CBSE sample paper 10th Polynomials

1. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5 respectively.

2. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

3. If a andb are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b-2a b

4. Find the zeroes of the quadratic polynomial 4 √3 x2 + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

5. Find the zeroes of the quadratic polynomial 4u2 + 8u and verify the relationship between the zeroes and the coefficients

6. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

7. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2 - 7x + 1, find the value 1/a + 1/b

8. Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the
Coefficients

9. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.

10. Find the remainder when x51+51 is divided by (x+1).

11. Find all the integral zeros of x3 -3x2 - 2x + 6

12. Obtain all zeros of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

13. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

14. If the zeroes of the polynomial are 3x2 − 5x + 2 are a+ b and a- b, find a and b.

15. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x). 

polynomials grade 10 test paper

1. Every linear equation in two variables has ___ solution(s).

(a) No (b) one (c) two (d) infinitely many

2. For a pair to be consistent and dependent the pair must have

(a) no solution (b) unique solution

(c) infinitely many solutions (d) none of these

3. Graph of every linear equation in two variables represents a ___

(a) point (b) straight line(c) curve (d) triangle

4. Each point on the graph of pair of two lines is a common solution of he lines in case of 

(a) Infinitely many solutions (b) only one solution (c) no solution (d) none of these

5.The pair of linear equations is said to be inconsistent if they have

(a) only one solution (b) no solution (c) infinitely many solutions. (d) both a and c

6. Find the value of k so that the equations x + 2y = – 7, 2x + ky + 14 = 0 will represent coincident lines.

7. Give linear equations which is coincident with 2 x + 3y - 4 = 0 Find the value of K so that the pair of linear equations :

(3 K + 1) x + 3y – 2 = 0   

 (K² + 1) x + (k–2)y – 5 = 0 is inconsistent.

8. Solve for x and y :    

2^x + 3^y = 17

2^{x + 2} – 3 ^y+1 = 5.

9. The area of a rectangle remain the same if its length is increased by 7 cm and the breadth is decreased by 3 cm. The area remains unaffected if length is decreased by 7 cm and the breadth is increased by 5 cm. Find length and breadth.

10. A no. consists of three digits whose sum is 17. The middle one exceeds the sum of other two by 1. If the digits are reversed, the no. is diminished by 396. Find the no.

CBSE CLASS 8 Maths Chapter- Percentage Test Paper

1.A number is increased by 10% and then decreased by 10 % . Find net increase or decrease per cent.

2. The price of petrol rose by 10% . By what percent must a person reduce consumption so that expenditure does not increase?

3. An alloy consists of 30% copper and 40% zinc, and the remaining is nickel. Find the amount of nickel in 20 kilograms of the alloy.
4. The price of petrol rose by 10% . By what percent must a person reduce consumption so that expenditure does not increase?

5. A man spends 40% of his income for his food, 15% for his clothes and 20% for house rent and saves the rest. How much percent does he save? If his income is Rs 34,400, fi nd the amount of his savings.

6. Jyothika secured 35 marks out of 50 in English and 27 marks out of 30 in Mathematics. In which subject did she get better marks and by how much?

7. A worker receives Rs 11,250 as bonus, which is 15% of his annual salary. What is his monthly salary?8. A reduction of the price of apples would enable a purchaser to get 2 kg apples more for Rs. 240 

Find. (i) Reduced price per kg of apple (ii) The original price kg of apple.

9. If A's salary is 50% more than B's salary . Then by what percent B's salary less than A's salary.

10. 140 litre of an acid contains 90% of acid and the rest water. How much water must be added to make the water 12.5% of resulting mixture?

CBSE FORMATIVE TEST PAPER CLASS 9th MATHS

Section – A (1 marks)
1. Abscissa of all the points on the x-axis is

(A) 0 (B) 1(C) 2 (D) any number

2. Ordinate of all points on the x-axis is

(A) 0 (B) 1 (C) – 1 (D) any number

3. Any point on the y-axis is of the form

(A) (x, 0) (B) (x, y) (C) (0, y) (D) ( y, y)

4. Any point on the y-axis is of the form

(A) (x, 0) (B) (x, y) (C) (0, y) (D) ( y, y)

5. The things which are double of the same thing are

(A) equal (B) unequal (C) halves of the same thing (D) double of the same thing


Section-B ( 4 marks)

cbse class 8 maths guide

JSUNIL TUTORIAL CBSE MATHS & SCIENCE

8th Quadrilateral and parallelogram

Download File

8th Math exponents test_paper

Download File

8th Math profit  and loss test papers

Download File

8th  Math discounts Sales tax test papers.

