8th Polygons Solved Questions Paper[CBSE Maths]

1.Q. Find the number of diagonals in an octagon?

Ans: Number Of Diagonals Of Polygon = n(n-3) / 2     

Where n is Number Of Sides

Here n = 8

Diagonals= [8(8-3)5]/2 = 20

2.Q. Find the number of sides of a polygon whose each exterior angle is 45⁰ .

Ans: Measure of Each Exterior Angle of a Polygon = 360/n

Each Exterior Angle = 45

45 = 360/n

Number of Sides = 360/45 =8

So Number of Sides = 8

3. Q. The sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles. Determine the number of sides of the polygon.

Ans: sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles.

We know that in a regular polygon sum of all the exterior angles = 360°

Therefore, sum of interior angles = 3 × 360° = 1080°

Again, we have sum of interior angles, S = (n - 2)180°, where n is the number of sides of the polygon

⇒ (n - 2)180° = 1080°
⇒ n - 2 = 6
⇒ n = 8
4. Q.  (a) What is the minimum interior angle possible for a regular polygon? Why?

 (b) What is the maximum exterior angle possible for a regular polygon?

Answer: The polygon with minimum number of sides is a triangle, and each angle of an equilateral triangle measures 60°, so 60° is the minimum value of the possible interior angle for a regular polygon. For an equilateral triangle the exterior angle is 180°-60°=120° and this is the maximum possible value of an exterior angle for a regular polygon.
The sum of the exterior angles of any polygon= 360⁰
Hence, the polygon of 8 sides is octagon.

5. Q. Find the measure of each exterior angle of a regular polygon of 9 sides.

Ans: Total measure of all exterior angles = 360

No. of sides = 9

Measure of each exterior angle = 360/9 = 40

6.Q. If the sum of the measures of the interior angles of a polygon equals the sum of the measures of the exterior angles, how many sides does the polygon have?

Direct and Inverse Proportions -NCERT Class VIII Maths Test Paper

1. 68 boxes of contain commodity require a shelf- length of 13.6 m. How many boxes of the same commodity would occupy a shelf- length of 20.4 m?

2. 11 men can dig 6 and 3/4  m long trench in one day. How many men should be employed for digging 27m long trench of the same type in one day?

3. 120 men had food provisions for 200 days. After 5 days, 30 men die due to an epidemic. How long will the remaining food last?

4. A car can finish a certain journey in 10 hours at the speed of 48km/hr. By how much should  its speed be increased so that it may take only 8 hours to cover the same distance?

5. In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?    

6. A worker is paid Rs.210 for 6 days work. If his total income of the month is Rs. 875, for how many did he work? 

7. A train 400m long is running at a speed of 72km/hr. How much time does it take to cross a telegraph post?

8. A train 360m long is running at a speed of 45 km/hr. What time will it take to cross a 140m long bridge?

9.A  train 210m long took 12 seconds to pass a 90 m long tunnel. Find the speed of the train.

10. If 5 men or 7 women can earn Rs 875 per day, how much would 10 men and 5women earn per day.

11. The cost of 16packets of salt, each weighing 900 g, is Rs 84. Find the cost of 27packets of salt, each weighing 1kg.

11. If 3persons can weave 168 shawls in 14 days, how many shawls will be woven by 8 persons in 5d ays?

12. If the cost of transporting 160kgof goods for 125kmis Rs60. What will be the cost of transporting 200kg of goods for 400km?

13. 6oxen or 8cows can graze a field in 28days. How long would 9oxen and 2cows take to graze the same field?

14. 6 men working 8 hours a day, earn Rs 8400per week. What will be the earning per week of 9men who work for 6hoursa day?

15. A fort had provision for 300men for 90days. After 20days, 50men left the fort. How long would the food last at the same rate? 

CCE CBSE Sample Papers Class VIII Mathematics

CCE CBSE Sample Papers Class VIII Mathematics 

Section-A

1. The Compound interest is

a) always less than the simple interest      
 b) always equal to the simple interest

c) always greater than simple interest       
d) always greater than or equal to simple interest.

