 4. 5
3. Q3 = 12 4. 28.75
1. 15.87 2. 10

4 Marks:

1. Q1 = 30, Q3 = 38 2. 33
5 Marks:

1. 2. Show to your subject teacher.

Probability

2 Marks:

1. 5 2. 7 3. 112 4. 1 5. 1
11 13 4 2

GREEN Mathematics Book-9 343

Model Set for Exam

Group A [3(1 + 1) = 6]

1. a. Write formula of S.P. if cost price and profit percent are given.

b. Write the formula of total surface area of cylinder .

2. a. If a = 0, find the value of 1 . A
5a 12cm
5cm
b. Which angle is the largest angle in the given figure? B 13cm C
xcm
A

3. a. If P and Q are mid point of AB and AC PQ
respectively, write relation between PQ and

BC. B C

b. Find the mode of the data: a, b, a, b, a, c, d, a, c and a.

Group B [4(2+2) + 3(2+2) = 34]

4. a. The minimum charge of telephone for the first 175 calls is Rs. 200. If
the charge for each additional calls is Rs. 1, find the charge for 360
calls.

b. After depreciation of 5% on the price of an article become Rs. 19000 .

find the price an article. 4cm

5 a. The volume of the prism shown in the adjoining 4cm
4cm
figure is 640cm³. Find the value of x and the total 4cm 4cm
surface area of the prism. 12cm

b. Find the area of path surrounded 10 m. square

ground by 3m wide path

c. How many bricks ceach of volume 750cm3 will be required to construct
a wall of 10m × 5m × 30cm?

6. a. Prove that : 1 + 1 – a + 1 1 = 1
xb + xa – b

b. Solve : 27x+1 = 81.

7. a. Simplify: 6 a5 4 a³ a²

344 GREEN Mathematics Book-9