Wednesday, 20 May 2020

Grade 10 : Pair of Linear equations in two variables @2

3. Pair of Linear equations in two variables


Grade : 10


1. For what value of k , will the following system of linear equations has no solution ?

3x + y = 1; (2k - 1) x + (k-1) y = 2k +1

2. Find the value of k for which the following system of linear equations has infinite solutions...

x + (k+1) y = 5; (k+1)x +9y = 8k -1

3. Find the values of p and q for which the following system of equations has infinite number of solutions.

4. For what value of k, will the system of equations x +2y =5, 3x +ky - 15 =0 has
i) a unique solution ? ii) no solution ?

5. Find the value of k for which each of the following systems of equations have infinitely many solution ?

i) 2x +3y = 2; (k+2)x +(2k+1)y = 2(k-1)

ii) kx +3y = 2k+1; 2(k+1)x +9y =7k+1

6. For what value of k the system of equations kx+3y=k-3; 12x +ky= k will have no solution ?

7. Find the values of a and b for which the following system of equations has infinitely many solutions ?

i) 2x + 3y-7 =0 ; (a-1)x + (a+1)y = (3a -1)

ii) (a-1)x + 3y =2; 6x+(1-2b)y =6

8. Jamila sold a table and a chair for Rs 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got Rs 1065. Find the cost price of each.


9. 

Susan invested certain amount of money in two schemes  and , which offer interest at the rate of  per annum and  per annum, respectively. She received Rs.  as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs.  more as annual interest. How much money did she invest in each scheme?



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Saturday, 16 May 2020

Grade 9 : Rationalisation @1


Rationalisation


Grade : 9


1. If both a and b are rational numbers find the values of a and b ?

1. (√3 - 1 )
     (√3 + 1)

2. Simplify by rationalising the denominator ?

2. 1/ (5+√2)

3. If √2 = 1.414, Find the value of √3 ➗ √6 up to three places of decimals

4. Simplify :

3/(5-√3)  +  2/(5+√3) 

5. Rationalise the denominator :

5. 3/2√5

6. √2 / √5

7. Express with rational denominator : (6 - 4√2 )/ (6 + 4√2)

8. If x =2+√3, find the value of 

  x3 + 1/x3

9.  If x = 3 +√8, find the value of 

  x2 + 1/x2 


10. Write the value of  ( 2+ √3 )(2-√3)



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Friday, 15 May 2020

Grade 8 : Rational Numbers @2

Rational Numbers 

Grade : 8


1. The sum of two rational numbers is 9/20. If one of them is 2/5, find the other ?

2. The sum of two rational numbers is -2/3. If one of them is -8/5, find the other ?

3. Which rational number should be added to -7/8, to get 5/9 ?

4. Which rational number should be subtracted from -5/6 to get 4/9 ?

5. The cost of 7 2/3 m of rope is Rs. 12 ¾. Find its cost per meter ?

6. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2 ?

7. If 24 trousers of equal size can be prepared in 54 m of cloth, what length of cloth is required for each trouser ?

8. Find 2 rational numbers between 1/5 and 1/2 ?

9. Find 5 rational numbers between 1/4 and 1/2 ?

10. Find 5 rational numbers between 3/5 and 3/4 ?

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Thursday, 14 May 2020

Grade 7: Olympiad Questions @2

Olympiad Questions


Grade: 7


1. Solve for x.   3(2x-1)+25% of x =97

2. How many minutes are there in 1 ¾ hr ?

3. The letters written on paper slips of the word MATHEMATICS are put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter M ?

4. (25% of 50% of 100%)   ÷ (25 of 100 x 50% of 100 ) = -----

5. If 9 is added to four times a number, it becomes the same as 3 is subtracted from five times the same number. This fact can be represented as -----

6. Diameter of Earth is 12756000m. Few years ago, a new planet was discovered whose diameter is 5/43 of the diameter of Earth. Find the radius of this planet in km ?

7. Given below are heights of 15 girls of class 8 measured in cm : 128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154. Find the range of the given data, median height of the girls?

