## Coordinate Geometry Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 3 Coordinate Geometry are given here. These questions will help the students to build a better understanding of the Coordinate Geometry concept in Maths. These Class 9 Chapter 3 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/coordinate-geometry-ncert-extra-questions-for-class-9-maths-chapter-3/

## Class 9 Coordinate Geometry Extra Questions

Extra Questions for Class 9 Maths Chapter 3 Coordinate Geometry

Coordinate Geometry Class 9 Extra Questions

Coordinate Geometry Class 9 Worksheet With Solutions

Coordinate Geometry Class 9 Questions With Solutions

Ch 3 Maths Class 9 Extra Questions

Class 9 Maths Ch 3 Extra Questions

Class 9 Maths Chapter 3 Extra Questions With Solutions

Coordinate Geometry Class 9 Worksheet

Class 9 Maths Chapter 3 Test Paper

Coordinate Geometry Class 9 Extra Questions With Solutions

Extra Questions For Class 9 Maths Chapter 3

## Linear Equations in Two Variables Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables are given here. These questions will help the students to build a better understanding of the Linear Equations in Two Variables concept in Maths. These Class 9 Chapter 4 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/linear-equations-in-two-variables-ncert-extra-questions-for-class-9-maths/

## Class 9 Linear Equations in Two Variables Extra Questions

Extra Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

## Polynomials Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 2 Polynomials are given here. These questions will help the students to build a better understanding of the Polynomials concept in Maths. These Class 9 Chapter 2 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/polynomials-ncert-extra-questions-for-class-9-maths/

## Class 9 Polynomials Extra Questions

Extra Questions for Class 9 Maths Chapter 2 Polynomials

Polynomials Class 9 Extra Questions

Polynomial Calculator is an online tool that helps to calculate the result of addition, subtraction, multiplication, and division of two polynomials.

Polynomial Class 9 Extra Questions

Class 9 Maths Chapter 2 Extra Questions

Is this a polynomial calculator allows you to divide two polynomials to find the quotient and the remainder of the division.

Polynomials Class 9 Important Questions

Polynomial Questions Class 9

Class 9 Maths Polynomials Extra Questions

Polynomials Class 9 Questions

Polynomials Class 9 Extra Questions With Answers Pdf

Extra Questions For Class 9 Maths Polynomials

## Lines and Angles Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 6 Lines and Angles are given here. These questions will help the students to build a better understanding of the Lines and Angles concept in Maths. These Class 9 Chapter 6 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/lines-and-angles-ncert-extra-questions-for-class-9-maths/

## Class 9 Lines and Angles Extra Questions

Extra Questions for Class 9 Maths Chapter 6 Lines and Angles
Lines And Angles Class 9 Extra Questions

Class 9 Lines And Angles Extra Questions

Lines And Angles Class 9 Worksheet With Answers

Lines And Angles Class 9 Important Questions

Lines And Angles Class 9 Questions

Extra Questions Of Lines And Angles Class 9

Class 9 Maths Ch 6 Extra Questions

Lines And Angles Class 9 Questions With Solutions

Questions On Lines And Angles For Class 9

Lines And Angles Class 9 Questions And Answers

Ch 6 Maths Class 9 Extra Questions

Extra Questions For Class 9 Maths Chapter 6

## Introduction to Euclid Geometry Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 5 Introduction to Euclid Geometry are given here. These questions will help the students to build a better understanding of the Introduction to Euclid Geometry concept in Maths. These Class 9 Chapter 5 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/introduction-to-euclid-geometry-ncert-extra-questions-for-class-9-maths/

## Class 9 Introduction to Euclid Geometry Extra Questions

Extra Questions for Class 9 Maths Chapter 5 Introduction to Euclid Geometry

## Triangles Class 9 Extra Questions

Extra questions for Class 9 Maths Chapter 7 Triangles are given here. These questions will help the students to build a better understanding of the Triangles concept in Maths. These Class 9 Chapter 7 questions are important for CBSE Class 9 Maths exams. https://meritbatch.com/triangles-ncert-extra-questions-for-class-9-maths-chapter-7/

## Â Class 9 Triangles Extra Questions

Extra Questions for Class 9 Maths Chapter 7 Triangles

Triangles Class 9 Extra Questions

## Introduction to Graphs Class 8 Extra Questions with Answers

Introduction to Graphs Class 8 Extra Questions Maths Chapter 15 are created from the examination perspective and hence will be a great help for studentsâ€™ exam preparation. These questions are available in PDF format and students can download them for free from Extra Questions for Class 8 Maths. https://meritbatch.com/introduction-to-graphs-ncert-extra-questions-for-class-8-maths-ch-15/

## Class 8 Introduction To Graphs Extra Questions

Extra Questions for Class 8 Maths Chapter 15 Introduction to Graphs

Introduction To Graphs Class 8 Extra Questions Question 1.
Write the coordinates of each point shown is the graph.

