Unit Scale Drawing and Bearing
20
20.1 Scale drawing - review
Let's have discussions on the following questions.
Is it possible to draw the actual size of your house on a sheet of paper?
Is it possible to locate the actual distance between any two places on a sheet of
paper?
Is it possible to draw the actual size of coronavirus on a sheet of paper?
It is not possible to draw the actual size of very large figure (or object) or very small
figure (or object) on a sheet of paper. Similarly, it is impossible to show lengths or
distance which are too great to draw full-size. In the case of large figure, we should
reduce their actual size and for smaller figure, we should enlarge their actual size in
drawing by taking a convenient scale.
A drawing that shows a real object smaller than (a reduction) or larger than (an
enlargement) the real object is called scale drawing.
Reduction Enlargement
20.2 Scale factor
The scale of the drawing is the ratio of the size of the drawing to the actual size of
the object. For example:
(i) A distance of 5 km (ii) A length of 80 m
Scale: 1 cm to 1 km (or 1:100000) Scale: 1 cm to 10 m (or 1: 1000)
Scale drawing Scale drawing:
0 1 2 3 4 5 km 0 10 20 30 40 50 60 70 80 m
The scale of a drawing is also known as the scale factor. It is used to reduce or
enlarge a figure according to the scale ratio.
Worked-out examples
Example 1: What is the actual length which is represented by 5.4 cm on a scale
drawing with scale of 1 cm to 10 m (or 1 : 1000)?
Solution:
Here, 1 cm represents 10 m
? 5.4 cm represent 5.4 u 10 m = 54 m
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Example 2: What is the actual distance between two places which is represented
by 4.5 cm on a map which is drawn to the scale 1 : 200000?
Solution: 200000
100
Here, the scale 1 : 200000 means that , 1 cm represents 200000 cm = m
= 2000 m = 2 km
Now, 1 cm represents 2 km
?4.5 represents 4.5 u 2 km = 9 km
Hence, the distance between two places is 9 km.
Example 3: A rectangular garden is 16 m long and 14 m broad. If the map scale is
1:400, what are the length and the breadth of the garden on drawing?
Solution:
Here, the scale 1 : 400 means, 1 cm represents 400 cm = 4m
4 m is represented by 1 cm.
1 m is represented by 1 .
4
1
16 m is represented by 4 u 16 cm = 4 cm 3.5 cm
(14 m)
? The length of the garden on drawing is 4 cm.
Also, 1 m is represented by 1 cm
4
1
14 m is represented by 4 u 14 cm = 3.5 cm 4 cm
(16 m)
? The breadth of the room on drawing is 3.5 cm.
Example 4. The height of a tree on the picture is 3 cm. If its actual height is 24 m,
find the scale of the drawing.
Solution:
Here, height of tree on the picture = 3 cm
Actual height of tree = 24 m = 24 × 100 cm = 2400 cm
Scale of drawing = ? 3 cm
Height of tree on picture 2400 cm 1
Now, scale of drawing = Actual height of tree = = 800 = 1 : 800
? Required scale of drawing is 1 : 800
EXERCISE 20.1
General Section - Classwork
Tell and write the answers as quickly as possible.
1. a) When the scale is 1:100, the actual length of 3 cm is ...................... m.
b) When the scale is 1:200, the actual length of 5 cm is .................. m.
c) When the scale is 1:300, the actual length of 4cm is ................... m.
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2. a) When the scale is 1:200, the map/drawing length of 6m is ................. cm.
b) When the scale is 1:500, the map/drawing length of 40m is ............... cm.
c) When the scale is 1: 800, the map/drawing length of 24m is ................ cm.
3. Let's study the information given in the table and fill in the blanks.
Length on map/drawing Scale Actual length
................. m
a) 2 cm 1:300 ................. m
................. km
b) 5 cm 1:2000
20 m
c) 6.5 cm 1:50000 32 km
72 m
d) ....................... cm 1:400
e) ....................... cm 1:800000
f) ....................... mm 1:9000
Creative Section - A
4. a) Sketch a tower of height 45 m according to the scale of 1 cm to 9 m.
b) The actual length and breadth of a rectangular play ground are 40 m and
30 m respectively. Draw the map of ground by taking a scale of 1 cm to 10 m.
c) A water tank is 20 m long, 10 m wide and 4 m high. Take a scale of 1 : 400.
Then, draw a map of the tank.
5. a) What is the actual length which is represented by 3.2 cm on a scale drawing
with scale of 1 cm to 4 m?
b) What is the actual height of a building which is represented by 8.5 cm on a
scale drawing with scale of 1:1000?
c) Find the actual length and breadth of a room which are represented by 6 cm
and 4 cm respectively on a scale drawing with scale of 1:200.
d) What is the actual distance between two places which is represented by
15 mm on a map which is drawn to the scale 1 mm to 5 km?
6. a) If 1 cm represents 5 m, what is the scale drawing length of 18 m?
b) The distance between two places is 50 km. What is the scale drawing
distance between these places with scale of 1 cm to 10 km?
c) A rectangular ground is 54 m long and 45 m broad. If the map scale is 1:900,
find the length and breadth on drawing.
d) The length and breadth of a rectangular garden are 24 m and 20 m respectively.
Find the scale drawing length and breadth of the garden with scale of 1:800.
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Creative Section - B 3 cm 3 cm 3 cm 2 cm
7. The scale drawing dimensions of the Kitchen Bed room 3 cm
Dinning
ground floor of a house are given alongside. 2 cm room
a) Find the actual dimensions of every 1 cm Toilet Living room
Passage
room with scale of 1:200. 2 cm
Storeroom
b) Find the actual area occupied by the 3 cm 2 cm 4 cm
kitchen room.
c) Calculate the actual area occupied by the house.
It's your time - Project work!
8. a) Let's choose an appropriate scale and draw a road map of your school from
your home.
b) Let's sketch the layout of ground floor of a house with an appropriate scale to
the following measurements. (i) Sitting room - 10 m by 8 m
(ii) a bed room - 8 m by 6 m (iii) a kitchen - 6 m by 4 m
(iv) a guest room 8 m by 6 m (v) a wash room - 4 m by 3 m
20.3 Bearing
From the given compass, let's study the different North (N)
directions. In the compass NOS represents
North–South and EOW represents East-West North West (NW) North East (NE)
directions. West (W) O East (E)
Furthermore, the angle between N and E is 90q. South West (SW) South (S) South East (SE)
The direction NE lies exactly in between N and
E. So, the angle between N and NE is 45q. We
take O as the point of reference and ON (North line) as base to find direction of any
object (or place) in terms of degrees measuring clockwise from the base line (ON).
The direction is usually written using three digits. For example,
the direction of NE from O is 045q. It is called bearing of NE from O. NW N
045° NE
The direction of E from O is 090q. It is called bearing of E from O. W O E
Similarly, the direction of SW from O is 225q. It is called bearing SW 225°
of SW from O and so on. SE
S
Thus, the bearing of a point (or place) is the angle in degrees
measured from the north line in clockwise direction.
The bearing of an object (or place) is usually written in three digits. So, it is also
called three-digit bearing (or three-figure bearing).
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Scale Drawing and Bearing
Worked-out examples
Example 1: Write down the bearings of A, B, and C places from O.
a) N b) N c) C N
60° A 25°
O O
120° O
B
Solution:
a) The bearing of A from O is 060q.
b) The bearing of B from O is (360q – 120q) = 240q.
c) The bearing of C from O is (360q – 25q) = 335q.
Example 2: State the bearing of point P from A.
a) N b) N c) N d) N
48° P A
A P
WA E WA EW 40° E W 25° E
60° S P
P
Solution: S S S
a) The bearing of point P from A is NAP = 048°
b) The bearing of point P from A is NAP = 1$S + SAP = 180° + 60° = 240°
c) The bearing of point P from A is NAP = 1$S – PAS = 180° – 40° = 140°
d) The bearing of point P form A is NAP = 1$W + WAP = 270° + 25°= 295°
Example 3: In the adjoining diagram, if the bearing of A from B is 080q, find the
bearing of B from A. N N1
Solution:
Here, bearing of A from B is 080q. 80° A
B
Since, BN // AN1, NBA and N1AB are co-interior angles.
? N1AB = 180q – 80q [Co-interior angles are supplementary.]
= 100q
? Bearing of B from A = 360q – 100q = 260q.
EXERCISE 20.2 N NE
General Section NW E
1. Let's tell and write the names of these eight points of the
WO SE
compass in full. SW
a) N is ....................................... NE is .......................... S
b) E is .......................................... SE is .........................
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c) S is .......................................... SW is ........................
d) W is ........................................ NW is .........................
2. Let's tell and write how many degrees are in the angles between .
a) N and E .................... b) N and NE ....................
c) N and S .................... d) N and SE ....................
e) N and W .................... f) N and SW ....................
g) N and W .................... h) N and NW ....................
3. Let's tell and write the bearings as quickly as possible.
a) N b) N c) N d) D N
75° A 80° 130°
O O
O B
C
O
300°
A from O ......... B from O ......... C from O ......... D from O .........
Creative Section - A
4. Let's study the adjoining map of MaBhaeintaddrai nagar Jumla
Nepal and answer the following Nepalgunj
questions. Jomsom
Gaighat
BBirhaatdnrIaalgpaaurrmPokhara
Butwal Kathmandu
Birgunj
a) If Kathmandu is the point of reference, write the compass directions of:
(i) Pokhara (ii) Biratnagar (iii) Mahendranagar
(iv) Ilam (v) Jumla (vi) Nepalgunj
b) If Butwal is the point of reference, write the compass directions of:
(i) Kathmandu (ii) Birgunj (iii) Baitadi
(iv) Bhadrapur (v) Jomsom (vi) Gaighat
5. Let's write down the bearings of all the planes shown below from A.
a) N b) N c) N
60° A 125°
A A
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d) N e) f) N
140° A N
45°
AA
6. Let's find the bearing of point P from O in each the following figures.
a) N b) N c) N
P
W O 20° E WO E W O E
30°
S 55° S
P N
d) N SP
f)
e) N
P 40° P
WO E WO E W O 130° E
150°
S P S
S
Creative Section - B
7. The bearings of A from B are given in the figures. Find the bearings of B from A.
a) N1 b) c) d) N1
N N N1 N N1 N
A
025° 065° A 087°
090°
B B B A B A
N N
e) f) g) h)
N N N1 N1
N1 N1
105° 140° B A
B B 210°
A B 330°
A
A
8. a) If the bearing of a place P from a point Q is 055°, find the bearing of Q from p.
b) If the bearing of Dharan from Birgunj is 084°, find the bearing from Dharan to
Birgunj.
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Unit Statistics
21
21.1 Statistics – Review
The modern age is the age of information and communication. In the various field
of the society, we need information in the form of numerical figures to accomplish
various economical, commercial, technical activities. Such numerical figures are
called data.
Statistics is a branch of mathematics that deals about the collection, tabulation, and
presentation of data.
21.2 Types of data and frequency table
The numerical information given below are the amounts of pocket money (in Rs)
brought by 20 students of class VII on a day.
20, 15, 20, 25, 20, 25, 10, 30, 20, 30,
25, 20, 15, 20, 30, 25, 40, 20 25, 40
The above data are not presented in the proper order. Such data are called raw data.
Now, let's arrange these data in the ascending order of the values.
10, 15, 15, 20, 20, 20, 20, 20, 20, 20,
25, 25, 25, 25, 25, 30, 30, 30, 40, 40
The above data which are presented in the proper order (either ascending or
descending order) are called arrayed data.
From an arrayed data, it is easier to observe how many times a particular figure is
repeated
Rs 10 is repeated only one time. o Frequency of Rs 10 is 1.
Rs 15 is repeated two times. o Frequency of Rs 15 is 2.
Rs 20 is repeated seven times. o Frequency of Rs 20 is 7.
Rs 25 is repeated five times. o Frequency of Rs 25 is 5.
Rs 30 is repeated three times. o Frequency of Rs 30 is 3.
Rs 40 is repeated two times. o Frequency of Rs 40 is 2.
In this way, a frequency is the number of times a figure (or value) occurs.
We can present the data and their frequencies in a table. Such table is called
frequency distribution table (or simply frequency table).
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Frequency table Frequency
Pocket money (in Rs) Tally marks 1
2
10 | 7
15 || 5
20 || 3
25 2
30 |||
40 || 20
Total
Tallying is a system of showing frequencies using diagonal lines grouped in fives.
Each time five is reached, a horizontal line is drawn through the tally marks to make
a group of five. The next line starts a new group. For example,
1 is |, 2 is ||, 5 is , 7 is ||, and so on.
21.3 Cumulative frequency table of ungrouped data
The word 'cumulative' is related to the word 'accumulated', meaning to 'pile up'.
The table given below shows the pocket money of 20 students.
Wages (in Rs.) Frequency (f) Cumulative frequency (c.f.)