2. In case of Compound interest, the principal

a) increases every year                                    b) remains same

c) decreases every year                                    d) increase for the first year and then decreases

3. Bananas are bought at the rate of 4 for Rs. 3. At what rate must they be sold to get a gain of 20% for each banana?

a) Rs 0.50 b) Rs 0.75 c) Rs 0.85 d) Rs 0.90

4. The square root of 0.09 is

a) 0.03 b) 0.3 c) 0.003 d) 3.0

5. The smallest number by which 9408 must be divided so that the quotient is a perfect square is

a) 2 b) 3 c) 7 d) None

6. The square root of ( 2⁵/2³)

a) 4 b) 10 c) 1 d) 2

7. A parallelogram each of whose angles measures 90o is ______.

(a)rectangle      (b)rhombus      (c)kite                   (d)trapezium

8. A parallelogram whose all sides are equal is called

(a)square     (b)rhombus  (c)rectangle    (d) trapezium

9. The two diagonals are not necessarily equal in a ………………. .

(a) rectangle      (b) square       (c) rhombus  (d) isosceles trapezium

10. The degree of the polynomial x² - 5x² y³ + 30x y - 576xy is ______

(A) – 576 (B) 4 (C) 5 (D) 7

Section B

11. Name each of the following parallelograms.

(i) The diagonals are equal and the adjacent sides are unequal.

(ii) The diagonals are equal and the adjacent sides are equal.

(iii) The diagonals are unequal and the adjacent sides are equal.

12. A trader buys an article for Rs. 1,200 and marks it 30% above the C.P. He then sells it after allowing a discount of 20%. Find the S.P. and profit percent.

13. A television set was sold after giving successive discounts of 10% and 20% respectively. Find sigle discount ?

14. In how much time will a sum of Rs. 1600 amount to ` 1852.20 at 5% per annum compound interest.

15. Find the difference between Simple Interest and Compound Interest for a sum of Rs.  8,000 lent at 10% p. a. in 2 years.

Section C

16. Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

17. Two adjacent angles of a parallelogram are (3x - 4)° and (3x + 16)°. Find the value of x and hence find the measure of each of its angles

18. A and B together can do a piece of work in 8 days, but A alone can do it 12 days. How many days would B alone take to do the same work?

19. Two persons A and B are engaged in a work. A can do a piece of work in 12 days and B can do the same work in 20 days. They work together for 3 days and then A goes away. In how many days 
will B finish the work?

20. A can do a piece of work in 10 days and B can do it in 15 days. How much does each of them get if they finish the work and earn Rs. 1500?

Section-C

21. Find the least number of six digits which is a perfect square. Find the square root of this number.

22. Six men working 10 hours a day can do a piece of work in 24 days. In how many days will 9 men working for 8 hours a day do the same work?

23. ABCD is a square and  Ac is a diagonal . Find the measure of ∠CAD.

24.  x + y + z = 0, prove that x ³+ y³ + z³ = 3xyz.

25. Factorize   (i)   y² –7y +12  (ii)  x⁴ – (y + z)⁴          

(iii) a⁴ – 2a²b² + b⁴  (iv) (l + m) ² – 4lm

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CBSE Sample Papers Class VIII Mathematics (2012-2013)

CBSE Sample Papers Class VIII Mathematics (2012-2013)

Section-A

1) A dealer buys a wrist watch for Rs.225 and spends RS.15 on its repairs. If he sells the same for RS.300, find his profit percent.

(a) 75% (b) 60% (c) 25% (d) 20%

2) Mona gets 98 marks in her exams. This amounts to 56% of the total marks. What are the maximum marks?

(a) 175 (b) 150 (c) 200 (d) 160

3) Akhil has to pay 4% sales tax in addition to the price of a certain article. Find the price of the article, if he pays Rs.260 in all.

(a) Rs.220 (b) Rs.250 (c) Rs.256 (d) Rs.200

4) The value of a machine depreciates every year by 10%. What will be its value after 2 years, if its present value is Rs.50,000?

(a) Rs.40,500 (b) Rs.40,050 (c) Rs.40,000 (d) Rs.45,000

5) Aby lent Rs.8,000 to his friend for 3 years at the rate of 5% per annum compounded annually. What amount does Aby get afer 3 years?

(a) Rs.9,000 (b) Rs.9,200 (c)Rs.9,216 (d) Rs.9,261

6) Find the amount on Rs.4,096 at the rate of 12 ½% per annum for 18 months compounded half-yearly.

(a) Rs.5,000 (b) Rs.4,913 (c) Rs.4,931 Rs.5,832

7) The present population of a town is 28,000. If it increases at the rate of 5% per annum, what will be its population after 2 years?