Download File

8th Math percentage test papers

Download File

NCERT CBSE Class 8th Maths : Profit and Loss

1. Summi  buys a colour T.V set for Rs. 15,200 and sells it at a loss of 20%. What is the selling price of the T.V set?

2. A scooty is sold for Rs.  13,600 and fetches a loss of 15%. Find the cost price of the scooty.

3. The cost price of 11 pens is equal to the selling price of 10 pens. Find the loss or gain percent

4. By selling a table for Rs. 1,320, a trader gains 10%. Find the C.P. of the table.

5. The cost price of 16 note books is equal to the selling price of 12 note books. Find the gain percent.

6. A man sold two articles at Rs. 375 each. On the first article, he gains 25% and on the other, he looses 25%. How much does he gain or lose in the whole transaction? Also, find the gain or loss percent in the whole transaction.

7. Anbarasan purchased a house for Rs 17,75,000 and spent Rs 1,25,000 on its interior  decoration. He sold the house to make a profit of 20%. Find the S.P. of the house.

8. After spending Rupees sixty thousand for remodelling a house, Amla sold a house at a profit of 20%. If the selling price was Rupees forty two lakhs, how much did she spend to buy the house?

9. Jaikumar bought a plot of land in the outskits of the city for Rs 21,00,000. Hebuilt a wall around it for which he spent Rs 1,45,000. And then he wants to sell itat Rs 25,00,000 by making an advertisement in the newspaper which costs him Rs 5,000. Now, find his profit percent.

10. A man sold two varieties of his dog for Rs 3,605 each. On one he made a gain of 15% and on the other a loss of 9%. Find his overall gain or loss. [Hint: Find C.P. of each]

11. A man sells two wrist watches at Rs 594 each. On one he gains 10% and on the other he loses 10%. Find his gain or loss percent on the whole

12. Raju bought a motorcycle for Rs 36,000 and then bought some extra fittings to make it perfect and good looking. He sold the bike at a profit of 10% and he got a selling price of Rs.44,000. How much did he spend for the extra fittings mad
http://jsuniltutorial.weebly.com/
http://cbseadda.blogspot.com/

NCERT CBSE Class 8th Maths : Percentage

1. Choose the correct answer.                        JSUNIL TUTORIAL

(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 _______.

(A) 100 (B) 200 (C) 150 (D) 300

(iv) The price of a scooter was  Rs  34,000 last year. It has increased by 25% this year. Then the increase in price is  Rs. _______.

(A) 6,500 (B) 8,500 (C) ` 8,000 (D) ` 7,000

(v) A man saves Rs 3,000 per month from his total salary of Rs 20,000. The percentage of his savings is.

(A) 15% (B) 5% (C) 10% (D) 20%

2. (i) 20% of the total number of litres of oil is 40 litres. Find the total quantity of oil in litres.

(ii) 25% of a journey covers 5,000 km. How long is the whole journey?

(iii) 3.5% of an amount is  Rs  54.25. Find the amount.

(iv) 60% of the total time is 30 minutes. Find the total time.

(v) 4% sales tax on the sale of an article is Rs 2. What is the amount of sale?

3. Meenu spends 2000 from her salary for recreation which is 5% of her salary. What is her salary?

NCERT CBSE Class 8th Maths : Discounts & Sales Tax

http://jsuniltutorial.weebly.com/                        http://cbseadda.blogspot.com/ 

CHAPTER: Discounts & Sales Tax

               Section A

1. Choose the correct answer:

(i) The discount is always on the _______.

(A) Marked Price (B) Cost Price (C) Selling Price (D) Interest

(ii) If M.P. = Rs.140, S.P. = Rs 105, then Discount = _______.

(A) Rs 245 (B) Rs 25 (C) Rs 30 (D) Rs 35

(iii) ______ = Marked Price – Discount.

(A) Cost Price (B) Selling Price (C) List Price (D) Market price

(iv) The tax added to the value of the product is called ______ Tax.