8. Sachin is younger than Rahul by 4 years. If their ages are in respective ratio of 7:9, then how old is Sachin ?

9. Two pens and three pencils cost Rs. 86. Four pens and a pencil cost Rs. 112. Find the cost of a pen and pencil respectively ?

10. A milkman buys milk at Rs 7, Rs 8, and Rs 8 per litre for three successive years. What approximately is the average cost per litre of milk if he spends Rs. 4000 each year ?

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Wednesday, 13 May 2020

Grade 6: Fractions @4

Fractions

Grade : 6


Word Problems :

1. In a vegetable garden 1/6 of the area is covered with lettuce and 5/12 with tomato plants. What fraction of the area is planted with these ?

2. Deepak and Amir bought a cake. Deepak ate 2/5 of the cake. Amir ate 3/10 of it.
a) who ate more? b) How much more ?

3. I bought one dozen bananas and ate 5  of them. What fraction of the total number of bananas left ?

4. Out of 50 identical articles, 36 are broken. Find the fraction of 
       a) the total number of articles and the articles broken.
       b) the remaining articles and the total number of articles

5. From a rope of  10 ½ m long,  4  5/8  m is cut off. Find the length of the remaining rope ?

6. A piece of cloth is 5m long. after washing it shrinks by 1/25 of  its length. What is the length of the cloth after washing ?

7. I bought wheat worth Rs. 12 ½, rice worth 25 ¾, vegetables worth 10 ¼  . If i gave a 100 rupee note to the shopkeeper, How much did he return to me ?

8. Out of 500 oranges in a box, 3/25 are rotten and 1/5 are kept for some guests. How many oranges are left in the box ?

9. An ornament piece is made of Gold and Copper. Its total weight is 96g. If 1/12 of the ornament  is copper, find the weight of Gold in it ?

10. A girl did half of some work on Monday and one- third of it on Tuesday. How much will she have to do on Wednesday in order to complete the work ?

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Grade : 5 Multiplication, Division @1

3. Multiplication, Division


Grade : 5


Multiply:

1. 4010 x 506

2. 60005 x 908

3. 5983 x 304

4. 8645 x 205

5. 9834 x 298

Divide:

6. 18468 ÷ 22

7. 30045 ÷ 25

8. 19687 ÷ 35

9. 46943 ÷ 58

10. 12686 ÷ 51



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Saturday, 9 May 2020

Grade 8: Rational Numbers @1

1. Rational Numbers 

Grade :8


1. What number should be added to -5/8 so as to get 5/9 ?

2. What should be subtracted from -3/4 so as to get 5/6 ?

3. Evaluate : (5/63)  -  (-8/21)

4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3) , find the other ?

5. The sum of two rational numbers is -8. If one of the numbers is (-15/7), find the other ?

6. What should be added to (1/2 + 1/3 + 1/5 ) to get 3 ?

7. What should be subtracted from (3/4 -2/3 ) to get -1/6 ?

8. Fill in the blanks : a)  -9/14 + ------- =  -1
           b) ------ + 15/23 = 4

9. Simplify :

a) -3/2 +5/4 - 7/4

b) 5/3 -7/6 + -2/3

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Grade 10 : Pair of Linear equations in 2 variables @1

3. Pair of Linear equations in two variables


Grade : 10


1. Solve the following systems of equations graphically:

a) 2x - 3y +13 =0, 3x - 2y +12 = 0

b) 2x + 3y +5 = 0, 3x - 2y -12 =0

c) x+y =4, 2x - 3y =3

d) 3x + 2y =12, 5x -2y =4

e) x + 2y - 7 = 0,  2x - y - 4 = 0

2. Determine graphically whether the system of equations x -2y = 2, 4x - 2y =5 is consistent or in-consistent.

3. Draw the graphs of the following equations on the same graph paper:
    2x +3y =12, x - y = 1.
   Find the coordinates of the vertices of the triangle formed by the two straight lines and the y axis.