10 1 1
15 2 1+2=3
20 7 3 + 7 = 10
25 5 10 + 5 = 15
30 3 15 + 3 = 18
40 2 18 + 2 = 20
20
Total
21.4 Grouped and continuous data
Let's consider the following marks obtained by 20 students in a Mock Test of
Mathematics.
25, 32, 45, 15, 8, 42, 26, 19, 28, 45,
36, 48, 22, 29, 18, 34, 6, 38, 41, 24
The above mentioned data are called individual data. Another way of organizing
data is to present them in a grouped form. For grouping the given data, we should
first see the smallest and the largest values. Then, we have to divide the data into
appropriate class intervals.
In the above data, smallest value is 6 and the largest value is 48. So, the class
intervals can be 0 – 10, 10 – 20,…, 40 – 50. The data arranged in this way are called
grouped data.
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The frequency table of the grouped data are given below.
Marks Tally marks No of students (f)
0 – 10 || 2
10 – 20 ||| 3
20 – 30 | 6
30 – 40 |||| 4
40 – 50 5
Total 20
Now, the cumulative frequency of above data can be constructed as follows.
Marks No. of Cumulative frequency (c.f)
students (f)
0 – 10 22 o 2 students obtained less
10 – 20 3 2+3 = 5 o 5 students obtained less than 20 marks
20 – 30 6 5+6 = 11 o 11 students obtained less than 30 marks
30 – 40 4 11+4 = 15 o15 students obtained less than 40 marks
40 – 50 5 15+5 = 20 o 20 students obtained less than 50 marks
Total 20
Thus, cumulative frequency corresponding to a class – interval is the sum of all
frequencies up to and including that interval.
21.5 Bar graph
We have already discussed to present data in frequency tables. Alternatively, we can
also present data graphically. Different types of diagrams are used for this purpose.
Here, we shall discuss about a bar graph (or bar diagram).
(i) Simple bar graph
A simple bar graph is drawn to present a single type of data. In a bar graph, data
are represented in a series of bars that are equally wide. Bars can touch each
other or be separated by gaps of equal width. The height of the bars represent
the frequency of the data.
We should follow the rules given below while drawing a bar graph:
Choose a suitable scale to represent the whole data. Mention the frequencies in
y-axis.
Decide how wide the bars are and how much space you leave between them.
Construct the bars of the same width and at equal distance.
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Worked-out examples
Example 1: The table given below shows the number of students in class 7 of
Solution: a school in five years. Represent the numbers in a bar graph.
Years (B.S.) 2073 2074 2075 2076 2077
No. of students 30 35 45 60 50
2073 2074 2075 2076 2077
(ii) Multiple bar graph
A multiple bar graph is drawn to show two or more related components of the
given data. For example, if we want to show the number of boys and girls of
a school separately, we should draw the multiple bar graph. The method of
drawing a multiple bar graph is exactly the same as a simple bar graph.
Example 2: The number of boys and girls in the primary level of a school are
given in the table below. Draw a multiple bar graph to show their
numbers.
Solution: Classes 1 2345
No. of boys 12 15 16 25 25
No. of girls 18 20 24 20 10
No. of boys and girls 35 20 24 25 25
30 15 16 20 10
5
25 23 4
Classes
20 18
15 12
10
5
0
1
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1. a) EXERCISE 21.1
b)
c) Define raw and arrayed data with examples.
d) Define frequency with examples.
Define cumulative frequency with examples.
2. a) Write a difference between a simple bar graph and a multiple bar graph.
The amount of pocket money (in Rs) brought by 20 students of class VII on a
day are given below. Let's construct a frequency distribution table with tally
marks.
30, 40, 25, 35, 40, 50, 40, 30, 25, 20,
40, 45, 35, 40, 30, 35, 40, 45, 30, 35
b) Daily wages (in Rs) of 30 workers in a factory are given below. Arrange the
data in proper order. Lets construct a frequency table to present the data.
850, 900, 600, 750, 800, 750, 600, 900, 800, 750,
700, 800, 750, 600, 750, 800, 900, 850, 750, 700,
800, 750, 700, 800, 850, 750, 800, 750, 700, 750.
c) In an interview of 20 married couples about their desired number of children,
the responses were as follows:
1, 2, 3, 2, 3, 1, 4, 2, 2, 1
4, 3, 1, 2, 2, 2, 1, 3, 1, 2
Let's present the above data in a frequency table using tally marks and answer
the following questions.
(i) How many couples desired a single child?
(ii) How many couples desired two children?
(iii) How many couples desired three children?
(iv) How many couples desired more than three children?
(v) What is the desirable number of children for the maximum number of
couples?
3. Let's construct the cumulative frequency table to represent the following
ungrouped data,
a) Age (in years) 6 8 10 12 14 16
No. of students 5 3 7 2 6 2
b) Weight (in Kg) 20 30 40 50 60 70
No. of persons 9 6 15 10 6 4
4. Let's construct the cumulative frequency table to represent the following
grouped data.
a) Marks obtained 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
No. of Students 2 4 7 10 9 4
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b) Age (in years) 0 – 15 15 – 30 30 – 45 45 – 60 60 – 75 75 – 90
No. of patients
20 10 6 9 15 4
c) Daily sales 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
(in Rs. 1000) 35 18 25 12 10
No. of Shops
5. a) The number of students in the primary level (class 1 to 5) are given below.
Draw a simple bar graph to show the number.
Classes 12345
No. of students 45 30 50 25 15
b) The table given below shows the number of students who secured 'A' grade in
S.E.E. from your school in the last five years. Let's draw a simple bar diagram to
show the data.
Years (B.S.) 2073 2074 2075 2076 2077
No. of students 25 40 30 45 40
6. a) The table given below shows the number of boys and girls of a school from
class 6 to 10. Illustrate the numbers by drawing a multiple bar graph.
Classes 6 7 8 9 10
No. of boys 10 20 15 25 20
No. of girls 15 10 20 15 10
b) Class 7 students conducted a survey and recorded the following number
of male and female who had positive results of rapid diagnostic test for
conronavirus in the last five days. Draw a multiple bar graph to show the
numbers.
Days Sunday Monday Tuesday Wednesday Thursday
No. of male patients 7 10 12 10 7
No. of female patients 3 5 4 3 5
c) The table given below shows the S.E.E. result of a school for the last 4 years
Let's draw a multiple bar graph to show the numbers.
Year (in B.S.) 2074 2075 2076 2077
'A+' grade 5 10 15 12
'A' grade 10 15 20 27
'B+' grade 15 5 15 11
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7. The multiple bar graph given below shows the number of boys and girls who
secured 'A' grade in the final examination from different classes. Answer the
following questions.
No. of boys and girls boys
girls
6 78 9
Classes
a) How many students are represented by a room in vertical column?
b) How many boys and girls secured 'A' grade in the final exam from class 6?
c) If all the students of class 7 have grade 'A' in the exam, how many students were
there in class 7?
d) If 80 students appeared in the exam from class 9, find the percentage of students
who secured 'A' grade.
e) If 30 boys appeared in the exam from class 8, find the percentage of boys who
could not secure 'A' grade.
f) If 20 students could not secure 'A' grade from class 6, find the percentage of
students who secured 'A' grade.
21.6 Average (or Mean)
Suppose Ram has Rs 10 and Hari has Rs 8.
Then, we often say that in average Ram and Hari have Rs 9.
Let's think how we get an average of Rs 9 from Rs 10 and Rs 8.
Now, let's answer what the averages of (i) 2 and 4 (ii) 5 and 9 (iii) 2, 3 and 4 are.
Thus, an average is a single number that represents the central value of a set of data.
Of course, an average indicates the quality of the given data.
An average of the given data is calculated by adding them together and dividing the
sum by the number of data.
i.e., Average = Total sum of the data
Number of data
If x is used to represent the data, n is used to represent the number of data and x is
used to represent the average or mean of the data, then
Average (x) = 6nx
Here, the symbol’ 6' means summation of whole data.
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Worked-out examples
Example 1: The marks obtained by 7 students of a class 7 in a mock test of
mathematics are given below. Find the average marks.
40, 34, 20, 22, 38, 28, 35
Solution:
Here, 6x = 40 + 34 + 20 + 22 + 38 + 28 + 35 = 217 and n = 7
? Average(x) = 6x = 217 = 31
n 7
Example 2: The ages (in years) of 6 children are given below. If the average
age of the children is 9 years, find the value of p.
9, 6, 8, 7, p, 13
Solution:
Here, 6x = 9 + 6 + 8 + 7 + p + 13 = 43 + p and n = 6
6x
Now, average (x) = n
or, 9 = 43 + p
or, 43 + p = 54 6
or, p = 54 – 43 = 11
Example 3: The average of marks obtained by Govinda in English and Maths
is 21. If the marks obtained by him in Science is also included, the
average is 24. How many marks did he obtain in Science?
Solution: Total marks in two subjects
2
Here, average marks in English and Maths =
or, 21 = x or, x = 42
2
Total marks in three subjects
Also, average marks including Science = 3
or, 24 = y or, y = 72
3
? Marks obtained in Science = y – x = 72 – 42 = 30.
Example 4: Ramesh obtained an average marks of 80 in Maths and Science
and an average marks of 70 in English and Science. If he obtained
75 marks in Science, find his marks in Maths and English.
Solution: average marks of Maths and Science = Total marks in two subjects
Here, 80 =
x2
or, 2
or, x = 160
? Total marks obtained in Maths and Science = 160
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Also, total marks obtained in English and Science = 70 u 2 = 140
The marks obtained in Science = 75
? The marks obtained in Maths = 160 – 75 = 85
The marks obtained in English = 140 – 75 = 65.
So, his marks in Maths and English are 85 and 65 respectively.
EXERCISE 21.2
General Section - Classwork
1. Let's tell and write the answers as quickly as possible.
a) Average of 4 and 6 is .................... b) Average of 3 and 5 is....................
c) Average of 3, 4, and 5 is.................... d) Average of 5, 10, and 15 is ..................
2. a) Average of 2 and x is 3, x = ............ b) Average of 3 and y is 4, y = ............
c) Average of p and 10 is 16, p = .......... d) Average of z and 12 is 10, z = .........
3. a) 6x = 20, n = 5, average = ........ b) 6x = 32, n = 8, average = ...........
c) n= 10, average (x) = 5, 6x = ......... d) average (x) = 6, n= 9, 6x = ............
Creative Section - A
4. Let's find the average of the following data.
a) 20, 11, 14, 10, 15 b) 30, 40, 34, 53, 45, 32
c) 11yrs, 10 yrs, 9 yrs, 14 yrs d) 5.4cm, 4.5 cm, 7.2 cm, 6.3 cm, 8.1 cm
e) average of first five prime numbers f) average of first five multiples of 6
5. a) If the average of 7, 12, 6, 10, and p is 8, find the value of p.
b) If the average of Rs 16, Rs 20, Rs 25, and Rs y is Rs 20, find Rs y.
6. a) The average rainfall of the last week was 35 mm. If the records of daily
rainfall from Sunday to Friday were 45 mm, 22 mm, 28 mm, 36 mm, 30 mm
and 24 mm, find the rainfall on Saturday.
b) The average age of Pratik, Debashis, Sunayana, and Buddhi is 16 years. If the
age of the first three children are 7 years, 13 years, and 20 years respectively,
how old is Buddhi?
Creative Section - B
7. a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300
in the last week. If he earned Rs 2,000 on Saturday, find his average of daily
income of the week.
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b) The average marks obtained by Anamol in English, Maths, and Science is 70.
If he obtained 60 marks in Nepali, find his average marks in 4 subjects.
8. a) The average income on Sunday and Monday of an electrician is Rs 1,800. If
his income on Tuesday is also included, the average income will be Rs 2,100.
Find his income on Tuesday.
b) The average of the marks obtained by Abdul and Mariya in Maths is 56.
If the marks obtained by Hari is also included, the average is 60. Find the
marks obtained by Hari.
9. a) Renu obtained an average marks of 70 in Science and Maths, an average
marks of 60 in Science and English. If she obtained 55 marks in Maths, find
her marks in Science and English.
b) The average age of Kishan and Dolma is 15 years and that of Dolma and
Shashwat is 14 years. If Kishan is 17 years old, find the age of Dolma and
Shashwat.
10. a) The average temperature of a town in the last week was 32°C. If the average
temperature recorded daily from Sunday to Wednesday was 30°C and that of
recorded daily from Wednesday to Saturday was 33°C, find the temperature
of the town recorded on Wednesday.
b) The average of 9 numbers is 23. If the average of first five numbers is 20 and
that of last five numbers is 25, what is the fifth number?
c) The average age of a husband and wife was 23 years at the time of their
marriage. After 10 years, they have now a daughter of 6 years, what is the
average age of the family at present?
21.7 Mean or average of ungrouped repeated data
When the data are repeated, we find the mean (or average) by making the frequency
table. Follow the steps given below to calculate the mean of ungrouped repeated
data.