(A) Sales Tax (B) VAT (C) Excise Tax (D) Service Tax

(v) If the S.P. of an article is Rs 240 and the discount given on it is ` 28, then the M.P.

is _______. (A) Rs 212 (B) Rs 228 (C) Rs 268 (D) Rs 258

Section B

1. A bicycle marked at Rs 1,500 is sold for Rs 1,350. What is the percentage of discount?

2. The list price of a frock is Rs 220. A discount of 20% on sales is announced. What is the amount of discount on it and its selling price?

3. An almirah is sold at Rs 5,225 after allowing a discount of 5%. Find its marked price.

4. A shopkeeper allows a discount of 10% to his customers and still gains 20%. Find the marked price of an article which costs Rs 450 to the shopkeeper.

5. A dealer allows a discount of 10% and still gains 10%. What is the cost price of the book which is marked at ` 220?

6. A television set was sold for Rs 14,400 after giving successive discounts of 10% and 20% respectively. What was the marked price?

7. 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.

8. Vinodh purchased musical instruments for Rs 12,000. If the rate of sales tax is 8%, find the sales tax and the total amount paid by him.

9. A refrigerator is purchased for Rs 14,355, including sales tax. If the actual cost price of the refrigerator is ` 13,050, find the rate of sales tax

10. Priya bought a suitcase for Rs 2,730. The VAT for this item is 5%. What was the price of the suitcase before VAT was added? Also state how much is the VAT?

11. The price marked on a book is Rs 450. The shopkeeper gives 20% discount on it in a book exhibition. What is the Selling Price?

12 . A television set was sold for Rs 5,760 after giving successive discounts of 10% and 20% respectively. What was the Marked Price?

13. Sekar bought a computer for Rs 38,000 and a printer for Rs 8,000. If the rate of sales tax is 7% for these items, fi nd the price he has to pay to buy these two items.

14. The selling price with VAT, on a cooking range is Rs 19,610. If the VAT is 6%, what is the original price of the cooking range?

6. Richard got a discount of 10% on the suit he bought. The marked price was Rs 5,000 for the suit. If he had to pay sales tax of 10% on the price at which he bought, how much did he pay?


15. The sales tax on a refrigerator at the rate of 9% is Rs 1,170. Find the actual sale price.

8. A trader marks his goods 40% above the cost price. He sells them at a discount of 5%. What is his loss or gain percentage?

16. A T.V. with marked price Rs 11,500 is sold at 10% discount. Due to festival season, the shop keeper allows a further discount of 5%. Find the net selling price of the T.V.

17. A person pays Rs 2,800 for a cooler listed at Rs 3,500. Find the discount percent offered.


18. Deepa purchased 15 shirts at the rate of Rs 1,200 each and sold them at a profit of 5%. If the customer has to pay sales tax at the rate of 4%, how much will one shirt cost to the customer?

19. Which is a better offer? Two successive discounts of 20% and 5% or a single discount of 25%. Give appropriate reasons.

20. What price should Suneeta mark on a sari which costs her Rs 2200 so as to gain 26 % after allowing a discount of 12 %?

Download http://jsuniltutorial.weebly.com/ 

CBSE Class VIII Math Questions of chapter factorization

What is factorization?

We can also write any algebraic expression as the product of its factors.

Factorization: The process of expressing any polynomial as a product of its factors is called factorization.

Examples: 6x³ =   (2x) (3x² )

A factor that cannot be factorized further is known as irreducible factor

2x² + x – 6 =(2x – 3) (x + 2)

Here  (2x – 3) cannot be factorized further

Also  (x + 2) cannot be factorized further

Factorization by taking out the common factor

In this method, we rewrite the expression with the common factors outside brackets.

Examples:

(i) 2x+6           = 2x+(2 x 3)

                         =2 (x+3) (Note that ‘2’ is common to both terms. )

(ii) 4x² +  20xy  = (4 x X x X)+(4 x 5 x X xY)

                         = 4x (x+5y) [Taking out the common term 4x]

Factorization by Grouping the terms

In this method, the terms in the given expression can be arranged in groups of two or three so as to get a common factor.

