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ICSE MOCK PAPER 2 2015

7 pages, 49 questions, 2 questions with responses, 2 total responses,

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MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent in reading the question paper. em ia The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and four questions from Section B. All intended marks for questions or parts of question are given in brackets [ ]. Be nja mi nA cad Mathematical tables are provided. SECTION A (40 Marks) (Attempt all questions from this Section). Question 1 (a) Find the value of 'k' if (x + 2) is factor of : x3 + k x2 - 4x - 12 Hence determine whether (x + 3) is also a factor (b) 5 2 If A = and B = 3 1 3 4 , is the product AB possible ? Give a reason. If yes, find AB (c) [3] [3] Vinamra borrowed Rs 20, 000 for two years. The rate of interest for the two successive years are 12% and 9% respectively. If he repays Rs 14400 at the end of first year, find the outstanding amount at the end of the second year. [4] Question 2 (a) From a pack of 52 cards all cards whose numbers are multiples of 4 are removed. A card is drawn at random. What is the probability that the card drawn is: (i) even numbered black card ? (ii) a face card (Jack, King or Queen) (b) Solve the following equation: [3] 1 x 13 =8 x Give your answer correct to two significant figures (c) [3] A P o O B em ia C 25 The figure above show tangents at A and B meeting at C; centre at O. If o ACO = 25 , find (ii) (iii) BCO Be nja mi nA cad (i) AOB APB [4] Question 3 (a) Aakriti has a recurring deposit account in a bank. She deposits Rs 2400 per month for 3 years. If she gets Rs 98388 at the time of maturity, find (i) (ii) (b) the interest paid by the bank, the rate of interest. E A [3] B F D (c) [3] C Consider the above figure. Calculate the area of the shaded region, if the 22 diameter of the semi circle is equal to 7 cm. Take = 7 ABC is a triangle and G ( 1,3) is the centroid of the triangle and A ( 1, 7), B ( 5, b) and C (a, 1) are vertices of the triangle, find the length of the side BC. [4] 2 Question 4 Solve the following inequation and represent the solution on the number line: 9 - 2x > 7 - 3x 1, (b) [3] x R Evaluate without using trigonometric tables: 2 2 sec 20o tan 25o cot 75o 2 + 3 cot 65o tan 15o cosec 70o (c) 2 em ia (a) [3] A mathematics aptitude test of 50 students was recorded as follows : Marks 50-60 70-80 80-90 90-100 4 Number of students 60-70 6 15 20 5 Be nja mi nA cad Draw a histogram for the above data using a graph paper and locate the mode. [4] SECTION B (40 Marks) (Answer any four questions in this Section). Question 5 (a) A manufacturer sells a computer to a wholesaler for Rs 20,000. The wholesaler sells it to a trader at a profit of Rs 4000 and the trader in turn sells it to a consumer at a profit of Rs 1600. If the rate of VAT is 8% find: (i) The amount of VAT received by the state government on the sale of this computer from the manufacturer and the wholesaler. (ii) The amount that the consumer pays for the computer. (b) A solid cone of radius 7.0 cm and height 14 cm is melted and cast into small spheres of radius 0.7 cm. Find the number of spheres formed. (c) coordinates of A (ii) equation of diagonal BD. [3] ABCD is a parallelogram with A (a, b), B (4, 7), C (3,6) and D (1, -5). Find (i) [3] [4] Question 6 (a) Using a graph paper, plot points A (4, 6) , B (-2, 2). (i) Reflect A and B in x-axis to get the images A' and B'. (ii) Write the co-ordinates of A' and B'. 3 (iii) State the geometrical name for the figure ABB'A'. (iv) Find the length of diagonal AB'. (b) Given below are entries in a saving's Bank A/C pass book. Calculate the [3] interest for six months from February to July at 6% per annum. Date Particulars Withdrawals Deposits Feb 9 B/F Feb 23 to self 3000 April 15 by cash - May 9 to self 1000 July 12 by cash - - 8000 em ia - - --- 2000 --- - --- 7000 --- Be nja mi nA cad (c) Balance [3] T P O Q R In the given figure O is the centre of the circle and RT is a tangent at T. If RT = 10 cm and RQ = 5 cm, calculate radius of the circle. [4] Question 7 (a) Given : p2 + 4 + p2 + 4 p2 4 then show p 2 = (b) p2 4 1 Let A = 2 =x 2( x 2 + 1) x 0 , 1 [3] 2 3 B= - 1 1 Find A2 + AB + B2 [3] 4 C (c) D B mi a A The figure shows a right angled ABC with BAC = 90o, CD = 7.2 cm, BD = 12.8 cm Prove ADB ~ CDA (ii) Find AD (iii) Find the ratio of the area of ADB to area of CDA. Be nja mi nA cad e (i) [4] Question 8 (a) Using step-deviation method, calculate mean marks of the following distribution. State the modal class also. Class Interval 0-50 Frequency (b) 4 50-100 100-150 8 16 150-200 200-250 250-300 13 6 3 The marks obtained by 200 students in an examination are given below: Using a graph paper, draw an Ogive for the distribution. Use Ogive to estimate: (i) the Median; (ii) the lower quartile; (iii) the number of students who obtained more than 75% marks in the examination and (iv) The number of students who did not pass, if pass percentage was 40. (Use the scale as 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis) 5 [5] Number of students 0-10 5 10-20 10 20-30 11 30-40 20 40-50 27 50-60 38 60-70 40 70-80 29 80-90 14 Be nja mi nA cad e mi a Marks 90-100 6 Question 9 (a) Mr. Gupta invested Rs 48000 in Rs 100 shares at a premium of Rs 20 paying 10% divided. At the end of one year he sells the shares at a premium of Rs 40. Find (i) the annual divided, (ii) the profit earned including his divided. (b) Draw a circle of radius 4.0 cm. Mark a point P outside the circle at a distance [3] of 7.0 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of tangent. (c) [3] Prove that [4] (1 + cot - cosec ) (1 + tan + sec ) = 2 Question 10 (a) The mean proportion between two numbers x and y is 3. The third proportional to the numbers x and y is 81. Find the numbers. (b) [3] In what period of time will Rs 4000 yield Rs 1324 as compound interest if compounded yearly ? (c) [3] o An observer finds the angle of elevation of the top of a building to be 30 . He walks 50 m towards it along a horizontal line passing through its base and finds that the angle of elevation changes to 60o. Find the height of the building correct to the nearest metre. [4] 6 Question 11 (a) M A B C N D mi a O In the figure given above AB and CD are two parallel chords and O is the centre of the circle. If the radius of the circle is is 10 cm, find the distance MN Be nja mi nA cad e between the two chords of length 16 cm and 12 cm respectively. (b) [3] A shopkeeper buys a certain number of books for R 360. If the cost per book was R 6 less, the number of books that could be bought for R 360 would be 2 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it. (c) [3] A and B are two on the x-axis and the y-axis respectively. P (-2, -3) is the mid point of AB. Find (i) Co-ordinates of A and B, (ii) Slope of line AB, (iii) Equation of line AB A O P (-2, -3) B 7 [4]

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