(a) 30,000 (b) 30,800 (c) 30,870 (d) 30,870

9) If the cost price of 18 mangoes is the same as the selling price of 16 mangoes, find the gain percent.

(a) 15% (b) 12.5% (c0 15.5% (d) 12%

10) What is the value of „m‟, if = ?  (5²)ⁿ m = (5^-7)²

a) 5 b) -2 c) -7 d) 2

Section-B( 3 marks questions)

11. What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

12. What is the least number by which 12348must be divided to obtain a perfect square?

13. x+ y + z = 0, prove that x³+ y³ + z3 = 3xyz.    Or,  Factorize:  (a8 – b8)

14.  If ( x2 + 1/x2) = 83 .  Find   X³- 1/X³

15.  Factorize (i) 25a² – 4b² + 28bc – 49c²     (ii) 5y² – 20y – 8z + 2yz         

16.A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

17. Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new  triangle and the given triangle is 5 : 4, find the perimeter of the given triangle

18. A dealer buys an article for Rs.380. At what price must he mark it so that after allowing a  discount of 5%, he still makes a profit of 25%?

19. Ajit buys a motorcycle for Rs.17600 including Value Added Tax. If the rate of VAT is 10%, what is the sale price of motorcycle?

20. Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides.

Section-C ( 5 marks questions)

21. ABCD is a rectangle. If BM and DN are perpendiculars from B and D on AC, prove that ∆ BMC ≅ ∆ DNA. Is it true that BM = DN?

23. If (x + l)(x + m) = x² + 4x+ 2 find l² +  m² and (l - m)²

24. ABCD is a parallelogram and line segments AE and CF bisect the angles A and C and meet DC and  AB at E and F respectively. Show that AE ∥ CF.

25. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides. 

ASSIGNMENT: Class: VIII, Subject : Maths Unit- Algebraic Identities Unit- Introduction to Graphs

CBSE TEST PAPER MATHEMATICS (Class-8)

• 8th Square And Square Roots Test paper
• Square and Square Roots
• Algebraic Expression
• Factorization
• Linear Equations
• Unitary Methods
• Percentage
• Profit and Loss
• Discounts & Sales Tax
• Compound Interest
• Quadrilateral

8th maths question paper

8th maths question paper

For All class 8th Maths test paper JSUNIL TUTORIAL

1. Choose the correct answer.


(i) There are 5 oranges in a basket of 25 fruits. The percentage of oranges is ___


(A) 5% (B) 25% (C) 10% (D) 20%


(ii) 2/25 = _______ %.


(A) 25 (B) 4 (C) 8 (D) 15


(iii) 15% of the total number of biscuits in a bottle is 30. The total number of biscuits is _______.

Read more »

Problem related to factorization,ratiolization

Problem-1 If the values of a – b and ab are 6 and 40 respectively, find the values of  a² + b² and (a + b)².

Solution: a² + b² = (a – b)² + 2ab = 6² + 2(40) = 36 + 80 = 116

  (a + b)² = (a – b)² + 4ab  = 6² + 4(40)= 36 + 160 = 196

Problem-2. If (x + p)(x + q) = x² – 5x – 300, find the value of p² + q².

Solution:

By product formula, we have (x + p) (x + q) = x² + (p + q)x + pq.

So, by comparison, we get p + q = –5, pq = –300.

Now, we have p² + q² = (p + q)² – 2 pq = (–5)² –2(–300) = 25 + 600 = 625.

Problem-3. If (x + a)(x + b)(x + c) ≡ x³ – 6x² + 11x – 6, find the value of a² + b² + c².

Solution:  From the product formula, we have

(x+a)(x+b)(x+c) = x³ + (a + b + c)x² + (ab + bc + ca)x + abc.

Comparing, we get a + b + c = –6, ab + bc + ca = 11, abc = –6.

∴ a² + b² + c² = (a + b + c)² –2 (ab + bc + ca) = (– 6)² – 2(11) = 36 – 22 = 14.

Problem-4 If a+b=2 and a2+b2=8,find a3+b3 and a4+b4.

Class 8th maths Test paper chapter COMPOUND INTEREST

1. Calculate the amount and compound interest on

(a) Rs 10,800 for 3 years at 12.5% per annum compounded annually (b) Rs 18,000 for 2.5 years at 10% per annum compounded annually(c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly.(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.

2. Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?

3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

4. I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?

5. Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get (i) after 6 months? (ii) after 1 year?

6. Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1.5 years if the interest is (i) compounded annually. (ii) compounded half yearly.

7. Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) The amount credited against her name at the end of the second year. (ii) The interest for the 3rd year.

Class 8th maths Test paper chapter COMPOUND INTEREST: 1. Calculate the amount and compound interest on (a) Rs 10,800 for 3 years at 12.5% per annum compounded annually (b) Rs 18,000 for 2.5 ye...

CBSE Maths Test paper for class viii

Maths Test paper for class viii: CBSE ADDA NCERT SOLUTION Rational Numbers for class 8 NCERT SOLUTION Rational Numbers for class 8 Linear Equations in One Variable for cl...

Mathematics Class VIII(Square and square root)

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CBSE SAMPLE PAPER MATHEMATICS (Class-8)

CBSE TEST PAPER 8TH MATHEMATICS SA-1

1. What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

2. What is the least number by which 12348must be divided to obtain a perfect square?

3. Find the cost of erecting a fence around a square field whose area is 9 hectares if fencing costs  Rs 3.50 

per metre

4. Find the least number of six digits which is a perfect square. Find the square root of this number.

5. Divide   (1)    x³ - 1 by x - 1    (2)     7 +15x -13x² +5x³ by 4 - 3x + x²

6. .  x+ y + z = 0, prove that x ³+ y³ + z³ = 3xyz.  Or, Factorize :  (a⁸ – b⁸)

7.  If ( x² + 1/x2) = 83 .  Find   X3- 1/X3

Or, , Factorize  (i) 25a² – 4b² + 28bc – 49c²     (ii) 5y² – 20y – 8z + 2yz          8. A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance 

upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

9. Three prizes are to be distributed in a quiz contest. The value of the second prize is five sixths the value of 

the first prize and the value of the third prize is four – fifths that of the second prize. If the total value of three 

prizes is Rs. 150, find the value of each prize.

10. (a) Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the 

given triangle is 5 : 4, find the perimeter of the given triangle

(b) The difference between two positive integers is 36. The quotient, when one integer is divided by the 

other is 4. Find the two integers.

11. Factorize

(1 x⁴ – (y + z)⁴                             (2) y² –7y +12                                    (3) 6xy – 4y + 6 – 9x

(4)  a⁴ – 2a²b² + b⁴                            (5)  (x² – 2xy + y²) – z²       

8th Factorization

1. Factorization

(1)   (a + b ) (1 – c ) – (b + c ) ( 1 – c ) 

 (2)  1 6 a²   +  40 a b  + 25 b²          

(3)  4x²/9  - 2/3 x y +  y² /4

(4)    5x²yz   -    5 x³y    

(5)   18 q² + 338 p² -  1 5 6 p q        

 (6)  -108 x² -  363 y² + 369 x y   

2.  Factorize  

(1)  16- 4x²                                        

(2)   20 x³ – 45 b⁴x               

(3)     4a² –  9 b²  –  c²  -  6bc

4)  25 ( x + 2y )²  - 36 (2x-5y)²           

(5)   a² +  2 a b + b² – c2 -2cd –d²

3. Factorize using a²+b²+c² +2ab+2bc+2ca

(1)  x² + y² + 25 z² – 2 x y – 10 y z + 10 z x

(2)  9x²  +  4y² + 49z² –  12 x y  +  28 y z – 42  z x 

(3)   4x⁶ + 9y⁶ + 16 x ⁶ + 12 x³ y³ + 16 x³ z³ + 24 y³z³  

 (4)  a⁸ + 256 b⁸ + 96 a⁴b⁴-16a³b² – 256a²b⁶

4. Factorize (x + a) (x + b) = x² + (a + b) x +a b

(1) x²+7x+ 10 

(2) x²+x-20  (3) x²-4x-21    

(4) 15x² + 13x + 2       

 (5) -6x² - 13x+5

5. Factorize

(1) 125 a³ + 150 a²b + 60 ab³ + 8ab³            

 (2)  x⁶ – 12 x⁴ b⁴ c + 6a²b⁵c² + b⁶c³  

(3) 81a³ + 24b³          

(4) 64a³b² – 125 b⁵   (5)  16 a³ – 54 b³      

(6)  8X + 1  (7) –a³  - 27b³  (8) 729a⁶ - 1

 (9) 8m³ + 64    (10) 1000 – 343 a⁹

6. Find the following products:

(1)  (9m + 2m  )( 81m² -18mn + 4n²)       

 (2) (5 - 2x ) (25 +10x + 4x²)      

(3) (3 + 5/x ) ( 9 – 15/x + 25/x²)

7. Find the value of  27x² + 64y² + 36xy(3x + 4y) , when x = 5 and y = -3.

8. Using the identity (x + a) (x + b) = x²  + (a + b)x + a b, evaluate  98 ´ 97

9.  x + y + z = 0, prove that x ³+ y³ + z³ = 3xyz.

