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) x*^{3}- 1 by x - 1 (2) 7 +15x -13x^{2}+5x^{3}by 4 - 3x + x^{2}
6. . x+ y + z = 0, prove that x

^{3}+ y^{3}+ z^{3}= 3xyz. Or, Factorize : (a^{8}– b^{8})
7. If ( x

^{2}+ 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 x

^{4}– (y + z)^{4 }(2) y^{2}–7y +12 (3) 6xy – 4y + 6 – 9x
(4) a

^{4}– 2a²b² + b^{4}^{ }(5) (x² – 2xy + y²) – z²
8th Factorization

1. Factorization

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

(2) 1 6 a

^{2}+ 40 a b + 25 b^{2}
(3) 4x

^{2}/9 - 2/3 x y + y^{2}/4
(4) 5x

^{2}yz - 5 x^{3}y
(5) 18 q

^{2}+ 338 p^{2 }- 1 5 6 p q
(6) -108 x

^{2}- 363 y^{2}+ 369 x y^{ }
2. Factorize

(1) 16- 4x

^{2}
(2) 20 x

^{3}– 45 b^{4}x
(3) 4a

^{2}– 9 b^{2 }– c^{2}- 6bc
4) 25 ( x + 2y )

^{2}- 36 (2x-5y)^{2}
(5) a

^{2}+ 2 a b + b^{2 }– c2 -2cd –d^{2}
3. Factorize using a

^{2}+b^{2}+c^{2}+2ab+2bc+2ca
(1) x

^{2}+ y^{2}+ 25 z^{2}– 2 x y – 10 y z + 10 z x
(2) 9x

^{2}+ 4y^{2}+ 49z^{2}– 12 x y + 28 y z – 42 z x
(3) 4x

^{6}+ 9y^{6}+ 16 x^{6}+ 12 x^{3}y^{3}+ 16 x^{3}z^{3}+ 24 y^{3}z^{3 }^{}^{ }(4) a

^{8}+ 256 b

^{8}+ 96 a

^{4}b

^{4}-16a

^{3}b

^{2}– 256a

^{2}b

^{6 }

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

^{2}+ (a + b) x +a b
(1) x

^{2}+7x+ 10
(2) x

^{2}+x-20 (3) x^{2}-4x-21
(4) 15x

^{2}+ 13x + 2
(5) -6x

^{2 }- 13x+5
5. Factorize

(1) 125 a

^{3}+ 150 a^{2}b + 60 ab^{3 }+ 8ab^{3}
(2) x

^{6}– 12 x^{4}b^{4}c + 6a^{2}b^{5}c^{2}+ b^{6}c^{3}
(3) 81a

^{3}+ 24b^{3}
(4) 64a

^{3}b^{2}– 125 b^{5}(5) 16 a^{3}– 54 b^{3 }
(6) 8X + 1 (7) –a

^{3 }- 27b^{3}(8) 729a^{6}- 1
(9) 8m

^{3}+ 64 (10) 1000 – 343 a^{9}
6. Find the following products:

(1) (9m + 2m )( 81m

^{2}-18mn + 4n^{2})
(2) (5 - 2x ) (25 +10x + 4x

^{2})
(3) (3 + 5/x ) ( 9 – 15/x + 25/x

^{2})
7. Find the value of 27x

^{2}+ 64y^{2}+ 36xy(3x + 4y) , when x = 5 and y = -3.
8. Using the identity (x + a) (x + b) = x

^{2 }+ (a + b)x + a b, evaluate 98 ´ 97
9. x + y + z = 0, prove that x

^{3}+ y^{3}+ z^{3}= 3xyz.
10. Factorize

(1) m

^{4}– 256
(2) y

^{2}–7y +12
(3) 6xy – 4y + 6 – 9x

(4) x

^{4}– (y + z)^{4}^{ }
(5) a

^{4}– 2a²b² + b^{4}^{ }
(6) (l + m) ² – 4lm

(7) (x² – 2xy + y²) – z²

(8) 25a² – 4b² + 28bc – 49c²

(9) 5y² – 20y – 8z + 2yz

(10) a

^{8}– b^{8}
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

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

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

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

4. Evaluate using algebraic identities (54)2 ; (78)2; (999)2

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

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

7. If a2 + b2 + c2 =20 , a + b + c = 6 find a b + b c + ca

8. If ( x2 + 1 / x2 ) = 83 . Find (x3 - 1 / x3 )

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

10. Factorise a3 + b3 + c3 - 3 a b c

11. Devide

(1) x3 - 1 by x - 1

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

12. 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

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

14. Find the product of

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

(2) (2x2 + 3x - 7)(3x2 -5x - 4)