(i) x³ -  3x² +  x – 3

= x² (x- 3) +1 (x- 3) [By grouping the first two and the last two and taking out the common terms]

= (x² + 1) (x- 3)

(ii) 2xy - 3ab + 2bx - 3ay = 2xy +2bx - 3ab - 3ay [Rearranging the terms]

= 2x (y + b) -3a (y+b) [Taking out the common terms]

= (2x-3a) (y+b)

Factorization by using Identities

(i) x² + 6 x + 9 =

Comparing x x² + 6 x + 9 with a² + 2 ab+  b ², we see that a = x, b = 3.

Now, x² + 6 x + 9 = x² + 2 x 3 x + 3²

Using, a² + 2 ab+  b ² = (a + b)²  , a = x and b = 3,

We get x² + 6 x + 9 = (x + 3)²  .

` The factors of x² + 6 x + 9 are (x + 3)and (x + 3) .

(ii) Comparing x² – 64 with a b 2 2 - , we see that a = x and b = 8

Using, a²  - b²        = (a + b) (a - b) ,

             x²  –  64  = x² – 8²

                          = (x + 8) (x - 8)

Factorization by using the Identity (x+ a) (x+ b) =  x² + (a+ b)x + ab

Factorize x² +  5x + 6

Comparing x² +  5x + 6 with x² + (a+ b) x + ab

For this  ab = 2 x 3 = 6  and a + b = 2 + 3 = 5

We have, ab = 6, a + b = 5 and x = x.

If ab = 6, it means a and b are factors of 6.

Let us try with a = 2 and b = 3. These values satisfy ab = 6 and a + b = 5.

Therefore the pair of values a = 2 and b = 3 is the right choice.

Using :          x² + (a+ b) x + ab  = (x+ a) (x+ b)

 x² +  5x + 6 =  x² + (2 + 3) x + 2 x 3  = (x+ 2) (x+ 3)

x² +  6x+  8 = x² + (2 + 4) x + 2 x 4  = (x+ 2) (x+ 4)

Factors  of 8              Sum of  factors

1, 8                                  9

2, 4                                 6

Hence the correct   factors are 2, 4

Factorise the following

NCERT CBSE Class 8th Maths : Algebraic Expressions

CBSE TEST PAPER 8th Algebric Expression

1.     Numerical coefficient of 8x³yz² is ________   

2.     Monomial is a ________________

^3.         Write like terms from 2x², 2x, 2x³, - 5x, 11x⁴                                          

4.     Write numerical coefficient of . 3x³yza² 

5.     Find area of rectangle with sides 3x and 5y      

6.     Factorise 3xy + 9x²y³7.     Divide 7x²y²z² ÷ 21xyz

8.     Subtract 5x² – 4y² + 6y – 3 from  7x² – 4xy + 8y² + 5x – 3y.

9.     Add 4y (3y² + 5y – 7) and 2 (y³ – 4y² + 5)         

10.  Simplify (a + b) (2a – 3b + c) – (2a – 3b) c.     

11.  . Simplify (a + b + c)(a + b – c)

12.  find the products. (i) (2a2 + 9) (2a2 + 5)  (ii) (0.4p – 0.5q)² 

13.  Simplify.  (m² – n²m)² + 2m³n²              

14.  Evaluate (i) 998²   (ii) 297 × 303 (iii) (1.02)² – (0.98)²15.  Find the value of x2+y2 if x+y =12 and xy= 14

16.  Find the value using algebric formula i] 93x94     ii]  704217.  Find value of x2+y2       if x+1/x=3

18.  By division show that x-1 is factor of x3-1

19.  Factories:         25-a2-b2-2ab

20.  Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c )