(i) Draw a table with 3 columns.
(ii) Write down the items (x) in ascending order in the first column.
(iii) Write the corresponding frequency (f) of each item in the second column.
(iv) Find the product of each item (x) and its frequency (f) in the third (fx) column.
(v) Find total of f column and fx column.
(vi) Divide the sum of fx by the sum of f, the quotient is the required mean.
Worked-out examples
Example 1: The marks obtained by the students of class VII in a mock test of
Maths are given in the table below. Find the mean marks.
Marks 10 20 30 40 50
No. of students 3 6 10 7 4
315Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Statistics
Solution:
Calculation of mean marks
Marks (x) No. of students (f) fx
10 3 30
20 6 120
30 10 300
40 7 280
50 4 200
Total N = 30 6fx = 930
Now, mean mark (x) = 6fx = 930 = 31
N 30
Example 2: If the mean of the data given below be 17, find the value of p.
x 5 10 15 20 25 30
f 25 10 p 4 2
Solution: fx
xf 10
50
5 2 150
10 5 20p
15 10 100
20 P 60
25 4
30 2 6fx = 370 + 20p
Total N = 23 + p
Now, mean (x ) = 6fx
N
or,
or, 17 = 370 + 20p
or, 23 + p
or,
391 + 17p = 370 + 20p
17p – 20p = 370 – 391
– 3p = – 21
or, p = 21 = 7
3
So, the required value of p is 7.
Vedanta Excel in Mathematics - Book 7 316 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Statistics
EXERCISE 21.3
General Section A – Classwork
1. Tell and write the unknown variables as quickly as possible.
a) 6fx = 36, N = 4, x = ................. b) 6fx = 60, N = 10, x = ...................
c) 6fx = 120, N = 30, x= ................. d) 6fx = 900, N = 15 , x = ..................
2. a) 6 fx = 40, x = 5, N = ................. b) 6 fx = 70, x = 7, N = ...................
c) 6fx = 300, x = 15, N = ................. d) 6fx = 600, x = 12, N = ...................
Creative Section - A
3. a) The marks obtained by the students of class VII in a maths test are given in
the table. Find the mean marks.
Marks 20 30 40 50 60
No. of students 4 9 11 4 2
b) Calculate the mean of daily wages (in Rs) of 60 workers from the given table.
Wages (in Rs) 280 300 320 360 380
No. of students 14 16 15 7 8
c) Calculate the average age of 40 people in a village.
Age (in years) 20 25 30 35 40 45
No. of people 4 6 8 10 8 4
Creative Section -B
4. a) Following are the marks obtained by 20 students of a class in a monthly test
of Maths. Present the marks in frequency table and find the mean marks.
60, 50, 40, 80, 50, 70, 50, 70, 80, 70
70, 40, 60, 70, 90, 50, 70, 40, 60, 80
b) The daily earnings (in Rs) of 25 household technicians are given below. Present
the earnings in frequency table and compute the average earning.
900, 1000, 800, 750, 700, 800, 600, 900, 750, 1000, 700, 750,
600, 800, 750, 900, 750, 600, 700, 700, 750, 800, 750, 800, 750
317Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Statistics
5. a) If the mean of the following frequency distribution is 8, find the value of p.
x 3 5 7 9 11 13
f 6 8 15 p 8 4
b) The mean of the data given below is 17. Find the value of p.
x 5 10 15 20 25 30
f 2 5 10 p 4 2
6. a) If the mean of the given data is 14, find the value of m 25
x m 10 15 20 m
f 7684
b) If the mean of the following data is 15, find the value of p. 25
x 5 10 15 20 5
f p 8 p 10
It's your time - Project work!
7. a) Let's make groups of 5 friends and conduct a survey inside your class to
find the amount of pocket money that your friends in each group brought
on a day.
(i) Find the average amount of pocket money of each group.
(ii) Find the average amount of pocket money of the whole students of your
class.
b) Let's conduct a survey to find the number of students of your school from
class 4 to class 8. Present the data in a frequency distribution table and find
the average (mean) number of students of these classes.
c) Let's conduct a survey to find the number of students of different ages from
class 6 to class 8 in your school. Present the data in a frequency table and
calculate the mean age. How much close your age from the mean age?
Vedanta Excel in Mathematics - Book 7 318 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
1. Set
Creative Section Exercise - 1.1
5. Answer the questions and discuss in the class. Then show to your teacher.
6. a) A = {natural numbers less than 5} b) B = {first five multiples of 5}
c) C = {prime numbers between 5 and 20} d) D = {factors of 6}
7. a) P = {11, 13, 17, 19} b) A = {F, O, T, B, A, L} c) F = {1, 2, 3, 6, 9, 18} d) M = {6, 9}
8. a) A = {x : x < 6, x natural number} b) B = {x : x is a prime, x < 10}
c) C = {x : x is a square number, x ≤ 25} d) D = {x : x is a factor of 8}
9. a) A = {12, 14, 15, 16, 18}, n(A) = 5 b) B = {1, 2, 3, 4, 6, 12}, n(B) = 6
c) Z = {–2, –1, 0, 1, 2}, n(Z) = 5 d) W = {0}, n(W) = 1
10. Please complete your project work and compare with your friends. Then discuss in the class.
Creative Section Exercise - 1.2
8. Answer the questions and discuss in the class. Then show to your teacher.
9. a) Equivalent sets b) Equal sets 10. a) Overlapping sets b) Disjoint sets
11. a) Subsets: {apple}, I proper subset : I b) Subsets: {1}, {2}, {1, 2}, I Proper subsets: {1}, {2}, I
c) Subsets: {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, I
Proper subsets: {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, I
d) Subsets: {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4},
{2, 3, 4}, {1, 2, 3, 4}, I
Proper subsets: {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4},
{2, 3, 4}, I
12. a) A = {1, 2, 3, 6}, B = {1, 2, 4, 8}, then X = {1, 2} b) P = {m, a, t, h}, Q = {t, h, i, n, k}, then Y = {t, h}
A B
13. a) A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 0 241836 12 14. and 15. Complete your project works and discuss
B = {1, 2, 3, 4, 6, 8, 12, 24}, in the class. Then show to your teacher.
P = {1, 2, 3, 4, 6, 8} 57 24
9
Exercise - 1.3
Creative Section
4. a) S C = {Sita} b) S C = {Ram, Sita, Krishna, Shiva, Shiva, Abdul, Laxmi, Shova, Hari, Joseph}
n(S C) = 9 c) S – C = {Ram, Krishna, Shiva, Abdul} d) C – S = {Laxmi, Shova, Hari, Joseph}
5. a) (i) A B = {a, e, i, o, u, b, c, d} (ii) A B = {a, e} (iii) A – B = {i, o, u} (iv) B – A = {b, c, d}
(i) A B (ii) A B (iii) A B (iv) A B
i ab i ab i ab i ab
o e c o e c o e c o e c
u d u d u d u d
AB AB A–B B–A
b) (i) P Q = {1, 3, 5, 6, 7, 9, 18} (ii) P Q = {1, 3, 9} (iii) P – Q = {5, 7} (iv) Q – P = {6, 18}
(i) P Q (ii) P Q (iii) P Q (iv) P Q
5 16 5 16 5 16 5 16
3 3 3 3
7 9 18 7 9 18 7 9 18 7 9 18
PQ PQ P–Q Q–P
c) (i) M N = {1, 2, 3, 4, 6, 8} (ii) M N = {1, 2} (iii) M – N = {3, 6} (iv) N – M = {4, 8}
(i) M N (ii) M N (iii) M N (iv) M N
3 14 3 14 3 14 3 14
6 28 6 28 6 28 6 28
MN M N M–N N–M
d) (i) A B = {1, 2, 3, 4, 5} (ii) A B = {2, 4} (iii) A – B = {1, 3, 5} (iv) B – A = I
A A A A
(i) B (ii) B (iii) B (iv) B
1 2 1 2 1 2 1 2
4 4 4 4
35 35 35 35
AB AB A–B B–A
319Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
6. a) (i) A = {7, 8, 9, 10, 11, 12, 13, 14, 15} (ii) B = {1, 3, 5, 7, 9, 11, 13, 14, 15}
A U BU
1 2516111115234 2 15
7 1 4 6 8 14
3 3 10 12 13
8 4
9 5 7 9 11
10
A P U B QU
b) (i) P = {2, 3, 5, 6, 7, 8, 10} 21 (ii) Q = {1, 4, 6, 8, 9, 10} 12
9 10 35
34 78 4 7
56
6 8 9 10
PQ
BU A BU
7. a) (i) A B = {2, 3, 4, 5, 6, 8} A 3 (ii) A B = {1, 7, 9, 10}
4 5 4 3
2 1 68 2 5
1 68 9 10 7 9
7 10
A B AB
A BU A BU
b) (i) A B = {6} 3 2 (ii) A B = {1,2,3,4,5,7,8,9,10,11,12} 1 3 6 2
5 4
1 9 12 6 4 9 12
5 8 11 8 11
7 10 7 10
A B AB
A BU A BU
c) (i) A – B = {1} 2 10 (ii) A – B = {2, 3, 4, 5, 6, 7, 8, 9, 10} 1 2
3 14 9 3 4 10
5 89
5 8 7 67
6 A A–B B U
A–B BU
A
d) (i) B – A = {10} 1 2 (ii) B – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} 1 2
4 10 3 4 10
3 89 5 89
67 67
5
8. a) U = {1, 2, 3, …, 15} B–A B–A
b) X Y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11} and X Y = {10, 12, 13, 14, 15}
c) X Y = {1, 3, 5, 7} and X Y = {2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15}
d) X – Y = {2, 4, 6, 8} and X – Y = {1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15}
e) Y – X = {9, 11} and Y – X = {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15}
9. a) A B C = {2, 3, 4, 5, 6, 7, 8, 10, 12} and A B C = {1, 9, 11}
b) A B C = {4, 6} and A B C = {1, 2, 3, 5, 7, 8, 9, 10, 11, 12}
c) (A B) C = {2, 3, 4, 6} d) (A B) C = {2, 3, 4, 6, 12}
10. a) A (A B) = {2, 4, 6, 8, 10, 12, 14} b) A (A B) = {2, 4, 6, 8, 10, 12, 14}
c) A – (A B) = {8, 10, 14} d) B – (A B) = {1, 3} e) A B = {1, 3}
f) A B = {8, 10, 14} g) A B = {1, 3, 5, 7, 8, 9, 10, 11, 13, 14, 15} h) A B = {5, 7, 9, 11, 13, 15}
11. Show to your teacher.
12. aa)nFd615.FP8 l=ea{s1e, 2co}mbp) lFe1t2e yoFu1r8 = {1, 2, 3, 6} and 13. a) wMit6hyMou8r=f{ri2e4n}ds. Tb)hMen5 disMcu10s=s {i1n0t,h2e0c}lass
14. project works compare
and show to your teacher.
2. Number system in different bases
Creative Section Exercise - 2.1
5. a) Two arab fifty-six crore twenty-eight lakh eighty thousand rupees; Two billion five hundred sixty-two
million eight hundred eighty thousand rupees.
Vedanta Excel in Mathematics - Book 7 320 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
b) Seven arab fifty-seven crore seventy-one lakh thirty thousand four hundred; Seven billion five
hundred seventy-seven million one hundred thirty thousand four hundred.
c) Thirteen kharab fifteen arab sixteen crore seventeen lakh rupees.
6. a 6,84,91,47,05,340 684,914,705,340 b) 37,815,668,521 37,81,56,68,521
7. a) 5 × 107 + 2 × 106 + 6 × 104 + 3 × 103 + 7 × 102 + 9 × 100
b) 4 × 108 + 8 × 105 + 1 × 103 + 5 × 102 + 3 × 101
c) 7 × 109 + 5 × 108 + 2 × 106 + 6 × 105 + 4 × 101 + 8 × 100
d) 2 × 1010 + 3 × 109 + 9 × 108 + 6 × 104 + 8 × 103 + 4 × 102 + 7 × 100
8. a) One crore sixty lakh (Sixteen million)
b) Four crore seventy-five lakh (Forty-seven million five hundred thousand)
c) Three arab forty crore (Three billion four hundred million)
d) Five arab thirteen crore (Five billion one hundred thirty million)
e) Two million seven hundred thousand (Twenty-seven lakh)
f) Six million nine hundred ninety thousand (Sixty-nine lakh ninety thousand)
g) Seven billion two hundred million (Seven arab twenty crore)
h) Eight billion three hundred sixty million (Eight arab thirty-six crore)
9. a) 750000 Seven hundred fifty thousand (Seven lakh fifty thousand)
b) 1915000000 One billion nine hundred fifteen million (One arab ninety-one crore fifty lakh)
c) 62500000 Six crore twenty-five lakh (Sixty-two million five hundred thousand)
d) 2520000000 Two arab fifty-two crore (Two billion five hundred twenty million)
10. a) Rs 32,40,000 Thirty-two lakh forty thousand rupees
b) Rs 67,500,000 Sixty-seven million five hundred thousand rupees
11. and 12. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
Creative Section Exercise - 2.2
4. a) 3 b) 5 c) 6 d) 10 e) 12 f) 18 g) 31 h) 58 i) 57 j) 101
5. a) 111111121002 b) 110000110002 012 c) 111100011120002 id))110000111000100202 e) 111100100001010212
6. f) g) h) g) 178 h) 283 j)
a) 8 b) 14 c) 17 d) 35 e) 53 f) 95 i) 194 j) 624
7. afaa)n)) 1d21344125512.5 Please cbgbo)))m412003p252le25t5e your projechcc)))t111w000021o514rk10s25 and compidd)a))1r12e4010w10051i1t0h52 your frien9ej))d.1a1s1.)02T10111h015e02n5=di1sc2u5 sbs)i1n0t1h0e1c2l>ass325
8.