Solution:

Extra Questions On Introduction To Graphs For Class 8 Question 2.
From the given figure, choose the letters indicate the location of the points.
(i) (3, 1)
(ii) (0, 5)
(iii) (3, 0)
(iv) (1, 2)
(v) (2, 3)
(vi) (8, 12)
(vii) (6, 10)
(viii) (0, 9)

Solution:
(i) D(3, 1), (ii) E(0, 5), (iii) F(3, 0), (iv) G(1, 2), (v) H(2, 3), (vi) B(8, 12), (vii) C(6, 10), (viii) A(0, 9)

Class 8 Maths Introduction To Graphs Extra Questions Question 3.
Draw the graph of the following table. Is it a linear graph?

Solution:

Yes, it is a linear graph.

Introduction To Graphs Class 8 Questions Question 4.
The given graphs show the progress of two different cyclists during a ride. For each graph, describe the riderâ€™s progress over the period of time. (NCERT Exemplar)

Solution:
(a) As time passes, the speed of cyclist I decreases steadily.
(b) Speed of cyclist II increases for a short time period, and then increases very slowly.

Extra Questions For Class 8 Maths Chapter Introduction To Graphs Question 5.
Match the coordinates given in Column A with the items mentioned in Column B. (NCERT Exemplar)

Solution:
(i) – (d), (ii) – (f), (iii) – (e), (iv) – (a), (v) – (b), (vi) – (c)

Class 8 Graph Questions Question 6.
The given graph shows the flight of an aeroplanes.

(i) What are the scales taken on x-axis and y-axis?
(ii) Upto what height the aeroplane rises?
(iii) What was the speed of the aeroplane while rising?
(iv) How long was the plane in level flight?
(v) How long did the whole flight take?
Solution:
(i) Scale on x-axis, 1 cm = 10 minutes
Scale ony-axis, 1 cm = 100 metres
(ii) The aeroplane rose upto 1000 metres.
(iii) The speed of the aeroplane while rising was 100 m per minutes.
(iv) The time taken by the aeroplane to be in level flight is 40 + 30 = 70 minutes
(v) Total flight time is 130 minutes.

Linear Graph Class 8 Extra Questions Question 7.
A bank gives 10% interest on the deposits by the Ladies. Draw a graph showing the relation between the amount deposited and the simple interest earned by the ladies and state following from the graph.
(i) The annual interest earned for an investment of â‚¹ 250
(ii) The investment one has to make to get an annual interest of â‚¹ 70.

Solution:
Required Graph is as under:

(i) â‚¹ 25 is Earned as annual interest for an investment of â‚¹ 250
(ii) â‚¹ 700 is to be invested to get an annual interest of â‚¹ 70.

Class 8 Chapter 15 Extra Questions Maths

## Direct and Inverse Proportions Class 8 Extra Questions with Answers

Direct and Inverse Proportions Class 8 Extra Questions Maths Chapter 13 are created from the examination perspective and hence will be a great help for studentsâ€™ exam preparation. These questions are available in PDF format and students can download them for free from Extra Questions for Class 8 Maths. https://meritbatch.com/direct-and-inverse-proportions-ncert-extra-questions-for-class-8-maths/

## Class 8 Direct And Inverse Proportion Extra Questions

Extra Questions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

### Direct and Inverse Proportions Class 8 Extra Questions Very Short Answer Type

Direct And Inverse Proportion Class 8 Extra Questions Question 1.
A train is moving at a uniform speed of 100 km/h. How far will it travel in 20 minutes?
Solution:
Let the distance travelled by train in 20 minutes be x km.

Since the speed is uniform, the distance travelled will be directly proportional to time.

Hence, the required distance is 33$$\frac { 1 }{ 3 }$$ km.

Direct And Inverse Variation Class 8 Question 2.
Complete the table if x and y vary directly.

Solution:
Let the blank spaces be filled with a, b and c.

Hence, the required values are a = 7, b = 15 and c = 7.5.

Direct And Inverse Proportion Class 8 Extra Questions With Solutions Question 3.
If the cost of 20 books is â‚¹ 180, how much will 15 books cost?
Solution:
Let the required cost be â‚¹ x.
Here, the two quantities vary directly.

Direct And Inverse Proportion Questions Question 4.
If x1 = 5, y1 = 7.5, x2 = 7.5 then find y2 if x and y vary directly.
Solution:
Since x and y vary directly.

Hence, the required value is 11.25.