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

16.The perimeter of a triangle is 6p2 - 4p + 9 and two of its adjacent side are

p2 - 2p + 1 and 3 p2 - 5p + 3. Find third side of triangle.

17. Find the least no. of 5 digits which is perfect square.

18. Find the greatest num. of 6 digits which is perfect square.

19. Evaluate

(1) (5-1 x 3-1 )-1 x 6-1 (2) ( 23x+1 +10 ) / 7 = 6

(3) [52x+1]/ 25 = 125 (4) (4/9)4 x (4/9) - 7 = (4/9) 2x – 1

Compound Interest

1. You invest Rs 5000 at 12% interest compounded annually. How much is in the account after 2 years,

assuming that you make no subsequent withdrawal or deposit?

2.Find the amount and the compound interest on Rs 4000 at 10% p.a. for 2½ years.

3.A man invests Rs 5000 for three years at a certain rate of interest, compounded annually. At the end of

one year it amounts to Rs 5600. Calculate (i) the rate of interest per annum, (ii) the interest accrued in the

second year, (iii) the amount at the end of the third year.

4. A sum of Rs 9600 is invested for 3 years at 10% per annum at compound interest. (i) What is the sum

due at the end of the first year? (ii) What is the sum due at the end of the second year? (iii) Find the

compound interest earned in two years. (iv) Find the difference between the answers (ii) and (i) and find the

interest on this sum for one year. (v) Hence write down the compound interest for the third year.

5. Find the difference between the S.I. and C.I. on Rs 2500 for 2 years at 4% p.a., compound interest

reckoned semi-annually.

6. Find the amount and the compound interest on Rs 8000 in 2 years if the rate is 10% for the first year and

12% for the second year.

7. A man invests Rs 6500 for 3 years at 4·5% p.a. compound interest reckoned yearly. Income tax at the

rate of 20% is deducted at the end of each year. Find the amount at the end of the third year.

8. Calculate the compound interest for the second year on Rs 8000 invested for 3 years at 10% p.a.

Find the sum which amounts to Rs 9261 at 10% p.a. compound interest for 18 months, interest payable half-

yearly.

9. On what sum will the compound interest for 2 years at 5% p.a. be Rs 246?

10. On what sum will the compound interest (reckoned yearly) for 3 years at 6¼% per annum be Rs

408·50?

11. A man invests Rs 1200 for two years at compound interest. After one year his money amounts to Rs 1275. Find the rate of compound interest. Also find the amount which the man will get after 2 years correct

to the nearest paise.

12. At what rate percent per annum compound interest will Rs 2000 amount to Rs 2315·25 in 3 years?

If Rs 50000 amounts to Rs 73205 in 4 years, find the rate of compound interest payable yearly.

13. In what time will Rs 15625 amount to Rs 17576 at 4% per annum compound interest?

14. In what time will a sum of Rs 2500 produce Rs 309 at 6% per annum compound interest?

15. In what time will a sum of Rs 800 at 10% per annum compounded half-yearly produce Rs 126·10?

16. The simple interest on a sum of money for 2 years at 4% p.a. is Rs 450. Find the compound interest on

this sum of money at the same rate (i) for 1 year if the interest is reckoned semi-annually. (ii) for 2 years if the interest is reckoned annually.

17. At what rate of compound interest will Rs 625 amount to Rs 729 after 2 years? Also find the maturity

value of Rs 625 after 2 years at the above rate of simple interest.