4. Draw the graphs of x - y +1 =0 and 3x + 2y -12 =0 . Determine the coordinates of the vertices of the triangle formed by these lines and x axis and shade the triangular area. Calculate the area bounded by these lines and x axis.

5. Solve the system of equations graphically and shade the region between the lines and the y axis.
   3x - 4y =7, 5x + 2y =3

6. Represent the pair of equations graphically and write the coordinates of the points where the lines intersects y axis .
x + 3y =6, 2x - 3y =12

7. Draw the graph of the equations x=3, x=5, 2x - y- 4 =0, Also, find the area of the quadrilateral formed by the lines and the x axis.

8. Solve the system of equations graphically .
    2x + y =6, 2x -y +2 =0.
   Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x axis and the lines with the y axis.

ANSWERS

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Sunday, 3 May 2020

Grade 6, 7 Fractions @3

Fractions

Grade : 6, 7


1. Ritu ate 3/5 part of an apple and the remaining apple was eaten by her  brother Somu. How much part of the apple did Somu eat. Who had the larger share ? By how much ?

2.  Find the Difference of 
          i) 13/24 and  7/16
    
          ii)  21/25 and 18/20

3. Arrange the following fractions in ascending order

          i) 3/8 , 5/6, 6/8, 2/4, 1/3 
         
         ii) 2/7 , 11/35, 9/14, 13/28

4. The cost of Mathematics book is Rs. 25 3/4 and that of Science book is Rs. 20 1/2 . which costs more and by how much ? (Consider above as mixed fraction)

5. A rectangular sheet of paper is 12 1/2 cm long and 10 2/3 cm wide. Find its perimeter.(Consider above as mixed fraction)

6. Fill in the blanks.

   i) 2/3  x -----   = 10/30
  
   ii) 3/5  x ------- = 24/75

7. Simplify:

i) 5 x 3/20  x 2/15

ii) 14/25  x 35/51 x 34/49

iii) 2/3 x 5/4 

iv) 2 1/3  x 2/5 

v) 3/5 x 12

8.  Find : i) 3/5 of a rupee

ii) 3/4 of a year

iii) 2/3 of a day

iv)5/8 of a kilogram

v) 7/25 of a litre

9. Sugar is sold at Rs. 17 3/4 per kg. Find the cost of 8 1/2 kg of a sugar.

10. A car runs 16km using 1 litre of petrol.  How much distance will it cover using 2 3/4 litres of petrol ?




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Friday, 1 May 2020

Grade 5, 6 Profit and Loss @1

Profit and Loss


Grade : 5, 6


Notes :

Selling Price :S. P
Cost of the Price : C.P
Profit : P
Loss :L
 If S.P > C.P then difference is Profit

If S.P < C.P then difference is Loss


1. C.P of a bag is Rs. 363. Vimala sell it for Rs. 450. Find the Profit ?

2. A collector buys a painting for Rs. 3,500. But sells it for Rs. 2,750. Find the gain or loss ? 

3. A furniture mart buys an old sofa set for Rs. 5380. They spend Rs. 1840 to put new covers on it and sell it for Rs. 8000. What is the profit or loss ?

4.  Rahul sold a puppet for Rs. 315 at a loss of Rs. 23. What was the cost of he puppet ?

5. Ali made a profit of Rs. 281 on a carpet he sold for Rs. 5389. What was the cost of the carpet ?

6.  C.P of a sari is 7880. Profit is 1090. What is the Selling price of the sari ? 

7. A dozen books are sold at Rs. 1648at a profit of Rs. 120. What is the cost price of the books ?

8. A painting was bought for Rs. 45,895. The frame was changed for Rs. 2,060. It was finally sold for Rs. 51,080. What was the loss or gain ?

9. A factory makes car wheels. If it sells each wheel at Rs. 5925 at a profit of Rs. 398, what is the cost price of the wheel ?

10. A chair costs Rs. 1046. If it is sold at a loss of Rs 191, what is its selling price ?

Answers


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