Class 8 Maths Ch 13 Extra Questions Question 5.
If 3 kg of sugar contains 9 Ã— 108 crystals. How many sugar crystals are there in 4 kg of sugar?
Solution:
Let the required number of crystals be x.

Hence, the required number of crystals = 1.2 Ã— 109.

Class 8 Maths Direct And Inverse Proportion Extra Questions Question 6.
If 15 men can do a work in 12 days, how many men will do the same work in 6 days?
Solution:
Let the required number of men be x.
Less days â†’ more men.
Thus the two quantities are inversely proportional to each other.

Hence, the required number of days = 30.

Extra Questions Of Direct And Inverse Proportion Class 8 Question 7.
A train travels 112 km in 1 hour 30 minutes with a certain speed. How many kilometres it will travel in 4 hours 45 minutes with the same speed?
Solution:
Let the required distance be x km.
More distance â†’ more time
Thus, the two quantities are directly proportional.

Hence, the required distance = 354.6 km.

Direct And Inverse Proportion Questions With Solutions Class 8 Question 8.
The scale of a map is given as 1 : 50,000. Two villages are 5 cm apart on the map. Find the actual distance between them.
Solution:
Let the map distance be x cm and actual distance be y.
1 : 50,000 = x : y

Hence, the required distance = 250 km.

Class 8 Maths Chapter 13 Worksheet Question 9.
8 pipes are required to fill a tank in 1 hr 20 min. How long will it take if only 6 pipes of the same type are used?
Solution:
Let the required time be â€˜tâ€™ hours.

Direct And Inverse Proportion Class 8 Worksheet With Answers Question 10.
15 men can build a wall in 42 hours, how many workers will be required for the same work in 30 hours?
Solution:
Let the required number of workers be x.
The number of workers, faster will they do the work.
So, the two quantities are inversely proportional.

x1y1 = x2y2
â‡’ 42 Ã— 15 = 30 Ã— x
â‡’ x = 21
Hence, the required number of men = 21

### Direct and Inverse Proportions Class 8 Extra Questions Short Answer Type

Question 11.
The volume of a gas V varies inversely as the pressure P for a given mass of the gas. Fill in the blank spaces in the following table:

Solution:
Since volume and pressure are inversely proportional.
PV = K

Question 12.
The cost of 5 metres of cloth is â‚¹ 210. Tabulate the cost of 2, 4, 10 and 13 metres of cloth of the same type.
Solution:
Let the length of the cloth be x m and its cost be â‚¹ y. We have the following table.

Question 13.
Six pumps working together empty a tank in 28 minutes. How long will it take to empty the tank if 4 such pumps are working together?
Solution:
Let the required time be t minutes.

Less pump â†’ More time
Since there is an inverse variation.
x1y1 = x2y2
6 Ã— 28 = 4 Ã— x
x = 42
Hence, the required time = 42 minutes.

Question 14.
Mohit deposited a sum of â‚¹ 12000 in a Bank at a certain rate of interest for 2 years and earns an interest of â‚¹ 900. How much interest would be earned for a deposit of â‚¹ 15000 for the same period and at the same rate of interest?
Solution:
Let the required amount of interest be â‚¹ x.

Hence, the required amount of interest = â‚¹ 1125.

Question 15.
A garrison of 120 men has provisions for 30 days. At the end of 5 days, 5 more men joined them. How many days can they sustain on the remaining provision?
Solution:
Let the number of days be x.

[âˆµ Remaining days = 30 – 5 = 25]
[Total men = 120 + 5 = 125]
Since there is an inverse variation.
x1y1 = x2y2
120 Ã— 25 = 125 Ã— x
x = 24
Hence, the required number of days be 24.

Question 16.
In a scout camp, there is food provision for 300 cadets for 42 days. If 50 more persons join the camp, for how many days will the provision last? (NCERT Exemplar)
Solution:
More the persons, the sooner would be the provision exhausted. So, this is a case of inverse proportion.
Let the required number of days be x.
Hence, 300 Ã— 42 = (300 + 50) Ã— x
300 Ã— 42 = 350 Ã— x
x = 36

Question 17.
If two cardboard boxes occupy 500 cubic centimetres space, then how much space is required to keep 200 such boxes? (NCERT Exemplar)
Solution:
As the number of boxes increases, the space required to keep them also increases.
So, this is a case of direct proportion.

Thus, the required space is 50,000 cubic centimetres.

Question 18.
Under the condition that the temperature remains constant, the volume of gas is inversely proportional to its pressure. If the volume of gas is 630 cubic centimetres at a pressure of 360 mm of mercury, then what will be the pressure of the gas if its volume is 720 cubic centimetres at the same temperature? (NCERT Exemplar)
Solution:
Given that, at constant temperature pressure and volume of a gas are inversely proportional.
Let the required pressure be x.