21.  If ( x + 1 / x ) = 4,  Find the value of      ( x2 + 1 / x2 ) and (x4 + 1 / x4 )

22.  If ( x - 1/ x ) = 3 .Find the value of   (x3 + 1 / x3 )

23.  Find the remainder obtained by dividing  x3 + 3x2 - 5x +4 by x + 1

24.  Evaluate using algebraic identities   (54)2, (78)2 (999)2

25.  . If x - y = 7  ,   xy = 9  Find the value of  x2 + y2

26.  If x + y = 12 , xy = 27  Find the value of x3 + y3

27.  If a2 + b2 + c2  =20 , a + b + c = 6  find  ab + bc + ca

28.  If ( x2 + 1 / x2 ) = 83 .  find  (x3 - 1 / x3 )

29.  What must be subtracted from   4p2-2pq- 6q2 - r +5 to get  - p2 + p q - 8q2 - 2r+5

30.Devide (i)    x3 - 1 by  x - 1   (ii) 7 +15x -13x2 +5x3 by 4 - 3x + x2

31.  Evaluate(i) 1.5 3 - 0.93  - 0.63  (ii) (a - b )3 ₊ (a + b )3  (iii) (x + 2y -3z)2 +(x - 2y +3z)2

32.  . If (x4 + 1 / x4 ) = 47    find the value of   (x3 + 1 / x3 )

33. Find the product of   

(i) (x4 + 1 / x4 ) and      ( x + 1 / x )   

(ii)  (2x2 +3x - 7)(3x2 -5x - 4)

34.  Two adjacent side of a rectangle are 5x2-3y2 and x2 - 2xy Find its perimeter

35.  The perimeter of of a triangle is 6p2 - 4p + 9 and two of its adjacent side are   p2 - 2p + 1 and  3p2 - 5p + 3. Find third side of triangle.http://jsuniltutorial.weebly.com/

1.     Numerical coefficient of 8x³yz² is ________        

2.     Monomial is a ________________

^3.         Write like terms from 2x², 2x, 2x³, - 5x, 11x⁴                                          

4.     Write numerical coefficient of . 3x³yza²

5.     Find area of rectangle with sides 3x and 5y        

6.     Factorise 3xy + 9x²y³

7.     Divide 7x²y²z² ÷ 21xyz 

8.     Subtract 5x² – 4y² + 6y – 3 from  7x² – 4xy + 8y² + 5x – 3y.

9.     Add 4y (3y² + 5y – 7) and 2 (y³ – 4y² + 5)           

10.  Simplify (a + b) (2a – 3b + c) – (2a – 3b) c.       

11.  . Simplify (a + b + c)(a + b – c)

12.  find the products. (i) (2a2 + 9) (2a2 + 5)  (ii) (0.4p – 0.5q)²   

13.  Simplify.  (m² – n²m)² + 2m³n²                

14.  Evaluate (i) 998²   (ii) 297 × 303 (iii) (1.02)² – (0.98)²

15.  Find the value of x2+y2 if x+y =12 and xy= 14

16.  Find the value using algebric formula i] 93x94     ii]  7042

17.  Find value of x2+y2       if x+1/x=3

18.  By division show that x-1 is factor of x3-1

19.  Factories:         25-a2-b2-2ab

20.  Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c )

21.  If ( x + 1 / x ) = 4,  Find the value of      ( x2 + 1 / x2 ) and (x4 + 1 / x4 )

22.  If ( x - 1/ x ) = 3 .Find the value of   (x3 + 1 / x3 )

23.  Find the remainder obtained by dividing  x3 + 3x2 - 5x +4 by x + 1

24.  Evaluate using algebraic identities   (54)2, (78)2 (999)2

25.  . If x - y = 7  ,   xy = 9  Find the value of  x2 + y2

26.  If x + y = 12 , xy = 27  Find the value of x3 + y3

27.  If a2 + b2 + c2  =20 , a + b + c = 6  find  ab + bc + ca

28.  If ( x2 + 1 / x2 ) = 83 .  find  (x3 - 1 / x3 )

29.  What must be subtracted from   4p2-2pq- 6q2 - r +5 to get  - p2 + p q - 8q2 - 2r+5

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

31.  Evaluate(1) 1.5 3 - 0.93  - 0.63  (2) (a - b )3 ₊ (a + b )3  (3) (x + 2y -3z)2 +(x - 2y +3z)2

32.  . If (x4 + 1 / x4 ) = 47    find the value of   (x3 + 1 / x3 )

33.  13.Find the product of   (1) (x4 + 1 / x4 ) and      ( x + 1 / x )   (2)  (2x2 +3x - 7)(3x2 -5x - 4)

34.  Two adjacent side of a rectangle are 5x2-3y2 and x2 - 2xy Find its perimeter

35.  The perimeter of of a triangle is 6p2 - 4p + 9 and two of its adjacent side are   p2 - 2p + 1 and  3p2 - 5p + 3. Find third side of triangle.