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PRE-BOARD EXAMINATION ICSE 2024 MATHEMATICS FM. TIME: 2% HRS Answer to this paper must be written on the paper provided separately. You wil not be allowed towrite during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt allthequestions from Section Aand any four questions from Section B. All working, including the rough work, must be clearly shown, and must be done on the same sheet as the rest ofthe answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [] Mathematical tables are provided. SECTION A (Attempt all questions fromthis section,) Questionl: Choose the correct answer to the questions from the given options. (Do not copy the question, write the correct [15] answer only.). () Which of the following statement is NOT correct (a) Two matrices are added only when they are of same order. (b) Amatrix is said to be zero matrix if all the elements are zero. (c) Amatrix of order(m xn) has (m +n) elements. (d) A matrix is said to be a square matrix if the number of rows are equal to number of columns. (i)The roots of the quadratic equation 3x6x + k=0 are real and equal, then the value of kis (b) 4 (a) -3 (c) - 4 (d) 3 (ii)The taxable value of a Woodland leather purse is 3500. If the rate of GST is 18%. Then the price of the leather purse will be (b)4031 (c) 4130 (d) 4330 (a) 4310 (iv) Recurring deposit account is also called as (a) Current account (b) Saving account (c) Fixed Deposit account (d) Cumulative Deposit account. (V) How many two digit numbers are divisible by 5? (a) 17 (b) 18 (c) 19 (d) 20 N. (vi) The table shows the values ofx and y, when x is proportional to y. What are the values of Mand M 14 |X 12 28 21 (a) M= 4, N=35 (b) M=6, N=49 (c) M=3, N=32 (d) M=6, N= 36 (vii) In the given figure PQ |TR, then by using condition of similarity: (a) PQ OP RT (6 PQ_ OP RT OR PQOR (C)rPQ (0) 00 OP OT OT OT OR 00 water. If their diameters are Two cylindrical pots contain the same amount of in the ratio 2: 3, the ratio of their height is: (a) 4:9 (b) 9:2 (c) 9:3. (d) 9:4 (ix) Event A : Celebration of Children's Day in India (Celebrated on 15th of October) name given to Kalam Abdul APJ What is the Event B: Birth Anniversary of Dr. celebrated on thesame day? What is the probability that both the event Aand Bare event, P(E) =0 () Complementary event Sure (c) =0 P(E) event. Impossible (a) Sure event, P(E) = 1 (b) such event? PE)=. reflection in x- axis in the quadrant: Third quadrant (d) Fourth quadrant (a) First quadrant (b) Second quadrant (c) ofthe circle. the radius, lies in than larger is circle a of centre the from (xi) A point whose distance quadrant. shows (X) A rectangle ABCD made in first diameter (a) interior (b) exterior (c) on the circle (d) (xii) sinA cot'A + cosA tan'A =? (c)0 (b) 2 (a) 1 30 e (d) -1 (xii) In the given figure AP +AQ cm (d) (3043 + 60) cm (a) 180 cm (b) 240 cm (c) 120v3 zero. of the line x = a, is equals to positive direction of x-axis measured in the (xiv) Assertion (A): The slope straight the with makes line Reason (R): The angle which a the angle of inclination of the line. false. and R are anticlockwise direction is called A and R are true (d) both A both (c) true R is false A is (a) A is true R is false (b) (xv) If the mean of the following |f (a) 2 4 2 3 1 X distribution is 2.6, then the value of p is 3 1 (b) 3 (c) 2.6 (d) 2.8 14cm and Question 2: 24cm, a conical cavity of diameter x 30cm x 35cm metal of solid From a rectangular [4] height 24 cm is removed. Find the vae of the remaining solid. volyme remaining solid. (b the surtace area of the months. If he bankand deposited 150 per month for 8 in a account deposit recurring (4] )Akash opened a of interest per annum. received1236 at the time of maturity, find2 the rate (4] sinA+coSA sinA-cosA (io Prove that sinA-coSA stnA+coSA Question 3: 1-2cos2A p and r, prove that Ifq is the mean proportionalbetween find Tangents at Aand B meet at C. If LACO =30 circle. the of centre the is O