Therefore, the required pressure is 315 mm of mercury.

## Playing with Numbers Class 8 Extra Questions with Answers

Playing with Numbers Class 8 Extra Questions Maths Chapter 16 are created from the examination perspective and hence will be a great help for studentsâ€™ exam preparation. These questions are available in PDF format and students can download them for free from Extra Questions for Class 8 Maths. https://meritbatch.com/playing-with-numbers-ncert-extra-questions-for-class-8-maths-chapter-16/

## Class 8 Playing With Numbers Extra Questions

Extra Questions for Class 8 Maths Chapter 16 Playing with Numbers

### Playing with Numbers Class 8 Extra Questions Very Short Answer Type

Playing With Numbers Class 8 Extra Questions Question 1.
Write the following numbers in generalised form.
(a) ab
(b) 85
(c) 132
(d) 1000
Solution:
(a) ab = 10 Ã— a + 1 Ã— b = 10a + b
(b) 85 = 10 Ã— 8 + 1 Ã— 5 = 10 Ã— 8 + 5
(c) 132 = 100 Ã— 1 + 10 Ã— 3 + 1 Ã— 2 = 100 Ã— 1 + 10 Ã— 3 + 2
(d) 1000 = 1000 Ã— 1

Class 8 Maths Chapter 16 Extra Questions Question 2.
Write the following in usual form.
(a) 3 Ã— 100 + 0 Ã— 10 + 6
(b) 5 Ã— 1000 + 3 Ã— 100 + 2 Ã— 10 + 1
Solution:
(a) 3 Ã— 100 + 0 Ã— 10 + 6 = 300 + 0 + 6 = 306
(b) 5 Ã— 1000 + 3 Ã— 100 + 2 Ã— 10 + 1 = 5000 + 300 + 20 + 1 = 5321

Playing With Numbers Class 8 Worksheet Question 3.
Which of the following numbers are divisible by 3?
(i) 106
(ii) 726
(iii) 915
(iv) 1008
Solution:
(i) Sum of the digits of 106 = 1 + 0 + 6 = 7 which is not divisible by 3.
Hence 106 is not divisible by 3.
(ii) Sum of the digits of 726 = 7 + 2 + 6 = 15 which is divisible by 3.
Hence 726 is divisible by 3.
(iii) Sum of the digits of 915 = 9 + 1 + 5 = 15 which is divisible by 3.
Hence 915 is divisible by 3.
(iv) Sum of the digits of 1008 = 1 + 0 + 0 + 8 = 9 which is divisible by 3.
Hence 1008 is divisible by 3.

Playing With Numbers Class 8 Extra Questions With Answers Question 4.
Prove that the sum of the given numbers and the numbers obtained by reversing their digits is divisible by 11.
(a) 89
(b) ab
(c) 69
(d) 54
Solution:
(a) Given number = 89
Number obtained by reversing the order of digits = 98
Sum = 89 + 98 = 187 Ã· 11 = 17
Hence, the required number is 11.

(b) Given number = ab = 10a + b
Number obtained by reversing the digits = 10b + a
Sum = (10a + b) + (10b + a)
= 10a + b + 10b + a
= 11a + 11b
= 11(a + b) Ã· 11
= a + b

(c) Given number = 69
Number obtained by reversing the digits = 96
Sum = 69 + 96 = 165 Ã· 11 = 15
Hence, the required number is 11.

(d) Given number = 54
Number obtained by reversing the digits = 45
Sum = 54 + 45 = 99 Ã· 11 = 9
Hence, the required number is 11.

Playing With Numbers Class 8 Worksheets With Answers Question 5.
Prove that the difference of the given numbers and the numbers obtained by reversing their digits is divisible by 9.
(i) 59
(ii) xy
(iii) xyz
(iv) 203
Solution:
(i) Given number = 59
Number obtained by reversing the digits = 95
Difference = 95 – 59 = 36 Ã· 9 = 4
Hence, the required number is 9.

(ii) Given number = xy = 10x + y
Number obtained by reversing the digits = 10y + x
Difference = (10x + y) – (10y + x)
= 10x + y – 10y – x
= 9x – 9y
= 9(x – y) Ã· 9
= x – y
Hence, the required number is 9.

(iii) Given number = xyz = 100x + 10y + z
Number obtained by reversing the digits = 100z + 10y + x
Difference = (100x + 10y + z) – (100z + 10y + x)
= 100x + 10y + z – 100z – 10y – x
= 99x – 99z
= 99(x – z)
= 99(x – 2) Ã· 9
= 11 (x – z)
Hence, the required number is 9.

