2000 ICSE mathematics Question paper
ICSE  X MATHEMATICS 2000 (TWO & HALF HOURS)
General Instructions :
Answer to this paper must be written on the paper provided separately. You will NOT be allowed to write during the first fifteen minutes. This time is to be spent in reading the question papers. The time given at the head of this paper is the time allowed for writing the answers . This Question Paper is divided into two sections. Attempt all questions from Section  A and any 4 questions from Section B. The intended marks for questions or for any parts of questions are given in brackets [ ]. All working, including rough work should be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. Mathematical papers are provided.
SECTION  A
Q.1) A shopkeeper buys an article for Rs.400 and marks it for sale at a price that gives him 80% profit on his cost. He, however, gives 15% discount on the marked price to his customer. Calculate : (i) the marked price of the article. (ii) the discount in rupees given to the customer. (iii) the actual percentage profit made by the shopkeeper. [5]
Q.2). 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. Calculate the rate of interest and the sum of money. [5]
Q3). The shaded area, in the given diagram, between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle. [Take p to be 22. 7] [6]
Q 4). Attempt this question on graph paper. (i) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both axes. (ii) Reflect A and B in the xaxis to A', B'. Plot these on the same graph paper. (iii) Write down (a) the geometrical name of the figure ABB'A' (b) the axis of symmetry of ABB'A (c) the measure of the angle ABB' (d) the image A" of A, when A is reflected in the origin (e) the single transformation that maps A' to A". [7]
Q 5). Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively. (i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction. (ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC. [8]
Q 6). A model of a ship is made to a scale of 1:200 (i) The length of the model is 4 m. Calculate the length of the ship. (ii) The area of the deck of the ship is 160000 m2. Find the area of the deck of the model. (iii) The volume of the model is 200 litres. Calculate the volume of the ship in m3. [8]
Q 7). Part of a geometrical figure is given in each of the diagrams below. Complete the figures so that both the xaxis and the yaxis are lines of symmetry of the completed figure.
Give the geometrical name of the completed figure. (You may use graph paper if required.) Free hand sketches would be sufficient. [
Q 8). In the diagram below, ABC is a triangle, DE is parallel to BC and AD/DB = 3/2.
(i) Write down AD/AB. (ii) Prove triangle ADE is similar to triangle ABC and write down the ratio DE/BC. (iii) Prove triangle DEF is similar to triangle CFB. Write down the ratio area of triangle DFE area of triangle DEC [5]
Section  B (48 Marks)
Answer any four questions. Q 9). (a) State with reason, whether the following are true or false. A, B, C are matrices of order 2×2. [4] (i) A. B = B. A (ii) A. (B. C.) = (A. B) .C (iii) (A+B)2 = A2 + 2A. B + B2 (iv) A. (B + C) = A. B + A. C.
Q 9 b). Given [8 2 ]. X = [12] [1 4 ] [10] Write down (i) the order of the matrix X, (ii) the matrix X. [3]
Q 9) c). In the figure below, AD is perpendicular to BC. tan B = ¾ and tan C=5.12. BC=56cm. Calculate the length of AD. [5]
Q 10). (a) (i) Write down the coordinates of the point P that divides the line joining A(4, 1) and B(17, 10)in the ratio 1 : 2. (ii) Calculate the distance OP, where O is the origin. (iii) In what ratio does the yaxis divide the line AB? [6]
10. (b) Mr. Sharma has 60 shares of nominal value Rs.100 and he decides to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs.50, quoted at 4% discount, paying 18% dividend annually. Calculate. (i) the sale proceeds (ii) the number of shares he buys (iii) his annual dividend from these shares. [6]
Q 11).
A) R = {(x, y)} : 2x + 3y < 10, x, y Î n}. Write down R as ordered pairs. [3] Sol. R= {(x, y) : 2x + 3y < 10, x, y Î N}. Ordered pairs of R are (1, 1), (1, 2), (2, 1) and (3, 1).
(B)Use graph paper for this question. Take 2 cm = 1 unit on both axes (i) Draw the graphs of x + y +3 = 0 and 3x  2y + 4 = 0. Plot only three points per line. (ii) Write down the coordinates of the pint of intersection of the lines. (iii) Measure and record the distance of the point of intersection of the lines from the origin in cm. [6]
Q.12. (a). Attempt this question on graph paper Age (yrs.) Number of Casualties Date of Accidents 515 6 1525 10 2535 15 3545 13 4555 24 5565 8 6575 7
(i) Construct the 'less than' cumulative frequency curve for the above data, using 2cm = 10 years, on one axis and 2cm = 10 casualties on the other. (ii) From your graph determine (1) the median; (2) the upper quartile. [6]
Q.12.(b) The diagram represents two inequations A and B on real number lines (i) Write down A and B in set builder notation. (ii) Represent A n B and A n B' on two different number lines. [6]
Q.13.(a) In the figure PQRS and PXYZ are two parallelograms of equal area. Prove that SX is parallel to YR. [4]
B). The total surface area of a hollow metal cylinder, open at both ends, of external radius 8 cm and height 10 cm is 338p cm2. Taking r to be inner radius, write down an equation in r and use it to state the thickness of the metal in the cylinder. [6]
Q 14). (a) Category : A B C D E F G Wages in Rs./day : 50 60 70 80 90 100 110 Number of Workers : 2 4 8 12 10 6 8
(i) Calculate the mean wage, correct to the nearest rupee. (ii) If the number of workers in each category in doubled, what would be the near mean wage? [5]
Q.14.(b). (i) Write down the equation of the line AB, through (3, 2), perpendicular to the line 2y = 3x + 5. (ii)AB meets the xaxis at A and the yaxis at B. write down the coordinates of A and B. Calculate the area of triangle OAB, where O is the origin. [7]
Q 15.(a). In the figure AB = AC = CD, angle ADC = 38°. Calculate (i) angle ABC. (ii) angle BEC. [3]
Q 15). (b). Given 5 cos A  12 sin A = 0, evaluate without using tables sin A + cos A 2cos A  sin A [3]
Q.15.(c). Use ruler and compasses only for this question. (i) Draw two circles of radii 4cm and 2.5 cm with their centres 9cm apart. (ii) Construct a transverse common tangent to the above circles. Measure and record its length. (iii) Calculate the length of the transverse common tangent and write down the difference between the calculated value and the measured value, correct to one decimal place. [6]
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