10.
and show to your teacher.
3. Operations on Whole Numbers
Creative Section Exercise - 3.1
3. a) 3 b) 3 c) 4 d) 6 e) 12 4. a) 6 b) 10 c) 18 d) 6 e) 7 f) 15 g) 16 h) 24
5. a) 6 b) 4 c) 6 d) 13 e) 3 f) 15 g) 13 h) 24 6. a) 15 b) 30
7. a) 10 l b) 12, 4 apples, 5 bananas, 8 guavas 8. a) 4 ft. b) 1m 40 cm
9. a) 18 classmates, 3 snickers, 4 kit kats, 5 cadburies b) 8, 7 orange colour, 5 maroon colour, 3 white colour
c) 25 people, 2 sweaters, 3 kambals, 4 jackets d) 7 fruits, 14 heaps
Creative Section Exercise - 3.2
3. a) 6 b) 12 c) 12 d) 18 e) 24 4. a) 18 b) 36 c) 36 d) 42 e) 24 f) 72 g) 150 h) 210
5. a) 24 b) 42 c) 90 d) 60 e) 48 f) 120 g) 180 h) 360 6. a) 48 b) 150
7. a) 60 l b) 4 m c) 4800 km 8. a) 7 : 00 a.m. b) 6:00 p.m. 9. a) 65 b) 52 10. a) 175 b) 100
11. and 12. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
Creative Section Exercise - 3.3
3. a) 2025 b) 7744 c) 15376 4. a) Yes b) No c) Yes d) No e) Yes
5. a) 8 b) 10 c) 12 d) 18 e) 28 f) 35 6. a) 14 b) 16 c) 21 d) 35 e) 64 f) 158
7. a) 5 b) 7 c) 15 d) 16 e) 2 3 f) 6 5 g) 14 2 h) 6 2 i) 6 5 j) 10 3 k) 360 2
6 8 16 25
7 9 13
8. a) 9 b) 9 c) 6 9. a) 8 b) 10 c) 14 d) 6 e) 7
5 4
321Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
10. a) 0.4 b) 0.9 c) 1.2 d) 1.4 e) 1.8 11. a) 625 b) 2025 c) 900 m2 d) 29
12. a) 20 b) 25 m c) 65 d) 115 13. a) (i) 2 (ii) 3 (iii) 5 (iv) 7 (v) 5
b) (i) 2 (ii) 5 (iii) 3 (iv) 6 (v) 21 14. a) 900 b) 144
15. a) 4 b) 44 c) 23 d) 25
16. and 17. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
Creative Section Exercise - 3.4
2. a) 216 b) 512 c) 729
d) 1728 e) 15625 3. a) 8 b) 27 c) 8 d) 343 e) 125
4. a) 4 b) 8 c) 9 27 64 125 729 64
2 4 5 7 8
d) 10 e) 18 5. a) 3 b) 5 c) 6 d) 12 e) 15
6. a) 0.2 b) 0.3 c) 0.5 d) 0.7 e) 1.1 7. a) 15 b) 14 c) 35 d) 10 e) 20
f) 6 g) 15 h) 6 i) 10 8. a) 216 cm3 b) (i) 729000 cm3, (ii) 729 l
9. a) 8 cm b) (i) 343000 cm3 (ii) 70 cm c) 2 m 10. a) Yes b) Yes c) No d) Yes e) No
11. a) (i) 3 (ii) 4 (iii) 6 (iv) 5 b) (i) 2 (ii) 3 (iii) 4 (iv) 5 12. a) 216 b) 216
13. and 14. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
4. Real Numbers
Exercise - 4.1
Creative Section
4. a) (i) Z1 Z2 = {–2, –1, 0, 1} (ii) Z1 Z2 = {–1} b) (i) Z3 – Z4 = I (ii) Z4 – Z3 = {–3, 3}
5. a) 4 b) 6 c) 10 d) 3 e) –3 f) –2 6. a) (ii) 5 km b) 19880 m c) 18°C
7. a) Loss of Rs 72 b) Profit of Rs 175
Exercise - 4.2
Creative Section
3. Please show the operations in number lines yourself a) 7 b) 3 c) –4 d) –11 e) 7 f) –9 g) 11 h) 1
4. a) 11 b) 5 c) 0 d) –2 e) –6 f) 6 g) –3 h) –12 i) –9 j) –2
5. a) 10 b) 4 c) –3 d) –9 6. a) 11 b) 2 c) 5 d) –4 7. a) 20 b) –35 c) 35 d) 8
8. a) –10 b) –15 9. a) –1°C b) Loss of Rs 130 c) 20
Exercise - 4.3
Creative Section
5. Please show the operations in number lines yourself a) 6 b) –8 c) –10 d) 12 e) 3 f) –2 g) –5 h) 3
6. a) 30 b) –28 c) –27 d) 80 e) 8 f) –3 g) –4 h) 7
7. a) –30 b) 40 c) 48 d) 72 e) –24 f) –50 g) 24 h) –48 i) –40 j) 120
8. a) –8 b) –6 9. a) –5 b) –4 10. a) 35 b) 60 c) Rs 120
11. Please complete your project works and compare with your friends. Then discuss in the class.
Exercise - 4.4
Creative Section
2. a) 2 b) 6 c) 28 d) –6 e) 15 f) 66 g) 7 h) 2 i) 3 j) 6 k) 5 l) 55
3. a) 77 b) 20 c) 24 d) 12 e) 4 f) 6 g) 5 h) 12 i) 3 j) 28
4. a) Rs 3,975 b) 7 c) 3 d) Rs 387 5. a) Diyoshana
6. and 7. Please complete your project works and compare with your friends. Then discuss in the class.
Creative Section Exercise - 4.5
5. Answer the questions yourself and show to your teacher.
6. a) 5 , 9 b) 9 , 17 c) 15 , 29 d) 0.3 , 0.4 e) 0.5, 0.375
2 4 2 4 2 4
7. a) 0.5 b) 0.6 c) 1.375 d) 0.6 e) 0.7
f) 0.714285 g) 1.307692
8. and 9. Please complete your project works and compare with your friends. Then discuss in the class.
5. Fraction and Decimal
Creative Section Exercise - 5.1
3. a) 1152 b) 4 1 c) 11 d) 2125 4. a) 3 b) 1 1 c) 7 d) – 1 e) 1 f) 3 5
4 42 4 20 8 24 6 12
Vedanta Excel in Mathematics - Book 7 322 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
g) –1 1 h) 1 1 i) 2 1 j)2 1 k)1 65 l) 6 11 5. a) 8 , 11 , Bhurashi b) first pipe
18 3 8 10 24 10 15
6. a) 634 kg 17 3 1 3 31
b) 275 20 km 7. a) 10 cm b) Pinky, 2 kg c) 4 GB 8. a) (i) 40 parts
(ii) 9 parts (iii) first pipe b) (i) 1 part (ii) Pratik c) (i) 1 part (ii) Daughter
40 4 8
Exercise - 5.2
Creative Section
3. a) 12 b) 721 c) 4 d) 1 e) 3 3 f) 421 g) 12 h) 1 i) 2 j) 331 k) 113 l) 4
9 2 4 10 3 5
m) 221 n) 132
5. a) Rs 5 4. a) Rs 65 b) Rs 288 c) 75 cm d) 300 m e) 750 g f) 240 students
b) Rs 70 c) 50 d) 16 cm e) 450 m f) 80 ml 6. a) 212 b) 1 c) 1 d) 1212 e) 2
15 6 e) 1210 3
14 g) 2110 12 3 1 7 2 2 5
f) 25 h) 17 i) 5 j) 3 k) 11 7. a) 10 b) 1 c) 3 d) 9 f) 24
8. a) 1 b) 1112 c) 116 d) 5 e) 3 f) 121 9. a) (i) Rs 16,000 (ii) Rs 12,000
24 6 8
b) (i) Rs 29,250 (ii) Rs 3,250 (iii) Rs 19,500 10. a) Rs 378 b) 42 c) Rs 2,500
d) (i) Rs 40,000 (ii) Rs 1,44,000 e) (i) 1200 (ii) 300 (iii) 45 11. a) (i) 14153 m (ii) 1253245 m2
b) 10121 m, 62081 m2 12. a) 100 km b) 55 l c) 48 d) 27 e) 2 hours f) 4
13.a) 14 hours b) 3 kg or 600 g c) 9 d) 8 days 14. a) (i) 9 (ii) 9,000 l b) 600 MB, 1800 MB
5 10
15. and 16. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
Creative Section Exercise - 5.3
3. Answer the questions and discuss in the class. Then show to your teacher.
4. a) 1.5 b) 0.6 c) 1.2 d) 0.83 e) 1.8 f) 0.5 g) 0.571428 h) 0.72
5. a) (i) 0.0002, 0.002, 0.02, 0.2 (ii) 0.025, 0.05, 0.2, 0.25 b) (i) 0.3, 0.03, 0.003, 0.0003
(ii) 0.54, 0.5, 0.4, 0.054 6. a) 3.3, 33.3, 333.3 b) 5.5, 55.5, 555.5 c) 1.6, 16.6, 166.6
d) 2.083, 20.83, 208.3 e) 8.181, 81.81, 818.181 f) 4.86486, 48.6486, 486.486
7. a) 3 b) 7 c) 4 d) 1 e) 1 f) 1 g) 4 h) 7 i) 18 j) 4 k) 8 l) 12
10 10 25 20 8 125 9 9 33 33 37 37
Creative Section Exercise - 5.4
3. a) 0.958 b) 1.564
c) 1.046 d) 14.76 e) 137.335 f) 0.122 g) 5.175 h) 4.995 i) 25.675
4. a) 0.31 b) 0.04 c) 163.34 d) 1.35 e) 8.74 f) 90.909 5. a) 6.3 b) 5.183 c) 18.688
d) 1.54 c) Rs 137.40 d) choose yourself
6. a) Rs 191 b) Rs 286
7. a) 13.8 cm b) 17.4 cm c) 15.1 cm 8. a) Rs 17.15 b) Rs 36.69 c) Rs 327.41
Creative Section Exercise - 5.5
4. a) 15 b) 3.304 c) 1.8306 d) 0.0465 e) 3.56 f) 43.8 g) 9.6 h) 3.4
5. a) 17.25 b) 1.93 c) 12.205 d) 3.976 e) 7 f) 2.4 g) –8 h) 0.9
6. a) (i) 45 mm (ii) 93 mm (iii) 4 mm b) (i) 0.2 cm (ii) 0.7 cm (iii) 1.8 cm
7. a) (i) 120 cm (ii) 360 cm (iii) 50 cm b) (i) 0.07 m (ii) 0.72 m (iii) 1.8 m
8. a) (i) 1600 m (ii) 4320 m (iii) 990 m b) (i) 0.004 km (ii) 0.045 km (iii) 0.84 km
9. a) (i) 1800 g (ii) 7350 g (iii) 50 g (iv) 480 g b) (i) 0.05 kg (ii) 0.2 kg
(iii) 1.26 kg (iv) 2.575 kg 10. a) (i) 2300 ml (ii) 4550 ml (iii) 75 ml (iv) 125 ml
b) (i) 0.005 l (ii) 0.02 l (iii) 0.35 l (iv) 1.59 l 11. a) Rs 1,129.65 b) Rs 75.50
12. a) 18.56 cm2, 18 cm b) 7.29 cm2, 10.8 cm c) 10.75 cm2, 13.6 cm d) 10.24 cm2, 12.8 cm
13. a) (i) 202.46 m (ii) 2464.56 m2 b) (i) 202 m, 2550.25 m2 c) (i) 25.5 m (ii) 124.5 m
d) 36.8 m, 1354.24 m2 14. a) 1250 b) 25 c) 85
15. Please complete your project works and compare with your friends. Then discuss in the class.
323Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
6. Ratio, Proportion and Unitary Method f) 7 : 12 > 4 : 9
Exercise - 6.1
Creative Section
4. Answer the questions and discuss in the class and show to your teacher.
5. a) 5 : 4 b) 10 : 1 c) 4 : 3 d) 3 : 8 e) 8 : 3 f) 3 : 10
6. a) 1 : 2 < 3 : 4 b) 2 : 5 > 1 : 3 c) 2 : 3 > 5 : 6 d) 4 : 7 > 3 : 8 e) 7 : 9 > 5 : 8
7. a) 2 : 5 b) 3 : 4 c) 2 : 3 8. a) (i) 2 : 5 (ii) 3 : 5 (iii) 2 : 3 b) (i) 4 : 5 (ii) 4 : 9 (iii) 5 : 9
9. a) 32 b) 35 c) 16 d) 40 10. a) 24 b) 24 years c) income = Rs 19,440 and expenditure = Rs 15,120
11.a) (i) 12 ft. (ii) 60 ft. (iii) 216 sq. ft. b) perimeter = 256 m and area = 3840 sq. m.