(iv) Given number = 203
Number obtained by reversing the digits = 302
Difference = 302 – 203 = 99 Ã· 9 = 11
Hence, the required number is 9.

Class 8 Maths Ch 16 Extra Questions Question 6.
If a, b, c are three digits of a three-digit number, prove that abc + cab + bca is a multiple of 37.
Solution:
We have abc + cab + bca
abc = 100a + 10b + c
cab = 100c + 10a + b
bca = 100b + 10c + a
Adding abc + cab + bca = 111a +111b + 111c
= 111 (a + b+ c)
= 37 Ã— 3 (a + b + c) which is a multiple of 37.
Hence proved.

### Playing with Numbers Class 8 Extra Questions Short Answer Type

Ch 16 Maths Class 8 Extra Questions Question 7.
Complete the magic square given below so that the sum of the numbers in each row or in each column or along each diagonal is 15.

Solution:
(i) A = 15 – (8 + 1) = 15 – 9 = 6
(ii) F = 15 – (8 + 5) = 15 – 13 = 2
(iii) C = 15 – (A + F) = 15 – (6 + 2) = 15 – 8 = 7
(iv) E = 15 – (1 + 5) = 15 – 6 = 9
(v) D = 15 – (E + F) = 15 – (9 + 2) = 15 – 11 = 4
(vi) B = 15 – (8 + 4) = 15 – 12 = 3
Hence the required square is

Playing With Numbers Extra Questions Question 8.
Find the values of P and Q from the given addition problem

Solution:
Here, 3 + Q = 7
â‡’ Q = 7 – 3 = 4
Now taking second column, we get
4 + 7 = 11 i.e. 1 is carried over to third column
â‡’ 1 + P + 2 = 9
â‡’ 3 + P = 9
P = 9 – 3 = 6
Hence the value of P = 6 and Q = 4

Class 8 Playing With Numbers Extra Questions Question 9.
Find the values of p, q and r in the following multiplication problem.

Solution:
6 Ã— 4 = 24, Here 2 is carried over second column
â‡’ 6 Ã— p + 2 – 3 Ã— 10 = 2 [âˆµ 21 – 3 Ã— 6 = 3]
â‡’ 6p – 30 = 0
â‡’ p = 5
Now the multiplication problem becomes,

Here 2 + r = 4
â‡’ r = 2
q Ã— 354 = 1062
â‡’ q = 3
Hence, p = 5, q = 3, r = 2

Questions On Playing With Numbers For Class 8 Question 10.
Observe the following patterns:
1 Ã— 9 – 1 = 8
21 Ã— 9 – 1 = 188
321 Ã— 9 – 1 = 2888
4321 Ã— 9 – 1 = 38888
Find the value of 87654321 Ã— 9 – 1
Solution:
From the pattern, we observe that there are as many eights in the result as the first digit from the right which is to be multiplied by 9 and reduced by 1.
87654321 Ã— 9 – 1 = 788888888

### Playing with Numbers Class 8 Extra Questions High Order Thinking Skills (HOTS) Type

Chapter 16 Maths Class 8 Extra Questions Question 11.
Complete the cross number puzzle with the given column.

Solution:

Hence the complete square is

Question 12.
The product of two 2-digit numbers is 1431. The product of their tens digits is 10 and the product of their units digits is 21. Find the numbers. Solution:
Let the required two 2-digit numbers be 10a + b and 10p + q as per the condition, we have
a Ã— p = 10 and b Ã— q = 21
a = 2 and p = 5 or a = 5 and p = 2
Similarly b Ã— q = 21
b = 3 and q = 7 or b = 7 and q = 3
10p + q = 57 or 10p + q = 53
and 10a + b = 23 or 10a + b = 27
Since the units digit of product 1431 is 1.
Numbers are 57 and 23 or 53 and 27.
Now 57 Ã— 23 = 1311 and 53 Ã— 27 = 1431 which is given.
Hence, the required numbers are 53 and 27.

## Visualising Solid Shapes Class 8 Extra Questions with Answers

Visualising Solid Shapes Class 8 Extra Questions Maths Chapter 10 are created from the examination perspective and hence will be a great help for studentsâ€™ exam preparation. These questions are available in PDF format and students can download them for free from Extra Questions for Class 8 Maths. https://meritbatch.com/visualising-solid-shapes-ncert-extra-questions-for-class-8-maths-chapter-10/

## Class 8 Visualising Solid Shapes Extra Questions

Extra Questions for Class 8 Maths Chapter 10 Visualising Solid Shapes

### Visualising Solid Shapes Class 8 Extra Questions Very Short Answer Type

Visualising Solid Shapes Class 8 Extra Questions Question 1.
Draw any four 3-dimensional figures.
Solution:

Visualising Solid Shapes Class 8 Worksheets Question 2.
Verify Eulerâ€™s formula for a right triangular prism.