18. Ram and Bhola each borrow equal sums for 3 years at 10% p.a. simple interest and compound interest

respectively. At the time of repayment, Bhola has to pay Rs 372 more than Ram. Find the sum borrowed

and interest paid by each.

19. The difference between the compound interest for a year payable half-yearly and the simple interest on a

certain sum of money lent out at 10% p.a. for a year is Rs 15. Find the sum of money lent out.

20. The difference between compound interest and simple interest in 3 years at 10% p.a. reckoned yearly is

Rs 18·60. Find the sum and the compound interest.

21. The amount at compound interest which is calculated yearly on a certain sum of money is Rs 1250 in one

year and Rs 1375 in two years. Calculate the rate of interest.

22. A certain sum of money amounts to Rs 10584 in two years and to Rs 11113·20 in three years, interest

being compounded annually. Find the interest rate percent and the original sum.

23. The compound interest and the simple interest on the same sum of money at the same rate percent per

annum are Rs 410 and Rs 400 respectively. Find the rate of interest and the sum of money.

24. The compound interest calculated yearly on a certain sum of money for the second year is Rs 880 and

for the third year it is Rs 968. Find the rate of interest and the original money.

25. The simple interest on a certain sum for 3 years is Rs 150 and the compound interest on the same sum at the same rate for 2 years is Rs 110. Find the rate of interest and the principal.

26. A sum of money lent at C.I. on 1st April 96 amounts to Rs 2420 on 1st April 98 and to Rs 2662 on 1st

April 99. Find the rate of interest and the sum.

27. The simple interest in 3 years and the compound interest in 2 years on a certain sum at the same rate are

Rs 1200 and Rs 832 respectively. Find (i) the rate of interest, (ii) the principal, (iii) the difference between

C.I. and S.I. for three years.

28. The value of a machine depreciates every year at the rate of 10% of its value. The machine was

purchased for Rs 40000 when new and it was sold for Rs 29160. Find the number of years that the machine was used.

29. A man borrowed a sum of money and agrees to pay off by paying Rs 3150 at the end of the first year

and Rs 4410 at the end of the second year. If the rate of compound interest is 5% p.a., find the sum

borrowed.

30. A man borrowed a certain sum of money and paid it back in 2 years in two equal instalments. If the rate

of compound interest was 4% p.a. and if he paid Rs 676 annually, what sum did he borrow?

31. A sum of Rs 16400 is borrowed to be paid back in 2 years by two equal annual instalments allowing 5% compound interest. Find the annual payment.

32. A loan of Rs 4641 is to be paid back by 4 equal annual instalments. The interest is compounded yearly

at 10%. Find the value of each instalment.

33. A man borrows Rs 6000 at 5% p.a. compound interest. If he repays Rs 1200 at the end of each year,

find the amount outstanding at the beginning of the third year.Answers

Solution

1. Rs 6272

2. Rs 5082; Rs 1082

3. (i) 12% (ii) Rs 672 (iii) Rs 6952·64

4. (i) Rs 10560 (ii) Rs 11616 (iii) Rs 2016 (iv) Rs 1056, Rs 105·60 (v) Rs 1161·60

5. Rs 6·08

6. Rs 9856; Rs 1856

7. Rs 7227·56

8. Rs 880

9. Rs 8000

10. Rs 2400

11. Rs 2048

12. 6¼%; Rs 1354·69

13. 5%

14. 10%

15. 3 years

16. 2 years

17. 1½ years

18. (i) Rs 227·25 (ii) Rs 459

19. 8%; Rs 725

20. Rs 12000; Rs 3600, Rs 3972

21. Rs 6000

22. Rs 600; Rs 196·60

23. 10%

24. 5% p.a., Rs 9600

25. 5% p.a., Rs 4000

26. 10%, Rs 8000

27. 20%; Rs 250

28. 10%, Rs 2000

29. (i) 8% (ii) Rs 5000 (iii) Rs 98·56

30. 3 years

31. Rs 7000 32. Rs 1275 33. Rs 8820 34. Rs 1464·10 35. Rs 4155

10th Maths SA-2 Chapter wise Test Papers Links |
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