12.a) Rs 26 b) Rs 39 c) boys = 20, girls = 12 d) son = Rs 10,000, daughter = Rs 15,000
e) Pratik = Rs 49,000, Debasis = Rs 35,000 f) male = 16, female = 12 g) adult = 4530, children = 5436
h) gold = 110 g, silver = 90 g
13.a) 36°, 54° b) 54°, 126° c) 40°, 60°, 80° 14. a) 5 b) 1 c) 3 d) 5
2
15. a) 15, 21 b) 20, 45
c) father = 44 years, son = 12 years d) Ram = 15 years, Hari = 20 years
e) mother = 30 years, daughter = 10 years f) brother = 12 years, sister = 15 years
16. a) 2 : 3 b) 5 : 2 17. a) 30, 60, 120 b) 100, 80, 60
18. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher.
Exercise - 6.2
Creative Section
4. Answer the questions and discuss in the class and show to your teacher.
5. a) Yes b) Yes c) No 6. a) 9 b) 28 c) 24 d) 40 e) 12 f) 6 g) 10 h) 7 i) 45
7. a) (i) 12 (ii) 21 (iii) 40 (iv) 45 b) (i) 12 (ii) 49 (iii) 25 (iv) 36
c) (i) 9 (ii) 7 (iii) 8 (iv) 6 d) (i) 2 (ii) 7 (iii) 9 (iv) 8
8. a) Rs 384 b) 550 km c) 9 packets d) 15 kg 9. a) 20 min b) 14 days c) 17 kg
d) 16 kg
10. a) 15 workers b) 15 workers c) 300 men d) 25 days
11. a) 5 b) 3 12. a) 3 b) 18 13. a) 40 days b) 12 hours c) 50 soldiers
14. and 15. Please complete your project works and compare with your friends. Then discuss in the class
and show to your teacher.
Exercise - 6.3
Creative Section
4. Answer the questions and discuss in the class and show to your teacher.
5. a) (i) Rs 850 (ii) 4 l b) (i) 55 km/hr (ii) 440 km c) (i) 540 km (ii) 6 l d) (i) Rs 35,000
(ii) 11 months 6. a) Rs 3,852 b) Rs 3,34,800 c) Rs 3,900
7. a) (i) Rs 432 (ii) Rs 1,296 b) Rs 20,000 8. a) (i) 90 m2 (ii) Rs 8,910
b) Rs 11,325 9. a) 50 dollars b) Nepali Currency Rs 11,920 10. a) (i) Rs 60,000(ii) Rs 40,000
b) Rs 2,45,000 c) (i) Rs 12,000 (ii) Rs 4,500 11. a) (i) 10 MB per second (ii) 3 minutes
b) 5.4 GB 12. a) 6 minutes b) 2 minutes c) 25 days d) 8 days
13. a) (i) 3000 days (ii) 75 days b) 36 days 14. a) 1 hour b) 6 more workers
15. a) (i) Rs 750 (ii) 5 quintals b) 2550 words, 150 minutes c) 2 days
16. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher.
7. Percent and Simple Interest
Creative Section Exercise - 7.1
4. a) 75% b) 40% c) 70% d) 9% e) 30% f) 48% 5. a) 1 , 0.04 b) 9 , 0.18 c) 9 , 0.45
25 50 20
d) 16 , 0.64 e) 3 , 0.75 f) 49 , 0.98 6. a) 25% b) 10% c) 48% d) 80%
25 4 50
Vedanta Excel in Mathematics - Book 7 324 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
7. a) Rs 18 b) 120 students c) 2410 people d) 60 marks e) 30 kg f) 891 villagers
8. a) Rs 700 b) Rs 1,400 c) 444 boys d) 300 km e) 300 kg f) 8,000 males
9. a) (i) 60%
10. a) 80% (ii) 40% b) (i) 30% (ii) 70% c) (i) 7 (ii) 13
20 20
b) (i) food = 32%, rent = 28%, education = 12% (ii) 28% 11. a) 20% b) 5%
12.a) 240 people b) (i) 352 girls (ii) 288 boys c) (i) education = Rs 4,170, food = Rs 6,950,
miscellaneous = Rs 2,780 (ii) expenditure = Rs 13,900, save = Rs 13,900 d) (i) 1,14,400
(ii) 1,18,976 13. a) (i) 500 students (ii) 240 girls b) (i) Rs 12,000 (ii) Rs 3,000 c) (i) 35%
(ii) 640 students (iii) 416 girls d) 9,000 males 14. a) Bibek b) Sunayana
15. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher.
Exercise - 7.2
Creative Section
2. a) Rs 150 b) Rs 1,800 c) Rs 1,620 d) Rs 2,940 3. a) Rs 1,600, Rs 1,936
b) Rs 2,000, Rs 2,810 c) Rs 4,400, Rs 5,060 d) Rs 9,600, Rs 12,456 4. a) 6% b) 5% c) 9% d) 8.5%
5. a) 2 years b) 3 years c) 5 years d) 2.5 years
6. a) (i) Rs 900 (ii) Rs 5,940 b) Rs 14,625 7. a) Rs 15,800 b) Rs 2,400 8. a) 2 years
b) 4 years 9. a) 9% b) 7% 10. a) profit = Rs 200 b) profit = Rs 360 11. a) Rs 19,500 b) Rs 34,200
12. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher. 8. Profit and Loss
Creative Section Exercise - 8.1
4. a) 8% b) 5% c) Rs 36, 10% d) Rs 35, 5% e) Rs 665 f) Rs 582 5. a) Rs 28
b) Rs 162 c) Rs 72, Rs 972 d) Rs 105, Rs 1,395 6. a) Rs 200 b) Rs 350
7. a) Rs 120 b) Rs 260 c) Rs 300 d) Rs 500 8. a) Rs 60, 25% b) (i) Loss Rs 30
(ii) 6.25% c) (i) Rs 64 per kg (ii) 25% d) Rs 31.50 per kg (ii) 10%
9. a) (i) Rs 72 (ii) Rs 792 b) (i) Rs 130 (ii) Rs 3,120 c) Rs 6,250 d) Rs 1,55,200
10.a) Rs 200 b) Rs 1,400 11. a) Rs 11 b) 10% c) 1% loss 12. a) 5% profit b) 11% loss
13. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher.
Exercise - 8.2
Creative Section
4. Answer the questions and discuss in the class and show to your teacher.
5. a) Rs 25 b) Rs 16 c) Rs 66, Rs 484 d) Rs 144, Rs 816 6. a) 4% b) 5% c) Rs 120, 10%
d) Rs 324, 20% 7. a) Rs 52 b) Rs 78 c) Rs 791 d) Rs 1,242
8. a) 180, Rs 203.40 b) Rs 400, Rs 440 c) Rs 760, Rs 874 d) Rs 900, Rs 1,017 9. a) (i) Rs 300 (ii) 20% b) 8%
10.a) (i) Rs 560 (ii) Rs 5,040 b) (i) Rs 948 (ii) Rs 516 (iii) Rs 732
11.a) (i) Rs 104 (ii) Rs 904 b) Rs 1,495 12. a) (i) Rs 160 (ii) Rs 1,440 (iii) Rs 187.20 (iv) Rs 1,627.20
b) (i) Rs 3,200 (ii) Rs 480 (iii) Rs 3,680 c) (i) Rs 5,700 (ii) Rs 6,441 d) Rs 10,170
e) Rs 7,820 13. a) Rs 1,520 b) 7 copies c) Shop B, selling price of shop B is cheaper than shop A.
14. Please complete your project works and compare with your friends. Then discuss in the class and show
to your teacher. 9. Algebraic Expressions
Creative Section Exercise - 9.1
3. Answer the questions yourself and discuss in the class and show to your teacher.
4. Monomial Binomial Trinomial
c) xyz j) – 6x2 l) 64 a) x2y + xy2 b) 9 – x2 d) pq + p + q f) a2 + a + 1 g) 3x2 + 7xy + 6y2
2 y2 e) x2 + y2 i) x2 + x h) 3x + xy – 8y2 k) 1 + x + xy
5. a) Yes b) No c) Yes d) No e) Yes f) No g) No h) Yes
e) 3 f) 4 g) 4 h) 6 i) 8
6. a) 2 b) 2 c) 4 d) 2 (v) 36 (vi) 216 8. Verify yourself and show to your teacher.
7. a) (i) 24 (ii) 48 (iii) 20 (iv) 40
325Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
Creative Section Exercise - 9.2
3. Answer the questions yourself and discuss in the class and show to your teacher.
4. a) 7x + 11y b) 4ab + 5bc c) 3at2 – at d) p3q2 + p2q3 e) 5t + 3tz – 6 f) 7x – y – 5
g) 2a + 7b + 1 h) 6x2 + 5x – 3 i) 4a2 + 7ab + 2b2 j) a2 + b2 + c2 + 2ab + 2bc + 2ca
5. a) 3pq b) 7x2y c) 8ab d) –5a2b3 e) 2m + 4n f) –2p2 + 8q2 g) 2x2 + 8x – 9
h) 3y3 + 2y2 – 2y + 5 i) –6a3b3 + a2b2 – 7ab – 3 j) 3.6x4 + 12.1x3 – 0.9x2 + 1.8x + 0.9
6. a) 8x – 7y b) 5a + 5b c) 6x2 – 7y2 d) 3a2 – 2a – 2 e) 8p2 – 5p + 3 f) 3x2 – 3y2 g) 7a + 2b
h) 5p + 3q i) 4x – 6y j) 6a2 + 2b2 – 3c2 7. a) 4xy b) 2ab – 2bc – 2ca c) 5x2y d) 2p2 + 5p + 3
8. a) –5a2 + 4a – 3 b) x2 + 5x – 6 9. Verify yourself and show to your teacher.
10.Please complete your project work and compare with your friends and show to your teacher.
10. Laws of Indices
Creative Section Exercise - 10.1
3. Answer the questions yourself and discuss in the class and show to your teacher.
4. a) 32 > 23 b) 34 > 43 c) 25 > 52 d) 210 > 102 e) 45 > 54 f) 35 > 53
5. a) 24 b) 33 c) 27 d) 73 e) 54 f) 202 g) 25 × 33 h) 32 × 53
6. a) 62 b) 102 c) 63 d) 152 e) 142 f) 212 g) 103 h) 362
7. a) 2 × 102, 2 × 103, 2 × 104, 2 × 105 b) 5 × 103, 5 × 104, 5 × 105, 5 × 106
8. a) 26 b) 212 c) 314 d) 511 e) (3a)5 f) 4 4 9. a) 24 b) 35 c) (2x)6 d) (3a)7
e) 34 f) 26 b) 71
g) 45 h) 24 10. a) 1 57 c) 1 d) 1 e) 1 f) 1
5 3 35 (5a)3 4p 24 33
g) 1 h) 1 11. a) 2 b) 5 c) 2 d) 4 e) 8 f) 8 12. a) a3 b) p7 c) x2
52 73 3 9 27 27
d) y2 e) 2x4 13. a) 26 b) 312 c) 56 d) 36 e) 212 f) 1 g) 1 14. a) 2 b) 3
c) 81 d) 1 e) 4 f) 100 c) 1 215 38 f) 1
15. a) 1 b) 1 d) 1 e) 1
16. a) (i) 1(ii) 2 (iii) 27 b) (i) 125 (ii) 729 (iii) 4 c) 11 d) 20
17. Verify yourself and show to your teacher.
18. Please complete your project works and compare with your friends .Then discuss in the class.
Creative Section Exercise - 10.2
4. a) 6x4 b) 12x4 c) –10a2b2 d) 15p2q3r2 e) 3m3n3 f) 24x3y2z2
5. a) 2x2 +4x b) 6x2 – 10x c) 6p3 - 3p d) –3p3 + 6p2 – 9p e) –6t4 – 3t3 + 6t2 f) x3yz – xy3z – xyz3
6. a) x2 + 5x + 6 b) 2x2 – x – 15 c) 3x2 + 4xy + y2 d) 4a2 – b2 e) x3 + y3
f) a3 – b3 7. a) a2 + 2ab + b2 b) a2 – 2ab + b2 c) a2 – b2 d) x2 + 5x + 6
e) y2 – y – 20 f) 6a2 + 7a – 20 g) 4p2 + 5p – 6 h) 6c2 – 13cd + 6d2 i) x2 – y2
j) 4x2 – 9y2 k) 49m2 – 9n2 l) x3 + 4x2 + 7x + 6 m) 2x3 – 10x2 + 17x – 15
n) a3 + b3 o) x3 – y3 8. a) mn b) ax + bx c) px + py
d) 6a2 + 2ab e) 2a2 + 3ab + b2 f) 24x2 + 14xy + 2y2 9. a) (8x2 + 10xy – 3y2)sq. m.
b) (6x2 – xy – y2)sq. m. c) (i) (15 ab + 10a – 9b – 6) sq. m. (ii) 35 sq. m.
d) (i) (35p2 – 11pq – 6q2) sq. m. (ii) 741 sq. m. 10. Verify yourself and show to your teacher.
