ICSE Board Class 10 Math Sample Papers 2008

 SAMPLE PAPER
 CLASS – X 
 MATHEMATICS
 
SECTION A                                                            (40 MARKS )
Answers all questions.

1.(a) The  polynomial kx3+3x2+8 when divided by x2 leaves a remainder which 
        is double the remainder left by the polynomial x210x + 2k when divided by x2 . Find the value of k.    
  (b) A piece of butter 3cm by 5cm by 12 cm is placed in a hemispherical bowl of 
      radius 3.25 cm. Will the butter overflow when it melts completely .   
 2. (a) If x2, 4 and 9 are in continued proportion , find the value of x.  
   (b) Find the equation of a line that passes through (1,3) and is parallel to the 
        line y= 3x + 2.                     
   (c) On a map drawn to a scale of 1: 125,000, a triangle plot of land has the 
       following measurements: AB = 10cm, BC = 8cm, ∠ ACB = 90°  . Calculate   
       (i)  The actual length of AB in Km.  (ii)  the area of the lot in square 
        kilometers.                              
3. (i) Calculate the mean , median and mode of the following  numbers :  12, 11, 
    10. 11, 12, 13, 14, 13, 15, 13.            
    (ii) If 8a+5b/8c+5d=8a-5b/8c-5d  prove that a/b=c/d
   (iii) If cos A=4/5 and cos B =24/25, evaluate (i) cosec2A  (ii) cot A + cot B.  
4. (i) Solve the following inequation and graph the solution on the number line:
        2x5  ≤ 5x + 4 < 11, x∈ R.               
   (ii) The price of a T.V set inclusive of sales tax of 9% is Rs. 40,221. Find the 
        marked price.                   
  (iii) Komal deposited Rs. 1,500 per month in a bank for 8 months under the 
       recurring Deposit Scheme .What will be the maturity value of her deposits 
       if the rate of interest is 12% per annum  and interest is calculated at the 
       end of every month.             
     
SECTION  B                                                ( 40 MARKS )
Answer any four questions.
5. (a) A,B and T are three points on a circle . The tangent at T meets BA 
    produced at P. Given that ∠ ATB = 32°  and that the ∠ APT = 78°  , calculate 
    the  angle subtended by BT at the centre of the circle.       
 
    (b) Write down the equation of the line whose gradient is 4/3 and which 
    passes through P, where P divides the line segment joining  A ( 2, 3) and B 
    (5,4) , in the ratio 2:5.     
 
    (c) An electric shaver is listed at Rs. 1500 with a discount of 20% . What  
    additional discount  % must be offered to a customer to bring the actual 
    selling price to  Rs. 1080  .    
6. (a) Construct a triangle ABC, in which AC= 7cm, BC= 8cm, AB= 6cm. (i) Mark 
    D, the mid point of BC. (ii) Construct the circle which touches AB at A , and 
    passes through D.                                                                                     
    
    (b) A man invests Rs. 7500 on buying shares of face value of Rs. 100 each at 
    a premium of 50% in a company . If he earns Rs. 550 at the end of the year 
    as dividend, find  (i) the number of shares he has in the company. (ii) what is 
    dividend percentage per share .          
  7. (a) Use graph paper for this question. Plot the points A(8,2) and B(6,4) . 
    These two points are the vertices of  a figure  which is symmetrical about x=6 
    and y= 2. Complete the figure on the graph . write down the geometrical 
    name of the figure.       
   (b) From a window A, 15m above the ground , the angle of elevation of the top 
    C of a tower is x° , where tan x = 5/2 and the angle of depression of the foot 
    D of the tower is y°  , where tan y  = ¼ . Calculate the height CD of the tower 
    in meters.        
   ( b) Solve y - 3y − 6 =2             
8. (a) The perimeter of a rectangular plot is 180m and its area 1800 m2
. If the length is x m, express the breadth in terms of x . Hence , form an equation in x. Solve the equation and find the length and the breadth of the rectangle. 
(b) Draw the graphs of 3y=122x and 2x3y=4. Write down the coordinates of 
     the point of intersection. Take 2cm = 1 unit on both the axes. 
(c ) The I.Q of 50 people  was recorded as follows:
   I.Q                 8090    90100   100110   110120   120130   130140
   No. of people     6            9             16             13            4             2
      Draw a histogram for the above data and estimate the mod.  )
9. (a) A circular garden has a circumference of 440m . It is surrounded by a 
     circular path which has been built at the cost of Rs. 63,756 at the rate of Rs. 
     6 per sq m. Find (i) the area of the path (ii) the radius of the outer circle. 
      (b) A manufacturer  produces  a good which cost him Rs.500. He  sells it to a 
     Wholesaler  at a price of Rs.500 and wholesaler  sells it to retailer at a price 
     of   Rs.600. The  retailer sells it to the customer at a price of Rs.800. If the 
    sales  tax charged is 5%. Find the  tax  charged under VAT by :
    (i) manufacturer, (ii)  wholesaler and (iii) retailer. Find the tax paid by the 
    customer     
    (c) The centre of a circle is (x + 2, y – 1).Find x and y if end points of diameter 
    are (2,  2) and (8,  2). Hence find the   radius.  (3)                                                         
10.(a) If 2 sin A – 1 = 0, show that : sin 3A = 3 sin A – 4 sin3A. 
     (b) The total amount collected for the picnic by certain number of students is           
Rs. 19,200. If there  were 10 more students , the amount each student  had to
pay would have been reduced by Rs. 160. find the total number of students
attending picnic.  
    (c) A bag contains 5 red , 4 black and 7 white balls. A ball is drawn from the
bag at random. Find the probability that the ball drawn is                                         
       (i) black (ii) black or white , (iii) not red.   
11. (a) Mr. Aggarwal had a Saving Bank Account in a bank. His passbook had
the following entries : 
      Date   2009       Particulars        Withdrawals  (in Rs.)    Depositst(in Rs.)                  Balance (in Rs.) 
         Jan.   21         By cash                 −                                        500                      500.00
          Mar.  18          To cheque          100.00                                   −                       400.00
          May  22            By cheque             −                             1,500.00                      1,900.00
          July   28            To cash             200.00                                  −                       1,700.00
         Sept.  03             By cash              −                                1,300.00                     3,000.00
He closes the account on 30th Oct. 2009 Calculate the amount he received if the
rate of interest is 6% p.a.    
(b)  The perpendicular AD on the base BC of   ABC intersects BC in D such
that BD = 3 CD. Prove that      2 AB2= 2 AC2+ BC2
 
(c) Alok invests Rs. 12800 for three years at the rate of 10% per annum
compound interest. Find :
(i) The sum due to alok at the end of the first year.
(ii) The interest he earns for the second year.
(iii) The total amount due to him at the end of the third year.