RSMATHS99.COM                                           

CONTENTS:              CLASS -7

1.       INTEGERS--------------------------------------------------------------------------

2.       FRACTIONS -----------------------------------------------------------------------                                              

3.       DECIMALS------------------------------------------------------------------------                                  

4.       RATIONAL NUMBERS ----------------------------------------------------------                                

5.       EXPONENTS ----------------------------------------------------------------------

6.       ALGEBRIC EXPRESSIONS------------------------------------ ------------------

7.       LINEAR EQUATION IN ONE VARIABLE--------------------------------------

8.       RATIO AND PROPORTION-----------------------------------------------------

9.       UNITARY METHOD -------------------------------------------------------------

10.   PERCENTAGE---------------------------------------------------------------------

11.   PROFIT & LOSS------------------------------------------------------------------- 

12.   SIMPLE INTEREST----------------------------------------------------------------                       

13.   LINES AND ANGLES--------------------------------------------------------------                     

14.   PROPERTIES OF PARALLEL LINES---------------------------------------------

15.   PROPERTIES OF TRIANGLES---------------------------------------------------

16.   CONGRUENCE---------------------------------------------------------------------

17.   CONSTRUCTIONS----------------------------------------------------------------

18.   REFLECTION AND ROTATIONAL SYMMETRY-----------------------------

19.   THREE- DIMENSIONAL SHAPES----------------------------------------------

20.   MENSURATION------------------------------------------------------------------

21.   MEAN, MEDIAN, MODE-------------------------------------------------------

22.   BAR GRAPHS----------------------------------------------------------------------

23.   PROBABILITY---------------------------------------------------------------------

24.   MULTIPLICATION OF A MONOMIAL AND BINOMIAL------------------  

25.   MULTIPLICATION OF TWO BINOMIALS------------------------------------

26.   INVERSE VARIATION ------------------------------------------------------------ 

 

RSMATHS99.COM                                           

EXERCISE-2A            FRACTIONS                                                                                                                                  

 

                Fraction s:    are whole numbers and b

            In     a is call as numerator and b as denominator     [trick to remember D = down]

Q1.     Compare the fractions:

            I]            . Hence, .

            Ii]        =  

            Iii]       .     

 

Q2.     Arrange in ascending order:

            I]         LCM of 4,6,9,12 = 3 x 2 x 2 x 3 = 36.

 

 

            Ii]     LCM of 5, 10 , 15, 20 = 5 x 2 x 3 x 2 = 60.

                   

            = 

 

Q3.     Arrange in desending order:

            I] 

             = ,  

            <  

            Ii] 

           

Q4.     Reenu got-   . Sonal got larger.

           

Q5.     Find the sum:  I]           ii]  

            Iii]        [LCM 4 x 3 x 2 x 2 = 48]

RSMATHS99.COM                                           

EXERCISE – 7A         LINEAR EQUATION IN ONE VARIABLE  

Solve the equation:

Q1.     3x – 5 = 0 => 3x = 5  => x =

Q2.     8x – 3 = 9 – 2x  => 8x + 2x = 9 + 3  => x = .

Q3.     7 – 5x = 5 – 7x => 5x + 7x = 5 – 7 => 12x = -12  => x =

Q4.     3 == 2x = 1 – x   => 2x + x = 1 – 3  => 3x = -2  => x = .

Q5.     2(x -2) + 3(4x - 1)= 0   => 2x -4 + 12x -3 = 0  => 2x + 12x = 4 +3  => x = .

Q6.     5(2x - 3) -3(3x - 7)= 5  => 10 x -15 – 9x +21 = 5 => x + 6 = 5 => x = 5-6 = 1.

Q7.     2x -

Q8.      =>

Q9.      =   =

Q10.   3x + 2x +4 = 20 – 2x +5  =>7x = 21   => x = 3.

Q11.   13y – 52 – 3y +27 -5y -20 = 0   => 5y = -45   =>y = -9.

Q12.   2m + 5 = 3(9m -10)= 9m – 30  => 2m – 9m = -30 -5 => -7m = -35 => m = 5.

Q13.   18x + 12 -30x + 5 = 3x -24 -35x + 30 + 9x => 17 – 12x = -23x + 6  => 11 = -11x => x = -1.

Q14.   T – 2t – 5 -5 + 10t = 6 + 8t – 3t + 12 => 9t -10 = 18 + 5t  => 4t = 28  => t = 7.

Q15.  

Q16.   = 3  =>  21x – 7 -5x = 3 x 35  => 16x = 105 + 7 = 122  => x =

RSMATHS99.COM                                           

EXERCISE-20B ,          AREA BETWEEN TWO RECTANGLES

Q1.

               

                Let ABCD be the given grassy plot and let EFGH be the inside boundary of

the path. Then length AB  75m and breadth BC =60m.

Area of the plt = (75 x 60)m2 = 4500m2.    Width of the path = 2m.

 EF= 75 – 2 X 2  => EF = 75 – 4 = 71m.  AND FG = 60 – 4 = 56m.

Area Of the rectangle EFGH = 71 X 56 = 3976m2.

Area of the path = area ABCD – area EFGH.

                        = 4500 – 3976 = 524m2.

Cost of construction of the path = Rs.(524 X 125)= Rs. 65500.

Q2.

                           

               Area of the plot = 95 x 72m = 6840m2.      Width of the path = 3.5m.