11.Please complete your project works and compare with your friends and discuss in the class.
Creative section-A Exercise - 10.3
3. a) x2 + 4x + 4 b) x2 + 6x + 9 c) x2 + 2xy + y2 4. a) x2 + 2x + 1 b) x2 + 4x + 4
c) x2 + 6x + 9 5. a) x2 + 6x + 9 b) x2 – 8x + 16 c) 4y2 + 12y + 9
d) x2 – 10xy + 25y2 e) 36m2 – 60mn + 25n2 f) 16x2 + 24xy + 9y2 g) a4 + 2a2x2 + x4
h) x2 + 2 + 1 i) y2 – 2 + 1 j) a2 – 1 +141a2 6. a) a2 + 6a + 9 b) 4a2 – 20a + 25
x2 y2 9x2 + 2 + 9x2
c) 4x2 + 12xy + 9y2 d) 4t2 + 2 + 1 e) f) c4 – 2c + 1
4t2 c2
7. a) a2 + b2 b) p2 + q2 c) x2 d) 9m2 e) 2a2 + 2t2 f) 4xy g) –24xy h) 80bc i) –60ab
8. a) (x + 3)2 b) (x – 4)2 e) (2x + 3y)2 (f) (5x – 4y)2
c) (2a + b)2 d) (p – 3q)2
g) (7a – 3b)2
h) x + 1 2 i) 2p – 1 2
x 2p
9. a) 2,401 b) 2,601 c) 9,801 d) 10,201 e) 9,98,001 f) 10,02,001
10. a) 5 b) 25 c) 13 d) 53 11. a) 14, 12 b) 23, 21 c) 11, 13 d) 38, 40
Vedanta Excel in Mathematics - Book 7 326 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
Creative section-A Exercise - 10.4
4. a) x2 – 4 b) x2 – 9
c) a2 – 25 5. a) x2 – 4 b) a2 – 9 c) 4p2 – 9 d) 4a2 – 25b2
e) x2 – 1 f) y2 – 4 g) x4 – y4 h) x4 – 81
6. a) a4 –4 b) x94 16 c) p4 – 81 (d) x4 – y4
1 – e) a4 – 16y4 f) 16x4 –81y4
7. a) 99 b) 1,599 c) 2,496 d) 9,996
8. a) 0.6 b) 0.7 c) 4 d) 7.1 e) 0.4 f) 0.015
9. a) x3 + 9x2 + 27x + 27 b) 8a3 –12a2 + 6a – 1 c) 8x3 + 36x2 + 54x + 27
d) p3 – 12p2q + 48pq2 – 64q3 e) 125 + 150b + 60b2 + 8b3 f) 8 – 36y + 54y2 – 27y3
g) a3 + 3a + 3 + 1 h) 8p3 – 6p + 3 – 1
a a3 2p 8p3
10. a) 8x3 + 12x2 + 6x + 1 b) x3 –9x2y + 27xy2 – 27y3 c) 8a3 + 36a2b + 54ab2 + 27b3
d) 64 – 48m+ 12m2 – m3 e) 1 – 6z + 12z2 – 8z3 f) 27x3 – 27x2 + 9x – 1
11. a) a3 + 8 b) a3 –8 (c) m3 + 27 d) m3 –27 e) 3x2y + 3xy2 f) 6x2y +2y3
12. a) (a + 1)3 b) (x + 2)3 c) (p – 3)3 d) (m – 4)3 e) (2a – b)3 f) (3x + 2y)3
13. a) 9 b) 52 c) 26 d) 63 14. a) 2 b) 110 c) 36 d) 234
15. and 16. Please complete your project works and compare with your friends .Then discuss in the class.
Creative section-A Exercise - 10.5
4. a) 2x2 b) 4 c) 2 d) 4a2b e) 6xy3 f) -4pq g) -5m5n2 h) 4a2t3 i) 7a
5. a) 2x+3 b) 2a2 – 3a c) 5y2 – 6y d) 1+2p – 3p2 e) 4x2 – 3x + 5 f) 2m2 – 3m – 4
g) 2a3b2 – 3a2b3 + 4ab h) 7 – 5xy2 – 4x2y i) 5pq – 6p2 – 4q2 j) 4x2y2z2 + 3xyz – 2
6. a) a - 2 b) a + 2 c) 3x - 1 d) 3x + 1 e) x + 3 f) x + 2
g) y + 4 h) y – 4 i) p – 5 j) p – 8 k) 4m – 3l) 5m – 2
m) 2x + 3 n) 3x – 4 o) 2p + 3q p) 4p – 5q 7. a) 2x – 3 b) x – 8
c) (x + 4) cm d) (x – 5) m 8. a) 2x4y4 9. a) x2 – 4x – 6 b) x2 – 4x + 5
c) a3 – a2b + ab2 – b3 d) a3 + a2b + ab2 +b3 e) a4 – a3b + a2b2 –ab3 + b3
f) a4 + a3b + a2b2 + ab3 + b3 g) x4 + x2y2 + y4 h) x3 + y3 10. a) (x – 7)m, 5m, 3m, 15m2
b) (x + 4)m, 19m, 7m, 133m2 11. a) x + 5, 200, 20, 10 b) x + 8, 1036, 37, 28
12. Please complete your project works and compare with your friends .Then discuss in the class.
Creative section Exercise - 10.6
5. a) 2x (a +b ) b) 2xy (x – y)
c) 2ab (x – y) d) 3mx ( x – 2) e) ax (x + a – 1)
f) 2x3y3(2x2y – xy2 – 4) g) (x – y)(a + b) h) (a + b) (x – y) i) (x – y) (2x + y)
6. a) (a + b) (x + y) b) (m + n) (a + b) c) (y + z) (x + y) d) (3a – b) (x – y) e) (4a – 3b) (x – 2y)
f) (x – z) (x + y) g) (ab + c) (a – bc) h) (ab + c) (ac – b) i) (x + a) (x + 4)
7. a) (a + 2) (a – 2) b) (x + 3) ( x – 3) c) (m + 4) (m – 4) d) (p + 5) ( p – 5)
e) (2a + 3b) (2a – 3b) f) (5x + 6y)(5x – 6y) g) (7p + 9q)(7p – 9q) h) (8b + 3c) (8b – 3c)
i) (10m + 7n)(10m – 7n) j) 2(2xy + 3) (2xy – 3) k) 3(5ab + 3xy)(5ab – 3xy) l) 5a (4a + b) (4a – b)
8. a) (a2 + 4) (a + 2) (a – 2) b) (x2 + 9) (x + 3) (x – 3) c) (y2 + 25) (y + 5) (y – 5)
d) (4p2 + q2) (2p + q) (2p – q) e) (9m2 + n2) (3m + n)(3m – n) f) (x2 + 4y2) (x + 2y) (x – 2y)
g) (a2 + b2) (a + b) (a – b) h) (4p2 + 9q2) (2p + 3q) (2p –3q)
9. a) (x + 1) (x + 2) b) (a + 3) (a + 4) c) (p + 2) (p + 4) d) (x + 2) (x + 5) e) (y – 3) (y – 5)
f) (x – 4) (x – 5) g) (m – 2) (m – 7) h) (b – 5) (b – 6) i) (x – 5) (x + 3) j) (x – 7) (x + 4)
k) (a + 6) (a – 2) l) (x + 8) (x – 3)
10. a) 130 b) 840 c) 1800 d) 200 e) 440 f) 2600 g) 399 h) 6,399 i) 9,999
11. and 12. Please complete your project works and compare with your friends .Then discuss in the class.
Creative section Exercise - 10.7
3. a) 3x b) 2yz c) x2y2 d) 3a e) 2x2y2 f) xy
4a 3 3a2b 2b 3 ab
5x3 3b y2 4ax 1 cz
4. a) 2y3 b) 5a c) a2 d) 3by3 e) xyz f) xy
Creative section Exercise - 10.8
3. a) 13x b) 3a c) 17y d) x e) 2ax f) 17by 4. a) x + y b) 3a + 2b c) x
4a x 8b 18y 5b 28ax a
327Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
d) 1 e) 1 f) x2 + y2 g) a2 – b2 h) x 1 y i) x 1 y
y x x + y a2 + b2 – +
11. Equation, Inequality and Graph
Creative Section Exercise - 11.1
5. Answer the questions yourself and show to your teacher.
6. a) x = 2 b) x = 3 c) x = 6 d) x = 7 e) x = 2 f) x = 1 g) x = 3 h) y = 8 i) x = 5 j) x = 4
7. a) x = 6 b) x = 18 c) x = –16 d) x = 10 e) x = 12 f) x = 6 g) x = 7 h) x = 5 i) x = 7 j) x = 2
k) x = 9 l) x = 5 m) x = 5 n) x = 2
8. a) Rs 200 b) Rs 500 c) 300 kg d) 300 km e) Rs 500 f) 400 students
9. a) 50 kg b) Rs 80 c) Rs 100 d) 40 km e) Rs 100 f) Rs 300 g) 200 h) Rs 600 i) 500
1 i) n = 6
10.a) x = 2 b) x = 1 c) x = 12 d) x = 12 e) x = 3 f) x = 1 g) x = 1 h) x = 2
11.Please complete your project work and compare with your friends and discuss in the class.
Exercise - 11.2
Creative Section
2. a) 15 b) 24 c) 38 3. a) 40°, 50° b) 14 c) 15, 18 d) 16, 18 4. a) 11, 12 b) 16, 18
c) 5, 7 d) 9, 11, 13 5. a) 13, 22 b) 12, 8 c) 9, 6 d) Rs 60, Rs 40 e) Rs 65, Rs 115
f) Rs 375, Rs 625 6. a) Rs 150 b) 7 c) Rs 1,500 d) 14 years e) 88
7. a) 51 km b) 720 c) Rs 1,000 d) Rs 1,000 e) Rs 2,000
8. a) Rs 260, Rs 390 b) Rs 24,000, Rs 30,000 c) Rs 30,000, Rs 45,000, Rs 75,000 d) 30°, 60°, 90°
e) 36°, 54° 9. a) 60 m b) Rs 2,400 10. a) 30 m, 25 m b) 30 cm, 20 cm c) 40 m, 20 m d) 60 m, 24 m
11. a) 10 years, 35 years b) 12 years, 36 years c) 11 years, 41 years d) 10 years, 30 years
e) 12 years, 36 years 12. Please complete your project works and compare with your friends. Then
discuss in the class. 13. Please search such types of interesting puzzles and perform in the class.
Exercise - 11.3
Creative Section
3. Answer the questions and show to your teacher.
4. a) x 5 b) x 8 c) –a z –7 d) p – 4 10 e) 12 z y + 4 f) –9 a – 4 g) x + 3 –6 h) y – 5 2
5. a) x < 3, x 3 b) y > –5, y –5 c) –a = –2, –a z –2 d) x + 4 < 6, x + 4 6
e) 10 > p – 9, 10 p – 9 f) p + r < q + r, p + r q + r
Exercise - 11.4
Creative Section
3. Answer the questions and show to your teacher. 4. Draw graph yourself and show to your teacher.
5. a) {0, 1, 2, 3} b) {1, 2, 3, 4, 5} c) {0, 1, 2, 3, 4, 5} d) {0, 1, 2, 3} e) {3, 4, 5}
f) {0, 1, 2, 3, 4} g) {3, 4, 5} h) {0, 1, 2, 3, 4} Draw graph yourself and show to your teacher.