Solution:
Number of vertices (V) = 6
Number of faces (F) = 5
and number of edges (E) = 9
Eulerâ€™s formula:
V + F – E = 2
â‡’ 6 + 5 – 9 = 2
â‡’ 2 = 2
Hence, the formula is verified.

Visualising Solid Shapes Class 8 Worksheets Pdf Question 3.
Find the number of vertices of hexagonal prisms.
Solution:
Number of vertices = 2 Ã— Number of sides = 2 Ã— 6 = 12

Visualising Solid Shapes Extra Questions Question 4.
Verify whether a polyhedron can have 10 faces, 20 edges and 15 vertices.
Solution:
We have
Number of faces F = 10
Number of edges E = 20
and number of vertices V = 15
Eulerâ€™s formula:
V + F – E = 2
â‡’ 15 + 10 – 20 = 2
â‡’ 5 â‰  2
Hence, it is not possible to have a polyhedron satisfying the above data.

Visualizing Solid Shapes Class 8 Extra Questions Question 5.
If F = 18 and V = 10, then find the value of E in Eulerâ€™s formula.
Solution:
We know that
V + F – E = 2
â‡’ 10 + 18 – E = 2
â‡’ 28 – E = 2
â‡’ E = 28 – 2 = 26
Hence, the required value of E = 26

Class 8 Maths Ch 10 Extra Questions Question 6.
Draw the front, side and top views of the following 3-D figures.

Solution:

Visualising Solid Shapes Class 8 Important Questions Question 7.
Draw the nets of the following polyhedrons.
(i) Cuboid
(ii) Triangular prism with a base equilateral triangle.
(iii) Square pyramid.
Solution:
(i) The net pattern of cuboid

(ii) The net pattern of a triangular prism

(iii) Net pattern of square pyramid

Ch 10 Maths Class 8 Extra Questions Question 8.
The given net is made up of two equilateral triangles and three rectangles.

(i) Name the solid it represents.
(ii) Find the number of faces, edges and vertices.
Solution:
(i) The given figure represents the net prims of the triangular prism
(ii) Number of faces = 5
Number of edges = 9
Number of vertices = 6

### Visualising Solid Shapes Class 8 Extra Questions Short Answer Type

Extra Questions For Class 8 Maths Visualising Solid Shapes Question 9.
Match the following:

Solution:
(a) â†’ (vi)
(b) â†’ (v)
(c) â†’ (ii)
(d) â†’ (i)
(e) â†’ (iii)
(f) â†’ (v)

Ncert Class 8 Maths Chapter 10 Extra Questions Question 10.
Using Eulerâ€™s formula, fill in the blanks:

 Faces Vertices Edges (a) 6 8 â€” (b) â€” 10 15 (c) 4 â€” 6 (d) 5 6 â€” (e) 8 12 â€” (f) 7 7 â€”

Solution:
(a) F + V – E = 2
â‡’ 6 + 8 – E = 2
â‡’ 14 – E = 2
â‡’ E = 14 – 2 = 12

(b) F + V – E = 2
â‡’ F + 10 – 15 = 2
â‡’ F – 5 = 2
â‡’ F = 2 + 5 = 7

(c) F + V – E = 2
â‡’ 4 + V – 6 = 2
â‡’ V – 2 = 2
â‡’ V = 2 + 2 = 4

(d) F +V – E = 2
â‡’ 5 + 6 – E = 2
â‡’ 11 – E = 2
â‡’ E = 11 – 2 = 9

(e) F + V – E = 2
â‡’ 8 + 12 – E = 2
â‡’ 20 – E = 2
â‡’ E = 20 – 2 = 18

(f) F + V – E = 2
â‡’ 7 + 7 – E = 2
â‡’ 14 – E = 2
â‡’ E = 14 – 2 = 12
Hence (a) â†’ 12, (b) â†’ 7, (c) â†’ 4, (d) â†’ 9, (e) â†’ 18, (f) â†’ 12

Questions On Visualising Solid Shapes Class 8 Question 11.
Name the solids that have:
(i) 4 faces
(ii) 8 triangular faces
(iii) 6 faces
(iv) 1 curved surface
(v) 5 faces and 5 vertices
(vi) 6 rectangular faces and 2 hexagonal faces
Solution:
(i) Tetrahedron
(ii) Regular octahedron
(iii) Cube and cuboid
(iv) Cylinder
(v) Square and a rectangular pyramid
(vi) Hexagonal prism

Extra Questions For Class 8 Maths Chapter 10 Question 12.
Complete the table:

 Solid F V E F + V E + 2 Cuboid â€” â€” â€” â€” â€” Triangular pyramid â€” â€” â€” â€” â€” Triangular prism â€” â€” â€” â€” â€” Pyramid with square base â€” â€” â€” â€” â€” Prism with square base â€” â€” â€” â€” â€”

Solution:

 Solid F V E F + V E + 2 Cuboid 6 8 12 14 14 Triangular pyramid 4 4 6 8 8 Triangular prism 5 6 9 11 11 Pyramid with square base 5 5 8 10 10 Prism with square base 6 8 12 14 14

Class 8 Maths Visualising Solid Shapes Extra Questions Question 13.
Use isometric dot paper to sketch a rectangular prism with length 4 units, height 2 units and width 3 units. (NCERT Exemplar)
Solution:
Steps:
1. Draw a parallelogram with sides 4 units and 3 units. This is the top of the prism (Fig. 1).

2. Start at one vertex. Draw a line passing through two dots. Repeat for the other three vertices. Draw the hidden edges as a dashed line (Fig. 2).

3. Connect the ends of the lines to complete the prism (Fig. 3).

## Algebraic Expressions and Identities Class 8 Extra Questions with Answers

Algebraic Expressions and Identities Class 8 Extra Questions Maths Chapter 9 are created from the examination perspective and hence will be a great help for studentsâ€™ exam preparation. These questions are available in PDF format and students can download them for free from Extra Questions for Class 8 Maths. https://meritbatch.com/algebraic-expressions-and-identities-ncert-extra-questions-for-class-8-maths/

## Class 8 Algebraic Expressions and Identities Extra Questions

Extra Questions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

### Algebraic Expressions and Identities Class 8 Extra Questions Very Short Answer Type

Algebraic Expressions And Identities Class 8 Worksheets With Solutions Question 1.
Write two examples of each of
(i) Monomials
(ii) Binomials
(iii) Trinomials
Solution:
(i) Monomials:
(a) 3x
(b) 5xy2
(ii) Binomials:
(a) p + q
(b) -5a + 2b
(iii) Trinomials:
(a) a + b + c
(b) x2 + x + 2

Algebraic Expressions Class 8 Extra Questions Question 2.
Identify the like expressions.
5x, -14x, 3x2 + 1, x2, -9x2, xy, -3xy
Solution:
Like terms: 5x and -14x, x2 and -9x2, xy and -3xy

Class 8 Maths Chapter 9 Extra Questions Question 3.
Identify the terms and their coefficients for each of the following expressions:
(i) 3x2y – 5x
(ii) xyz – 2y
(iii) -x – x2
Solution:

Class 8 Algebraic Expressions Extra Questions Question 4.
Add: -3a2b2, –$$\frac { 5 }{ 2 }$$ a2b2, 4a2b2, $$\frac { 2 }{ 3 }$$ a2b2
Solution:

Algebraic Expressions And Identities Class 8 Extra Questions With Answers Question 5.
Add: 8x2 + 7xy – 6y2, 4x2 – 3xy + 2y2 and -4x2 + xy – y2
Solution:

Class 8 Maths Algebraic Expressions Extra Questions Question 6.
Subtract: (4x + 5) from (-3x + 7)
Solution:
(-3x + 7) – (4x + 5) = -3x + 7 – 4x – 5 = -3x – 4x + 7 – 5 = -7x + 2

Questions On Algebraic Expressions For Class 8 Question 7.
Subtract: 3x2 – 5x + 7 from 5x2 – 7x + 9
Solution:
(5x2 – 7x + 9) – (3x2 – 5x + 7)
= 5x2 – 7x + 9 – 3x2 + 5x – 7
= 5x2 – 3x2 + 5x – 7x + 9 – 7
= 2x2 – 2x + 2

Algebraic Expressions Class 8 Worksheets With Answers Question 8.
Multiply the following expressions:
(a) 3xy2 Ã— (-5x2y)
(b) $$\frac { 1 }{ 2 }$$ x2yz Ã— $$\frac { 2 }{ 3 }$$ xy2z Ã— $$\frac { 1 }{ 5 }$$ x2yz
Solution:

Ch 9 Maths Class 8 Extra Questions Question 9.
Find the area of the rectangle whose length and breadths are 3x2y m and 5xy2 m respectively.
Solution:
Length = 3x2y m, breadth = 5xy2 m
Area of rectangle = Length Ã— Breadth = (3x2y Ã— 5xy2) sq m = (3 Ã— 5) Ã— x2y Ã— xy2 sq m = 15x3y3 sq m

Algebraic Expressions Extra Questions Class 8 Question 10.
Multiply x2 + 7x – 8 by -2y.
Solution:

### Algebraic Expressions and Identities Class 8 Extra Questions Short Answer Type

Extra Questions On Algebraic Expressions For Class 8 Question 11.
Simplify the following:
(i) a2 (b2 – c2) + b2 (c2 – a2) + c2 (a2 – b2)
(ii) x2(x – 3y2) – xy(y2 – 2xy) – x(y3 – 5x2)
Solution:
(i) a2 (b2 – c2) + b2 (c2 – a2) + c2 (a2 – b2)
= a2b2 – a2c2) + b2c2 – b2a2) + c2a2 – c2b2)
= 0
(ii) x2(x – 3y2) – xy(y2 – 2xy) – x(y3 – 5x2)
= x3 – 3x2y2 – xy3 + 2x2y2 – xy3 + 5x3
= x3 + 5x3 – 3x2y2 + 2x2y2 – xy3 – xy3
= 6x3 – x2y2 – 2xy3

Ncert Class 8 Maths Chapter 9 Extra Questions Question 12.
Multiply (3x2 + 5y2) by (5x2 – 3y2)
Solution:
(3x2 + 5y2) Ã— (5x2 – 3y2)
= 3x2(5x2 – 3y2) + 5y2(5x2 – 3y2)
= 15x4 – 9x2y2 + 25x2y2 – 15y4
= 15x4 + 16x2y2 – 15y4

Chapter 9 Class 8 Maths Extra Questions Question 13.
Multiply (6x2 – 5x + 3) by (3x2 + 7x – 3)
Solution:
(6x2 – 5x + 3) Ã— (3x2 + 7x – 3)
= 6x2(3x2 + 7x – 3) – 5x(3x2 + 7x – 3) + 3(3x2 + 7x – 3)
= 18x4 + 42x3 – 18x2 – 15x3 – 35x2 + 15x + 9x2 + 21x – 9
= 18x4 + 42x3 – 15x3 – 18x2 – 35x2 + 9x2 + 15x + 21x – 9
= 18x4 + 27x3 – 44x2 + 36x – 9

Algebraic Expressions Class 8 Questions Question 14.
Simplify:
2x2(x + 2) – 3x (x2 – 3) – 5x(x + 5)
Solution:
2x2(x + 2) – 3x(x2 – 3) – 5x(x + 5)
= 2x3 + 4x2 – 3x3 + 9x – 5x2 – 25x
= 2x3 – 3x3 – 5x2 + 4x2 + 9x – 25x
= -x3 – x2 – 16x

Extra Questions Of Algebraic Expressions For Class 8 Question 15.
Multiply x2 + 2y by x3 – 2xy + y3 and find the value of the product for x = 1 and y = -1.
Solution:
(x2 + 2y) Ã— (x3 – 2xy + y3)
= x2(x3 – 2xy + y3) + 2y(x3 – 2xy + y3)
= x5 – 2x3y + x2y3 + 2x3y – 4xy2 + 2y4
= x5 + x2y3 – 4xy2 + 2y4
Put x = 1 and y = -1
= (1)5 + (1)2 (-1)3 – 4(1)(-1)2 + 2(-1)4
= 1 + (1) (-1) – 4(1)(1) + 2(1)
= 1 – 1 – 4 + 2
= -2

Class 8 Chapter 9 Maths Extra Questions Question 16.
Using suitable identity find:
(i) 482 (NCERT Exemplar)
(ii) 962
(iii) 2312 – 1312
(iv) 97 Ã— 103
(v) 1812 – 192 = 162 Ã— 200 (NCERT Exemplar)
Solution:

Class 8 Ch 9 Maths Extra Questions Question 17.

Solution:

Question 18.
Verify that (11pq + 4q)2 – (11pq – 4q)2 = 176pq2 (NCERT Exemplar)
Solution:
LHS = (11pq + 4q)2 – (11pq – 4q)2 = (11pq + 4q + 11pq – 4q) Ã— (11pq + 4q – 11pq + 4q)
[using a2 -b2 = (a – b) (a + b), here a = 11pq + 4q and b = 11 pq – 4q]
= (22pq) (8q)
= 176 pq2
= RHS.
Hence Verified.

Question 19.
Find the value of $$\frac { { 38 }^{ 2 }-{ 22 }^{ 2 } }{ 16 }$$, using a suitable identity. (NCERT Exemplar)
Solution:

Question 20.
Find the value of x, if 10000x = (9982)2 – (18)2 (NCERT Exemplar)
Solution:
RHS = (9982)2 – (18)2 = (9982 + 18)(9982 – 18)
[Since a2 -b2 = (a + b) (a – b)]
= (10000) Ã— (9964)
LHS = (10000) Ã— x
Comparing L.H.S. and RHS, we get
10000x = 10000 Ã— 9964
x = 9964