                EF = 95 – 2 x 3.5m = 95 – 7 = 88m.   and FG = 72 – 7 = 65m.

            Area Of the rectangle EFGH = 88 x 65 = 5720m2.     

Area of the path = area ABCD – area EFGH. = 6840 – 5720 = 1120m2.

Cost of construction of the path = 1120 x 80 = Rs.89600.

And cost of laying the grass = 5720 x 40 = Rs. 228800.

Total expenses = Rs.89600 + 228800 = Rs.318400.

Q3.

                                     

Area of ABCD = 5 x 1.3 = 6.5m2.    EF = 5m – 2 x 0.25 = 5m – 0.50m = 4.5 m.

            FG = 1.3 – 0.50 = 0.8m2 .   Area of EFGH = 4.5 x 0.8 = 3.6 m2.

            Area of the border = 6.5 – 3.6 = 2.9m2. 

            Cost of printing the border = Re 1 per 10cm2 =

            Since, 0.0010m2 printing cost = Re1

                     1m2    “          “          =

                     29m2  “          ‘          

Q4.

                               

EF = 38 + 2 x 2.5 = 38 + 5 = 43m.    FG = 25 + 5 = 30m.

            Area ABCD = 38 x 25 = 950m2.      Area of EFGH = 43 X 30 = 1290m2.

            Area of path = 1290 – 950 = 340 x 120 = Rs.40800.

Q5.

                                   

EF = 9.5 + 2 x 1.25 = 9.5 + 2.50 = 12m. FG = 6 + 2.50 = 8.50m.

            Area of EFGH = 12 x 8.50 = 102m2.  Area ABCD = 9.5 x 6 = 57m2.

            Area of verandah = 102 – 57 = 45m2.

 Cost of cementing the floor of verandah = 45 x 80 = Rs.3600.

---------------------------------------------------x----------------------------------------------------

RSMATHS99.COM                                           

EXERCISE – 21C. MODE  OF UNGROUPED DATA

                MODE = 3(Median) – 2(mean)

Q1.     Find the mode of data:

            i] 4, 6, 7, 8, 8, 8, 8, 10, 11, 15

            Clearly, 8 occurs maximum no. of times. Hence, mode = 8.

            ii]  18, 21, 23, 27, 27, 27, 27, 27, 36, 39, 40.

            Clearly, 27 occurs maximum no. of times. Hence, mode = 27.

Q2.     28, 31, 32, 32, 32, 32, 34, 36, 38, 40, 41.

            Clearly, 32 occurs maximum no. of times. Hence, mode of the age = 32 yrs.

Q3.    

Daily wages (in Rs.) (xi)

No. of workers   (fi )

Cumulative frequency

Fi  x  xi

100

6

6

600

125

8

14

1000

150

9

23

1350

175

12

35

2100

200

10

45

2000

 

N =

 

 

Here n = 45, which is odd.

              Median =   rd  term.     Median =   Rs. 150.

            Also,    mean  =     =   

              Mode  = 3(Median) – 2(mean)  = 3 x 150 – 2 x 1.67

            = 450 – 313.34 = Rs. 136.66

Q4.    

     Marks  obtained

     No of students

Cumulative frequency

           f1 x1

               ( x1 )

               ( f1)

                

 

15

2

2

30

17

5

7

85

20

10

17

200

22

12

29

264

25

8

37

200

30

4

41

120

                                       

N =   = 45

 

899

 

Hence n = 31 , which is odd

             Median = th term =    =  = 21 th term

               median = 22 , Also,    mean  =     =   

              Mode  = 3(Median) – 2(mean)  = 3 x 22 – 2 x 21.92 = 66 – 43.84 = 22.16.

--------------------------------------------------------X-------------------------------------------------------------

RSMATHS99.COM                                           

UNITARY METHOD  EXERCISE – 9A

Q1.     Cost of 15 oranges = Rs.110

            Cost of 1 orange =                               [less orange, less cost]

                cost of 39 oranges =   [more orange, more cost]          

Q2.     For Rs.260, sugar bought = 8 kg

            For Rs.1,     sugar bought=

            For Rs.4420, sugar bought =

Q3.     For Rs. 6290, silk bought = 37m.

            For Rs.1, silk bought =   

            For Rs.4625, silk bought = 26m.  [hints:37 x 17=629, 17 x 26= 442]

Q4.     For Rs.1110, worker work = 6 days.

            For Rs.1,   worker work =

            For Rs.4625, “        “     =     [5 x 222=1110, 5 x 925 = 4625]

Q5.     In 42ltrs , car covered a distance = 357km

            In 1ltr,      car   “            “     “        =  

            In 12 ltrs,  car   “     “        =           

Q6.     Travel by rail  900km, fare =   Rs.2520,

            Travel by rail  1km ,   fare =       

            Travel by rail  360km ,   fare =   x 360 = Rs.1008.

RSMATHS99.COM                                           

If you want all chapter solution then please go to the home page and click contact. You can contact with us through Ph. No. 8873141785. E-mail: info@rsmaths99.com or

Singh.sanjaykumar10@gmail.com . You can touch the given email address  and directly email from your own email. If you want to ASK any maths related question then you ask through email we will reply you as soon as possible. If internet connectivity is problem in your area then don’t worry we will provide you the whole solution in pdf format also through your convenient media.