6. a) {…, –1, 0, 1, 2, 3} b) {4, 5, 6, …} c) {…, –1, 0, 1, 2, 3} d) {2, 3, 4, …}
e) {–5, –4, –3, …, 0, 1, 2, …} f) {2, 1, 0, –1, –2, …} g) {–3, –4, –5, …}
h) {6, 7, 8, …} i) {5, 6, 7, …} j) {4, 5, 6, …} k) {1, 0, –1, –2, …} l) {6, 7, 8, …}
m) {–3, –4, –5, …} n) {–5, –4, …, 0, 1, 2, …} o) {–5, –6, –7, …}
p) {0, –1, –2, –3, …} Draw graph yourself and show to your teacher.
7. a) {5, 6, 7} b) {2, 3, 4, 5, 6, 7} c) {–3, –2, –1, 0, 1, 2, 3} d) {0, 1, 2, 3, 4, 5} e) {–2, –1, 0, 1, 2, 3}
f) {–3, –2, –1, 0, 1, 2, 3, 4, 5} Draw graph yourself and show to your teacher.
8. a) (i) 2x + 2 < 12 (ii) {4, 3, 2, 1, 0, –1, …} b) (i) 3x + 7 ≥ –8 (ii) {–5, –4, –3, … 0, 1, 2, 3, …}
c) (i) 4x – 5 ≤ 3 (ii) {2, 1, 0, –1, –2, …} d) (i) 7 – 5x ≥ –3 (ii) {2, 1, 0, –1, –2, …}
x
e) (i) 5 – 3 ≤ 4 (ii) {3, 4, 5, …} 9. a) 2x – 2 > x + 1, {4, 5, 6, …}, 2x – 2 > x – 3, {0, 1, 2, 3, …}
Exercise - 11.5
Creative Section
4. a) (i) x 0 1 2 3 4 5 (ii) x 0 1 2 3 4 5 (iii) x 0 1 2 3 4 5
y4 5 678 9 y –3 –2 –1 0 1 2 y0 1234 5
(iv) x 0 1 2 3 4 5 (v) x 0 1 2 3 4 5 (vi) x 0 1 2 3 4 5
y 1 3 5 7 9 11 y –1 2 5 8 11 14 y 3 7 11 15 19 23
Vedanta Excel in Mathematics - Book 7 328 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
b) (i) y = x + 4 (ii) y = x – 3 (iii) y = x (iv) y = 2x + 1 (v) y = 3x – 1 (vi) y = 4x + 3
y b) y = 2x + 3
5. a) y = 3x – 2 x xy
–8 x –3 –2 –1 0 1 2 3
x –2 –1 0 1 2 –2 –5 y –3 –1 1 3 5 7 9 –3 –3
y –8 –5 –2 1 4 –2 –2 –1
–1 1 –1 1
0 4 0 3
1 1 5
2 2 7
3 9
6. a) x 0 1 2 3 4 b) x 2 3 4 5 6
y=x+2 2 3 4 5 6 y=x–1 1 2 3 4 5
c) x 1 2 3 4 5 d) x 0 1 2 3 4
y = 2x 2 4 6 8 10 y = 2x + 1 1 3 5 7 9
7. a) y = x + 2 (0, 2), (1, 3), (2, 4), (3, 5) b) y = 2x (1, 2), (2, 4), (3, 6), (4, 8)
c) y = 2x + 1 (1, 3), (2, 5), (3, 7), (4, 9), (5, 11) Draw graph yourself and show to your teacher.
8. a) x 0 1 3 –1 –3 b) x 1 2 3 4 5
y = x + 2 2 3 5 1 –1 y = x – 2 –1 0 1 2 3
c) x –2 0 2 6 9 d) x –3 –1 0 4 7
y = x + 3 1 3 5 9 12 y = 9 – x 12 10 9 5 2
e) x –1 –4 0 2 5 f) x –3 –2 136
–11 –8 1 7 16
y = 2x + 1 –1 –7 1 5 11 y = 3x – 2
Draw graph yourself and show to your teacher.
9. a) y = 2x + 1, (0, 1) (1, 3), (2, 5), (3, 7), (4, 9) b) y = 2x – 1, (0, –1), (1, 1), (2, 3), (3, 5), (4, 7)
c) y = 3x + 2, (0, 2), (1, 5), (2, 8), (3, 11), (4, 14) d) y = 3x – 2, (0, –2), (1, 1), (2, 4), (3, 7), (4, 10)
10.Please complete your project work and compare with your friends and discuss in the class.
12. Coordinates
Creative Section Exercise - 12.1
4. Answer the questions yourself and show to your teacher.
5. a) (3, 3) b) (–4, 3) c) (–2, –3) d) (1, –2) e) (3, 0) f) (0, 2) 6. Plot the points in graph papers yourself.
7. Plot the points in graph papers yourself and draw the shapes.
8. Plot the points in graph papers yourself and find the coordinates of the point of intersection of lines so
obtained. 9. Complete the given works in graph papers and show to your teacher.
10. and 11. Please complete your project work and compare with your friends and discuss in the class.
Creative Section Exercise - 12.2
3. Answer the questions yourself and show to your teacher.
4. Complete the drawing yourself and compare with your friends. Then show to your teacher.
5. a) X-axis as axis of reflection: a) (2, –4) b) (5, 3) c) (–2, –8) d) (–1, 7) e) (0, –6) f) (–9, 0)
Y-axis as axis of reflection: a) (–2, 4) b) (–5, –3) c) (2, 8) d) (1, –7) e) (0, 6) f) (9, 0)
6. Draw the images in graph papers and find the coordinates of the vertices of images. Then show to your
teacher.
7. a) X-axis as axis of reflection: a) A'(2, –5), B'(6, –3),C'(4, –8) b) P'(–4, –6), Q'(–3, –4), R'(–1, –2)
c) X'(–6, 4), Y'(–3, 1), Z'(–1, 3) d) E'(2, 7), F'(5, 3), G'(2, 1)
Y-axis as axis of reflection: a) A'(–2, 5), B'(–6, 3), C'(–4, 8) b) P'(4, 6), Q'(3, 4), R'(1, 2)
c) X'(6, –4), Y'(3, –1), Z'(1, –3) d) E'(–2, –7), F'(–5, –3), G'(–2, –1)
8. a) A'(3, –6), B'(2, –4), C'(5, –7) b) P'(–2, –5), Q'(–4, 3), R'(3, 6) c) X'(–2, 7), Y'(4, –8), Z'(–3, –5)
d) K'(5, 4), L'(–2, 6), M'(–3, –3) 9. a) E'(–1, 3), F'(–4, –5), G'(2, –2), E"(1, 3), F"(4, –5), G"(–2, –2)
b) A'(2, 7), B'(–3, 6), C'(–4, –2), A"(–2, 7), B"(3, 6), C"(4, –2) 10. a) A(2, –5), B(5, 0), C(3, –1) b) Y-axis
11. Please complete your project work and compare with your friends and discuss in the class.
329Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
Creative Section Exercise - 12.3
3. Draw the images and show to your teacher.
4. a) (–2, 6), (2, –6) b) (–5, –3), (5, 3) c) (7, 1) (–7, –1) d) (9, –4), (–9, 4) e) (5, 0), (–5, 0) f) (0, 8) (0, –8)
5. a) (–2, –1) b) (–3, 4) c) (5, 7) d) (1, –6) e) (0, –6) f) (4, 0)
6. and 7. Draw images in graph papers and find the coordinates of the vertices of images. Then show to
your teacher. 8. a) A'(5, –2), B'(7, 3), C'(–4, –2) b) X'(–8, 7), Y'(–4, –5), Z'(3, 1)
9. a) P'(4, 9), Q'(–1, 6), R'(5, –2) b) E'(–1, –5), F'(3, –6),G'(–4, 2)
10. and 11. Please complete your project work and compare with your friends and discuss in the class.
Exercise - 12.4
1 and 2. Draw the images of the figures after the displacement. Then compare with your friends and show
to your teacher.
3. Please complete your project work and compare with your friends and discuss in the class.
13. Geometry: Angles
Creative Section Exercise - 13.1
2. Answer the questions yourself and show to your teacher.
3. a) Yes b) Yes c) No d) No 4. a) 30° b) 10° c) 75° d) 62° e) 39°
5. a) 70° b) 45° c) 30° d) 110° e) 135° 6. a) 80°, 100° b) 58°, 122°
c) 36°, 54° d) 50°, 40° e) 150° f) 110°, 70° g) 60° 7. a) 70° b) 105° c) 60° d) 140°
e) 75°, 105° f) 72°, 108° g) 30°, 60°, 90° h) 39°, 81°, 60° i) 50°, 75°, 55°
j) 18°, 36°, 54°, 72° k) x° = z° = 160°, y° = 20° l) a° =x° = 45°, 3a° = y° = 135°
m) 50°, 60°, 70°, 50°, 60°, 70° n) 40°, 88°, 52° o) 2x° = a° = 60°, 3x° = 90°, b° = 40°, 2b° = 80°
p) x° = p° = 40°, (x + 25)° = 65°, (x + 35)° = 75°, q° = 35°, 3q° = 105°
8. Compare your verifications with friends and show to your teacher.
9. a) 67° b) 70° c) 42° d) 10°
10. Please complete your project work and compare with your friends and discuss in the class.
Creative Section Exercise - 13.2
4. Answer the questions yourself and show to your teacher.
5. Identify the given pairs of angles yourself and compare with your friends. Then show to your teacher.
6. a) x°= y° = 45° b) a° = b° = 40°, c° = 140° c) p° = q° = 60°, r° = 120° d) a° = b° = c° = e° = 65°,
d° = 115° e) x° = w° = 70°, z° = 110°, y° = 70° f) a° = 70°, b° = 75°, c° = 105°, d° = 110°, e° = 110°,
f° = 105° g) x° = y° = w° = 85°, z° = 95° h) x° = y° = 50° i) a° = 145°, b° = c° = 35°
j) x° = y° = 65°, z° = 115° k) a° = 115°, b° = c° = 65° l)b°=30°,a°=25° m)x°=z°=80°,y°=100°
n) w° = 100°, x° = y° = z° = 80° o) x° = 25°, y° = 35°, a° = b° = 120°
p) x° = 55°, y° = z° = 60°, w° = 65°
7. a) x° = y° = 60°, 2x° = 120° b) 135°, 135° c) 115°, 65° d) 123°, 123°
8. a) x° = 60° b) x° = 310° c) y° = 90° d) x° = 120°
9. Compare your verifications with your friends and show to your teacher. f) x° = 80°, y° = 80°
10. a) x° = 30° b) x = 18°
11. Please complete your project work and compare with your friends and discuss in the class.
14. Triangle, Quadrilateral and Polygon
Creative Section Exercise - 14.1
5. Answer the questions yourself and show to your teacher.
6. Compare your answers with your friends and show to your teacher.
7. a) 63° b) 30°, 60° c) 36°, 54° d) 40°, 80° e) 48°, 60°, 72°
8. a) 75° b) 36°, 108° c) 40°, 50° d) 30°, 60°, 90° e) 50° f) 96° g) 25°, 75°
h) m° = n° = 63° i) x° = y° = 55°, 70° j) a° = b° = 70°, c° = 40° k) x° = y° = 65°, z° = 50°
l) x° = y° = 70°, z° = 110° 9. a) x° = 30°, y° = 35°, z° = 115° b) x° = 56°, z° = 44°, y° = 80°
c) a° = c° = 68°, b° = 62° d) x° = 47°, y° = 64°, z° = 68° e) a° = b° = c° = 58°, d° = 64°
f) x° = 50°, y° = z° = 65° g) x° = 55°, y° = z° = 40° h) a° = b° = 26°, 2a° = 52°
10. Compare your verifications with your friends and show to your teacher.
11. a) a° = b° = c° = 45° b) and c) verify yourself and show to your teacher.
12 and 13. Please complete your project work and compare with your friends and discuss in the class.
Vedanta Excel in Mathematics - Book 7 330 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Answers
Creative Section Exercise - 14.2
4. Answer the questions yourself and show to your teacher. 5. a) 4 cm b) 3 cm c) 35° d) 30°
e) 4 cm f) 5 cm g) 3 cm h) 5 cm 6. a) 50° b) 45°, 90° c) 30°, 60°, 120°, 150°
d) 45°, 135°, 60°, 120°, e) 48°, 72°, 96°, 144° 7. a) 55°, 110° b) 65°, 130°, 75°
c) 57°, 171°, 62°, 70° d) 35°, 140°, 105°, 80° e) 100°, 80°, 60°, 120° f) 70°, 110°, 36°, 144°
g) 100°, 80°, 85°, 95° h) 50°, 100°, 80°, 40° 8. a) x° = 60°, y° = z° = 120°
b) a° = c° = 70°, b° = d° = 110° c) p° = q° = 50°, r° = s° = 130° d) x° = 15°, y° = 20°, w° = z° = 145°
e) w° = 65°, x° = y° = 55°, z° = 60° f) x° = y° = s° = q° = 75°, p° = r° = 105°
g) x°= y°= z°= a° = c° = 60°, b° = 120° h) x° = y° = 120° 9. a) 130°, 60°, 120° b) x° = y° = 35°, w° = 25°
c) x° = a° = 70°, y° = b° = 48°, c° = 42°, d° = 20° 10. a) 45° b) 34° c) 70°
11. Please complete your project work and compare with your friends and discuss in the class.
Creative Section Exercise - 14.3
2. a) 180° b) 360° c) 540° d) 720° e) 900° f) 1080° g) 1260° h) 1440°
3. a) 60° b) 90° c) 108° d) 120° e) 128.57° f) 135° g) 144° h) 150°
4. a) 120° b) 90° c) 72° d) 60° e) 51.43° f) 40° g) 36° h) 30°
5. a) n = 6 b) n = 7 c) n = 8 d) n = 10 6. a) n = 5 b) n = 6 c) n = 8 d) n = 10
7. a) n = 4 b) n = 5 c) n = 6 d) n = 10
8. a) 108°, 72° b) 120°, 60° c) 45°, 135° d) 80°, 100°
9 and 10. Please complete your project work and compare with your friends and discuss in the class.
