MODEL TEST PAPER -1 ICSE (1)

Time Allowed: 2.30 hours    Max. Marks: 80
General Instructions:
          Attempt all questions from section A and any four questions from section B.
          All working, including rough work, must be clearly shown , and must be done 
         on the same sheet as the rest of the answer.
   Omission of essential working will result in loss of marks.
 The intended marks for questions or parts of questions are given in the bracket [  ]
                mathematical tables are provided.
                     -------------------------------------

SECTION - A (40 Marks)
       (Attempt all questions from this Section)
_____________________________________________


Question 1: Choose the correct answers to the questions from the given options:  [15]

    i) A dealer in Mumbai sold a washing machine to a consumer in Mumbai for Rs18000. If the rate of GST is 18%, then SGST is:
    a) Rs1620 b) Rs3240 c) nil d) none

   ii) Roots of the equation 3x² - 2 √6 x +2= 0 are :
    a) ±√(2/3) b) √(2/3), √(2/3) c) - √(2/3) , -√(2/3) d) -√(2/3), -√(3/2)

  iii) if x - 2 is a factor of x²- 7x + 2m, then value of m is:
    a) 5 b) 6 c) 4 d) 3

  iv) The transpose of matrix 1     5      4
                                                  -2     1      6 is:
  a) 1  -2 b) -2  1  6  c) 1  -2  d) 4  5  1 
      5    1      1  5  4       5   1       6  1 -2
      -2   6                        4   6

   v) 21% of 100 shares at Rs140 gives rate of return as:
   a) 10%  b) 120%  c) 15%  d) 25% 

   vi) The reflection of the P(0,3) in the y-axis is:
     a) (0,-3) b) (3,0) c) (0,3) d) 0,0)

   vii) In the figure, all answer are in cm.
 The length of AD is: 
a) 12cm b) 14cm c) 16cm d) 18 cm

  viii) Richa attaches a conical attachment to one side of the coin. The radius of coin and conical attachment is same. Which of the following is the surface area of the combined solid?
a) coin base + coin CSA b) coin base area + coin CSA + cone CSA c) total surface area of coin + total surface area of cone d) total surface area of cone.

   ix) Which term of the GP 18, 12, 8,.....is 512/729?
  a) 9th b) 10th  c) 11th  d) 12th

   x) if a coin is tossed 3 times, what is the probability of getting on a tail each time ?
a) 1/8 b) 1/4 c) 1/16 d) 1/6

  xi)  Two similar jugs have heights of 4cm and 6cm respectively. If the capacity of the smaller jug is 48cm³, then capacity of the larger jug is:
   a) 100 cm³ b) 130 cm³ c) 152cm³ d) 162cm²

  xii)  x-axis divides the line segment joining the points (2,-3) and (5,6) in the ratio:
a) 1:2 b) 2:1 c) 3:5  d) 2:3

  xiii) In the given figure, O is the centre of the circle. If angle AOB= 40°, then angle ABC is equal to:
  a) 50° b) 40° c) 60° d) 70°

  xiv) The sum of first 16 terms of the AP 10, 6, 2,.... is:
a)  -320 b) 320 c) - 350 d) -300

   xv) Assertion (A): The median of the following data is 12.5, 12, 13, 15, 11, 12, 14, 16, 10, 12, 13
         Reason(R): The value of the middle most observation obtained after arranging the data in an assending and descending order is called the median of the data.
   a) A is true, R is false b) A is false, R id True c) both A and R are True d) both A and R are false.

Question 2:
i) A conical tent is accommodate 77 persons. Each person master have 16 m³ of air to breathe. Given the radius of the tent as 7m, find the height of the tent and also curved surface area.      [4]
 
ii) Amit Kumar invests Rs36000 in buying Rs100 shares at Rs20 premium. The dividend is 15% per annum. Find :
    a) the number of shares he buys 
    b) his yearly dividend.
    c) the percentage return on his investment.       [4]

iii) The sum of three numbers in GP is 35 and their product is 1000. Find the numbers.          [4]