10. Factorize   

(1)  m⁴ – 256                           

(2) y² –7y +12                          

 (3) 6xy – 4y + 6 – 9x    

(4)  x⁴ – (y + z)⁴                             

(5) a⁴ – 2a²b² + b⁴                            

(6) (l + m) ² – 4lm

(7) (x² – 2xy + y²) – z²            

 (8) 25a² – 4b² + 28bc – 49c²      

(9) 5y² – 20y – 8z + 2yz   

(10) a⁸ – b⁸

8th Linear Equations In One and two Variable

1. The perimeter of a rectangular swimming pool is 154 metres. Its length is 2m more than twice its breadth. 

What are the length and breadth of the pool.

2. Sum of two numbers is 95. If one exceeds the other by 15 find the numbers.

3. Two numbers are in the ration 5:3. If they differ by 18, find these numbers

4. Three consecutive integers add up to 51. What are these integers?

5. The sum of three consecutive multiples of 8 is 888. Find the multiple.

6. Three consecutive integers are as such when they are taken in increasing order and multiplied by 2, 3, and 

4 respectively, they add up to 74. Find these numbers.

7. The number of boys and girls in a class is in 7:5 ratio. The number of boys is 8 more than that of girls. Fin 

their numbers.

8. The ages of Rahul and Haroon are in the ratio of 5:7. Four years from now sum of their ages will be 56 

years. Find their present age.

9. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The 

sum of their ages is 135. Find their ages.

10. Fifteen years from now Ravi’s age will be 4 times his current age. What is his current age.

11. Lakshmi is a cashier in a bank. She has notes of denominations of Rs. 100, 50 and 10 respectively. The 

ratio of number of these notes is 2:3:5 respectively. The total cash with Lakshmi is 4,00,000. How many 

notes of each denomination does she have?

12. I have total Rs 300 in coins of denominations of Rs.1, Rs.2, and Rs. 5.The number of Rs. 2 coins is 3 

times the number of Rs. 5 coins. The total number of coins is 160. How many coins of each denomination 

are with me.

13. The organizers in an essay competition decide that winner will get a prize of Rs. 100 and a participation 

who doesn’t win gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find the number of 

winners if the total number of participants is 63.

14. If in a rational number denominator is greater than numerator by 8. If you increase the numerator by 17 

and decrease the denominator by 1, you get 3/2 as result. Find the number.

15. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The final result is 3 

times her original number. Find the number

16. A positive number is 5 times another number. If 21 is added to both the numbers then one of the new 

numbers becomes twice of another new numbers. Find the original numbers.

17. Sum of the digits of a two digit number is 9. When we interchange the digits the new number is 27 

greater than the earlier number. Find the number.

18. One of the digits of a two digit number is three times the other digit. If you interchange the digits and add 

the resulting number to original number you get 88 as final result. Find the numbers.

19. Sahoo’s mother’s present age is six times Sahoo’s present age. Five year from now Sahoo’s age will be 

one-third of his mother’s age. Find their current age.

20. There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate 

of Rs. 100 per metre it will cost village panchayat Rs.75000 to fence the plot. What are the dimensions of 

the plot.

21. Hasan buys two kinds of cloth materials for school uniform. Shirt material cost him Rs. 50 per metre and 

trousers material cost him Rs. 90 per metre. For every 2 metres of the trousers material he buys 3 metres of 

shirt material. He sells them at 12% and 10% profit respectively. His total sale is Rs. 36,660. How much 

trousers material did he buy? ( 200m)

22. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The 

rest 9 are drinking water from the pond. Find the total number of deer in the herd.

23. A grandfather is 10 times older than his granddaughter. He is also 54 years older than her. Find their age.

24. A man’s age is three times his son’s age. Ten years ago his age was five times his son’s age. Find their 

current age.

 25. Hari and Harry’s age are in the ratio of 5:7. Four years later the ratio of their ages will be 3:4. Find their 

current age.

8th Algebraic Expression & Compound Interest