figure (ii) In the given (c) ZAPB (a) ZBCO (b) reflexLAOB (4) A 30 Using the data of the by some candidate in an examination. obtained marks the represents histogram M) The 22.5] diagrams, calculate the mean marks. [use the assumed mean as 20 11 : (00) 35 20 40 15 Marks SECTION-B questions from this section) four (Attempt any Ouestion 4: (b) the matrix X shares when the price rises to 30, and the sells He 15. at shares 10 8%, (ii) Anubhav invests 4500 in shares at 125. Calculate: invests the proceeds in 12% 100 a) the sale proceeds. (3] b) the number of125 shares he buys. dividend. income from =10cm, AC Given c) the change in his annual respectively. are right angled at Band M (iii) In the given figure AABCand AAMP ~AAMP, (b) Find the length of AB and BC, (4] AABC AP = 15cm and PM = 12cm.(a) Prove ) Given x-4 Write (a) the order of the matrix X, Question 5: /0 Calculate lower quartile, upper quartile and inter quartile-range from the following frequency distributon. 25 3 31 8 40 34 10 45 10 15 48 50 9 6 60 2 31 (i) Tanishqbuys the following items from a departmental store: Items Pulse Milk Food Quantity Face Cream 500 ml GST 5% 12% 18% Rate { 80kg 3kg 7300kg 2kg 200 He pays <1500 to the departmental store. How much rupees did the departumental store retun to Tanishq? 31 (ii) In the given figure, AE and BC intersect each other at point D. If 2CDE=90, AB = Scm, BD = 4cm and CD -9cm, find DE. Ouestion 6: 1 ? Show the working in support of your answer. () ls7a term of the G.P.: () The equation of aline is 3x +4y -7=0. Find 27 (a) the slope of the line, (b) the equation of aline perpendicular to the given line and passing through the intersection of the line X-y+2=0 and 3x+y-10 =0. (ii) A girl fills acylindrical bucket 32cm in height and 18cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24cm, find (a) its radius and (b) its slant height. (leave your answer in square root form) Question 7: (i) The duration of telephone calls in a week at a school were recorded as below: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Time in seconds No. of calls 14 19 27 Draw a cumulative frequency curve and locate the median. 43 29 16 80-9090-100 12 twoships on opposite sides of of depression () From the top of alight house 100 mhigh the angles of nearest metre. 48 and 36 respectively. Find the distance between thetwo ships tothe number line Question 8: it onthe real represent and set (0) Solve the following inequation, write down the solution -2+ 10x s 13x+ 10<24 +10x, xEZ. =b+C. [3) (1) In the given figure, O is the centre of thecircle. Prove that a and(2,7). the segment joining the points (1,3) divide -9=0 y + 3x line the which [4] ( )Determine the ratio in herd had gone to the forest, Twice the square root of the in seen was camels of herd a of () One fourth number of camels. on the bank of river. Find the total mountain and the remaining 15 camels were 2ab Question 9: [3] ifx=. a+b. proportion, find the value of () Csing theproperties of 5.5 cm and z ABC = 120 ABC in which base BC=6cm, AB = (iii)Construct a triangle triangle ABC. (a) Construct a circle circumscribing the so that D is equidistant from B and C. (b) Draw cyclicquadrilateral ABCD Ouestion 10: (3] polynomial 3x+ 2x? -19x + 6. the completely factorise theorem, Remainder () Using equally likely to the same week (Monday to Saturday). Each is in shop particular a visiting are persons Two (i) the probability that both will visit the shop on visit the shop on any one day as on another. What is (3] Consecutive days. (c) days, different (b) day, same (a) the 1cm = Iunit along both the Xand Yaxis. (ii) Use a graph paper for this question taking [4] -2), E (2, -5) and F (0, -5). (a) Plot the points A (0, 5), B (2, 5), C (5, 2), D (5, axis and name them B',C, D' and E' (b) Reflect the points B, C, D and E on the YAlso write the coordinates. (c) Name the figure BCDEED'CB' formed. (d) Name a line of symmetry for the figure
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