15. Congruency and Similarity
Creative Section Exercise - 15.1
5. Answer the questions yourself and show to your teacher.
6. and 7. Compare your verification with friends and show to your teacher.
8. a) 3 cm b) 12 cm c) 6 cm d) 10 cm
9. Verify yourself and compare with your friends. Then show to your teacher.
10.Please complete your project work and compare with your friends and discuss in the class.
16. Construction
Complete the geometrical constructions yourself and show to your teacher.
17. Circle
Creative Section Exercise - 17.1
3, 4, 5 and 6. Answer the questions yourself and show to your teacher.
7. Please complete your project work and compare with your friends and discuss in the class.
18. Perimeter, Area and Volume
Creative Section Exercise - 18.1
3. a) 13.5 cm b) 12 cm c) 28 cm d) 14 cm e) 16 cm f) 17.5 cm
g) 20 cm h) 28 cm i) 88 cm j) 12 cm k) 23 cm l) 42 cm
4. a) (i) 13.8 cm (ii) 20.5 cm b) (i) 26 cm (ii) 29.6 cm c) (i) 32cm (ii) 57 cm
d) (i) 44 cm (ii) 132 cm 5. a) 53 cm, 26.5 cm (b) 19.5 cm (c) 4.6 cm
6. a) (i) 72 cm (ii) 216 m (iii) Rs 5,400 b) 1.5 km c) (i) 180 m (ii) 180 m (iii) 45 m
7. a) (i) 86 m (ii) 430 m b) (i) 96 m (ii) 288 m (ii) Rs 5,760 c) Rs 8,00,000
8. a) 924 m, 4620 m b) Rs 44,352 c) 49 m d) 42 m
9. a) (i) 120 m (ii) 20 m b) 28 m, 18 m 10. a) 25 cm b) 20 cm 11. a) (i) A (ii) C
b) (i) A (ii) Father chose the garden with the least perimeter to minimize the cost of fencing
12. Please complete your project work and compare with your friends and discuss in the class.
Exercise - 18.2
Creative section
3. a) 63 cm2 b) 156.25 cm2 c) 70 cm2 d) 63 cm2 e) 72 cm2 f) 96 cm2 g) 154 cm2 h) 616 cm2
4. a) 200 cm2 b) 270 cm2 c) 81 cm2 d) 220 cm2 e) 658 cm2 f) 987 cm2
5. a) 110 cm2 b) 350 cm2 c) 297cm2 d) 96 cm2 e) 198 cm2 f) 96 cm2 g) 150 cm2 h) 350 cm2
6. a) (i) 36 cm2 (ii) 225 cm2 b) (i) 78cm2 (ii) 210cm2 c) (i) 16.5 cm2 (ii) 84 cm2
d) (i) 616cm2 (ii) 962.5cm2 7. a) (i) 196 cm2 (ii) 196 cm2 (iii) Rs 22,344 b) (i) 36 m (ii) 1296 cm2
331Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Answers
(ii) Rs 64,800 c) (i) 18 m (ii) 72m (iii) Rs 2,880
8. a) (i) 1440 m2 (ii) Rs 1,29,600 b) (i) 150 m2 (ii) Rs 12,000 c) (i) 32m, 16 m (ii) 512 m2
(iii) Rs 23,040 d) (i) 25 m (ii) 110 m 9. a) (i) 7 cm (ii) 154 cm2 b) (i) 35 cm
(ii) 3,850 cm2 c) (i) 98 m, 49 m (ii) Rs 5,28,220 10. a) No b) Circular shape covers more area.
Exercise - 18.3
Complete your works and compare with your friends. Then show to your teacher.
Creative section Exercise - 18.4
2. a) 150 cm2, 125cm3 b) 162 cm2, 90cm3 c) 470cm2, 600 cm3 d) 96 cm2, 64cm3
3. a) 236 cm2, 240cm3 b) 252cm2, 202.5cm3 4. a) 572 cm3 b) 2805cm3
5. a) 150 cm2, 125cm3 b) 294 cm2, 343cm3 c) 600cm2, 1000cm3 d) 937.5 cm2, 1953.125cm3
6. a) 450cm2, 300cm2 b) 1100cm2, 1000cm2 7. a) 720cm2, 576cm2 b) 1125cm2, 900cm2
8. a) 3cm b) 5.5 cm c) 6 cm d) 9 cm 9. a) 2cm b) 3cm c) 4 cm d) 5 cm
10. a) 3000 l b) 9216 l c) 7680 l d) 5000 l 11. a) 168 cm2 b) (i) 120m3 (ii) Rs 7,200 c) (i) 6 m
(ii) 36m2 (iii) Rs 1,800 d) 4500 l 12. a) (i) 2m (ii) 8 m3 b) (i) 5 m (ii) 150 m2 c) 6 cm d) 9 cm
13. a) (i) 12cm, 6cm (ii) 288 cm2 b) (i) 14m, 7 m (ii) 98m2 (iii) Rs 4,410
14. a) (i) 6cm (ii) 216cm2 b) 864cm2 15. a) 1m b) 1.5 m 16. a) 10 b) 64
17. Please complete the project works and compare with your friends. Then show to your teacher.
19. Symmetry, Design and Tessellation
Exercise - 19.1
Compare your works with friends and show to your teacher.
Creative Section Exercise - 19.2
1. Answer the questions yourself and show to your teacher.
2. and 3. Complete the works and compare with your friends. Then show to your teacher.
20. Scale Drawing and Bearing
Creative Section Exercise - 20.1
4. Complete the drawings and compare with friends. Then show to your teacher.
5. a) 12.8 m b) 85 m c) 12 m, 8 m d) 75 km 6. a) 3.6 cm b) 5 cm c) 6 cm, 5 cm d) 3cm, 2.5 cm
7. a) Kitchen: 6 m × 4 m, Dinning: 6 m × 4 m, Bed room: 6 m × 4 m, Toilet: 6 m × 2 m,
Storeroom: 6 m × 4 m, Living room: 8 m × 6 m, Passage: 4 m × 6 m b) 24 m2 c) 180 m2
8. Please complete your project work and compare with your friends and discuss in the class.
Creative Section Exercise - 20.2
4. Answer the questions yourself and compare with your friends .Then discuss in the class and show to
your teacher. [Eg. From Kathmandu, the direction of Pokhara is NW.]
5. a) 060° b) 090° c) 125° d) 220° e) 270° f) 315°
6. a) 070° b) 125° c) 240° d) 320° e) 120° f) 050° 7. a) 205° b) 245° c) 267° d) 270°
e) 285° f) 320° g) 30° h) 150° 8. a) 235° b) 264°
21. Statistics
Exercise - 21.1
Answer the questions yourself and show to your teacher.
Complete drawings and compare with friends. Then show to your teacher.
Creative Section Exercise - 21.2
4. a) 14 b) 39 c) 11 yrs d) 6.3 cm e) 5.6 f) 18
5. a) 5 b) Rs 19 6. a) 60 mm b) 24 yrs
7. a) Rs 1400 b) 67.5 8. a) Rs 2700 b) 68
9. a) 85, 35 b) 13 yrs, 15 yrs 10. a) 28° C b) 18 c) 24 yrs
Creative Section Exercise - 21.3
3. a) 37 b) Rs 318 c) 33 4. a) 62.5 b) Rs 772 5. a) 25 b) 7 6. a) 5 b) 6
7. Please complete your project work and compare with your friends and discuss in the class.
Vedanta Excel in Mathematics - Book 7 332 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
Evaluation Model Set
Class: VII Full Marks: 100
Subject: Mathematics Time: 3 hrs.
Attempt all the questions.
Group-A [5u(1+1) = 10] A U
1. (a) What does the shaded portion represent in the Venn-diagram B
given alongside? Q
N
(b) Write down the identity element of addition. NE
2. (a) What does R denote in the formula I = P1T00R? E
(b) Write down the image of the point A (4, 1) under the reflection about x-axis
3. (a) If x = 2 and y = 0, what is the value of xy.
(b) Factorize: p2 – 9
4. (a) What is the circumference of a circle having radius r cm? R
P
(b) From the given figure, write the alternate angle of ³RUN.
5. (a) In the given data, what is the frequency of 70? T
80, 60, 70, 90, 80, 60, 70, 80, 80, 60, 80, 80, 70, 80, 70, 90 MU
S
N
(b) What is the compass bearing of NE in the given figure? WO
Group-B (17u 2= 34) S
6. (a) If A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7, 9} then find A B and A – B.
(b) Convert 110012 into decimal number.
(c) Make the mathematical expression and simplify:
3 times the difference of 17 and 7 is divided by 5
7. (a) Find the least number which is exactly divisible by 12, 15, and 20.
(b) There are 560 students in a school. If the number of boys and girls are in the
ratio 4:3, find their numbers.
(c) Last week, the rate of vegetable was Rs 50 per kg and this week it is increased to
Rs 55 per kg, find the percentage of increase in the price.
8. (a) The perimeter of a squared handkerchief is 1 m. Find its length of side and area.
(b) Find the area of the parallelogram given alongside. 7.5cm
9. (a) Simplify: (xa)b – c × (xb)c – a × (xc)a – b 10cm
2x 7x
(b) Find the product of: (a + 2b) (a – 2b) (a2 + 4b2)
(c) Find the HCF of: 2x – 4 and x2 – 4
10. (a)
Divide: 4a3b2 ÷ 12a4b3
(b) 5x3y2 10x4y3
11. (a)
Solve the inequality 3x + 1 10 and show it in a number line.
Find the value of x from the figure given alongside.
333Approved by Curriculum Development Centre, Sanothimi, Bhaktapur Vedanta Excel in Mathematics - Book 7
Model Questions
(b) By what axiom, 'ABC and 'PQR are A P
congruent to each other? Also, write a pair of
corresponding sides. B CQ R
(c) If the angles of a quadrilateral are in the ratio 1: 2: 3: 4 then find them.
Group-C (14u4 = 56)
12. P and Q are the subsets of a universal set U. If U = {1, 2, 3, … , 10}, P = {2, 4, 6, 8, 10}
and Q = {2, 3, 5, 7}, find P Q . Also, show it in a Venn-diagram.
13. Find the square root of 2025 by division method.
14. Simplify: 1 5 ÷ [2 1 ÷ { 3 – 1 ( 2 – 7 )}]
9 3 4 2 3 24
15. Jasmin bought 100 glass tumblers at the rate of Rs 15 each. 10 of them were broken
and she sold the remaining at the rate of Rs 16 each. Find her profit and loss percent.
16. A businessman deposited Rs 60,000 in a commercial bank at 5% p.a. How long should
he deposit the sum to receive an amount of Rs 69,000?
17. A cubical room contains 216 m3 of air.
(i) Find the length of its floor.
(ii) Find the area of its floor.
(iii) Find the cost of carpeting the floor at Rs 154 per sq. m.
18. If x – y = 5, find the value of x3 – y3 – 15xy.
19. Simplify: m + n
m2 – n2 m2 – n2
20. The area of rectangular field is (x2 + 9x + 20)m2 and its length is (x + 5)m
(i) Find its breadth
(ii) If x = 10 m, find the actual length, breadth, and the area of the land.
21. A father is 20 years older than his son. Five years ago, he was three times as old as his
son was. Find their present ages.
22. The vertices of 'ABC are A (2, 3), B (-1, 0), and C (0, 5). Draw the 'ABC on a graph paper
and reflect it about y – axis, find the coordinates of its image and draw it on the same
graph paper.
23. From the table given below, calculate the mean mark
Marks obtained 10 20 30 40 50
No. of students 2 4 74 3
24. Find the sizes of unknown angles from the figure given alongside. x 3x 2x
y
z
25. Construct a rectangle ABCD in which diagonals AC = BD = 5cm and they bisect each
other making an angle of 600.
Vedanta Excel in Mathematics - Book 7 334 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
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Vedanta Excel Maths Book 7
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