Question 3:
i) Pawan deposited Rs150 every month in a bank for 8 months under the recurring deposit scheme. Find the maturity value of his deposit,  if the interest is calculated every month and the rate of interest is 8% per annum.       [4]

ii) Find the equation of a line passing through the point (-2,3) and having the x-intercept of 4 units.     [4]

iii)  Use graph paper to solve the question.
    a) plot the point P(0,3), Q(3, -2) and O(0,0).
    b) plot E, the image of Q, when reflected in the y-axis and write its coordinates.
    c) What is the geometrical name of the figure PQOE ?      [5]

______________________________________
SECTION - B(40 Marks)
(Attempt any questions from this Section)
_______________________________________


Question 4:
i) A dealer in Patna(Bihar ) supplies goods worth Rs15000 to a dealer in Sonepat (Haryana). The dealer in Sonepat supplies the same goods to a dealer in Rohtak (Haryana) at a profit of R3000. If the rate of GST 18%, calculate:
    a) The cost of goods to the dealer in Rohtak.
    b) Net GST paid by the dealer in Sonepat .                [3]

ii) Solve the equation 4x² - 5x - 3=0 and give your answer corrected to decimal places.      [3]

iii)  On a map drawn to a scale if 1: 250000, a triangular plot of land has the following measurement AB= 3cm,  BC =4cm and angle ABC=90°, Calculate 
    A) the actual length of AB in km
    B) the area of the plot in km².         [4]

Question 5:
i) If A= 0    -1 & B= 1      3 & C= 1     0
             2     5          6      4         -3    -2 find A(B + C).        [3]

ii) Two circles touch externally at P.  A tangent touches the circles at A and B. Prove that the tangent at P bisects AB.       [3]

iii) The polynomials (px³+ 3x²- 3) and (2x³ - 5x +p) when divided by (x -4) leave the same reminder. Find the value of p.        [4]

Question 6:
i) Find the Co-ordinates of the points of trisection of the line segment joining the points A(5,-3), and B(2,-9).       [3]

ii) Prove : cotA - tanA = (2cos²A -1)/(sinA cosA).      [4]

iii) How many terms of the AP 72, 66, 60,.... must be taken to give the sum 0?    [4]


Question 7:
i) The daily wages of 80 workers in a project are given below:
  Wages     Number of workers 
400-450         2
450-500         6
500-550        12
550-600        18
600-650        24
650-700        13
700-750         5
 Use a graph paper to draw an ogive for the distribution. (Use a scale of 2 cm = Rs50 on x-axis and 2 cm= 10 workers on y-axis). Use your ogive to estimate:
 a) the medium wage of the workers.
 b) the lower quartile wage of workers.
 c) the number of workers who earn more than Rs625 daily .       [5]

ii) A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be x kmph, form an equation and solve it to evaluate x.       [5]

Question 8:
i) In a lottery are 5 prizes and 20 blanks. What is the probability of getting a prize ?   [3]

ii) Construct a quadrilateral ABCD in which AB= 5cm, BC= 4cm, angle B= 60°, AD= 5.5cm and D is equidistant from AB and BC.        [3]

iii) In the given figure, PQ is a tangent to the circle at A, AB and AD are bisectors of angle CAQ and angle PAC.  If angleBAQ=30°, prove that:
a) BD is a diameter of the circle.
b)  ABC is an isosceles triangle.      [4]


Question 9:
i) Solve the following inequation and graph the solution set on the number line :
- 1/5 ≤ 3x/10  +1 < 2/5, x ∈ R.            [3]

ii) Calculate the mean of the following distribution using step deviation method:
Marks       number of students 
 0-10           10
10-20           9
20-30          25
30-40          30
40-50          16
50-60          10               [3]

iii) In the figure, ABCD is a parallelogram. P is a point on BC such that BC : PC = 1 : 2. DP produced meets AB produced at Q. Given ar(∆CPQ) is 20m², find .
a) ar(∆DCP)
b) ar(∆ || gm ABCD).           [4]

Question 10:
i) Using properties of proportion, solve for x. Given that x is a positive:
{2x + √(4x² -1)}/{2x - √(4x² -1)} = 4.         [3]

ii)  Draw a circle with centre O and radius 3.1cm. Take a point P outside the circle at a distance of 6.2cm from its centre. Draw two tangent to the circle from the point P.   [3]

iii)  An aeroplane at an altitude of 1500m finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.     [4]

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