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ICSE Class X Mid-term 2024 : Mathematics

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ST. FRANCIS SCHOOL, PALAYUR HALF YEARLYEXAMINATION 2024-2025 Class: X Date: 04-09-2024 Mark: 8Om Time:2 1/2 Hrs MATHEMATICS Altempt all questions from section . Attempl any four questions from Section 5 Section A (Attempt all questions) Question 1 Choose the correct answers to the questions from the given options. 1. The selling price of' ashirt cxcluding CisT is Rs 800. If the rate ofGST is 12% then the total price of the shirt is c) Rs 896 d) Rs 848 a) Rs 704 b) Rs 96 then the value of kis aroot of the equation x+kx- -0 2. Ifis 4 2 d)-1/2 c)1/2 b)-2 3. If a.8,12 and 32 are in proportion the value of a is d)6 c)4 b)3 a) 2 4. When 2x*-x*-3x+2 =0 is divided by x+1 then the remainder is d)0 c)-2 b)-3 a) 2 probability The random. at drawn is marble 5. A bag contains 3 red and 2 blue marbles. A of drawing a black marble is d) c) b) a) 0 a) 2 6. If A=[3 -2|B= Assertion (A):Product AB of the two matrices A and B is possible B Reason (R): Number of columns of A is = Number of rows in the matrix a) A is true, R is false b) A is false R is true c) Both A and R are true and R is the correct reason for A d) Both AandR are true and R is not the correct explanation reason for A 7. Given x+2 < +3 andx is a prime number. The solution set for x is d) {0,1} c) {1} b) a) {0} and C (x,4) are the vertices of AABCis the centroid of the A is G(4.3) A(1,4) 8.therti y B (4,1) * is eq al to dy4 c) 7 b) 1 a) 2 9. If intwo triangles DEF and PQR,<D =<Q and <R=<Ethen which of the following is not true? FE EF_ DF PR c) RP PQ DE QR DF EF DE PQ RP QR 10. ABCD is acyclic quadrilateral. If <BAD=(2x+5) and <BCD = (x+l0) then x is A D B b)45 d)s c) 55 11. If two cylinders of the same lateral surface area have their radii in the ratio 4:9 then the ratio of their heights is d) 9:4 b) 3:2 c) 4:9 a) 2:3 a) 65 progression 12. Which term of the arithmetic b)10th a) 9th 21,42,63,84,... is 2109 c) 11th 13,The points which divides the line segmentjomng tne 1:2 lies in the a) First quadrant b) second quadrant d) 12th /n the ratio points (7,-6) and (3,6) (3,6)/n c) third quadrant 14. Geometic mean of 9 and 64 is b)3 a) 24 c) 8 d) fourth quadrant d)1| line x =2 is 15. The reflection of the point A(4,-1) in the c)(0,1 ) b) (8,-1) a) (0,-1) d) None of these Question 2 1. While factorising a given polynomial using remainder and factor theorem. a student 2x'+7x+2x-3 finds that 2x+1 is a factor of 2Y-tA! 2y -l 2 a) Is the student's solution correct stating that 2X*I is a factor of the given polynomial2 b) Give avalid reason for your answer. Also lactorize the given polynomial completely.(4) 2. In what ratio is the line joining the points PS,3)and Q(-5,3) divided by the y axis?. Also find the coordinates of the point of intersection. (4) 3. PORS is a cyclic quadrilateral. Given that <QPS = 73 <PQS = 55 and <PSR 82 calculate a) sRS h<PSQ bRQS d) PRQ (4) Question 3 1. In a Geometric progression the first term is 24 and the Sh term is 8. Find the 9th term and the sum to 10terms (4) 2. Study the graph and answer each of the following a) Write the coordinates of A,B,C and D b) Given that C is the image of point A. Name and write the equation of the line of reflection c) Write the coordinates of image of D under reflection in the y axis d) What is the name given to a point whose image is itself? e) On joining the points A,B,C,D and A in order a figure is formed. Name the (5) closed figure. 3. Solve the following quadratic equation x + 4x -8 -0. Give your answer correct to one (4) decimal place. SECTION B(40 MARKS) (Attempt any four questions) Question 4 1. The following bill shows GST rate and the marked price of artiCies S.No B VIDYUTH ELECTRONICS Item LED TV set MP4 Player Marked Price Rs12000 Rss000 Quantity Rate of GST 28% 18% Find the total amount to be paid (including GST) for the above bill. (3) 2. Solve the inequality and write the solution set and represent it on the number line 3-2x > x + 1-x 2x , XE R (3) 3 3. Using ruler and compass only for the construction <ABC = 60 ,AB -6cm, BC =5 cm a) Construct the locusof all pointswhich are cquidistant from AB and BC b) Construct the locus of all points equidistant from A and B. c) Mark the point which satisfies both conditions (i) and (ii) as P Hence construct a circle with centre P and passing through A and B (4) Question 5 1. IfA-A4 4Afind A. IfA? =pA then find the value ofp. 2. Use componendo - dividendo to find the valu of x when x'+3x 3x2+1 (3) 14 13 (3) 3. In AABC, <ABC=<DAC, AB = 8cm, AC =cm, AD=5cm a) Prove that AACD~ABCA b) Find the length of BC c) Find the length of CD d) Find the area of AACD: area ofABCA B (4) Question 6 1. 2nd and 45 term of an AP are 10 and 96 respectively. Find a) The common difference b) First term c)Sum of first 15 terms. (3) 2. A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 litres per second. a) How much time will it take to empty half the tank if it is 3m in diameter? b) Also find the cost of painting the closed tank if cost of painting is Rs 26 per m' Use pi = 22/7. (4) 3. If x-2 is a factor of the expression 2x'+ax+bX-14 and when the expression is divided byx-3, it leaves a remainder 52. Find the values of a and b. (3) Question 7 1. Cards marked with numbers 1,2,3,...,20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is b) Divisible by 3 c) A perfect square a) A prime number (3) 2. In the figure given below O is the centre of the circle and AB is adiameter. IfAC=BD and <AOC= 72 Find each of the angles <ABC,<BAD,ABD (4) 3. There are 3 nositive numbers in GP sue nat ther product is 335 and the result of product of first and second number added to the product of second and third is 750. (3) Find the numbers. Question 8 Aand B 1. a) From the given figure write down the c0ordinates of of P coordinates the b) IfP divides AB inthe ratio 2:3 find B 2 3 4 S (3) 2. If-AB - AB-5C and C=evaluate 5 (3) 18m of 3. acopper rod of diameter 1cm and length 8 cm is drawn into a wire of length uniform thickness. Find the (4) a) thickness of wire b) Total surface area of wire (use pi =22/7) Question 9 is 2 find 1. The first and last term of aGP are 3and 96 respectively. If the common ratio (3) 'n' the number of terms of GP and sum ofnterms. (3) 2. Find the amount for the following intra state transaction Cost per 100 item(in Rs) No. of items 25 GST rate % 12 200 250 180 300 30 12 40 18 50 28 60 8 3. A line segment AB joining the points A(-4.6) and B(8,-3). Find a) the ratio in which AB is divided by the Y axis b) Thecoordinates of point of intersection c)the length of AB Question 10 1. Using remainder and factortheorem factorisethegiven polynomial 3. completelyx'+1Ox? (3) more, 20 were offchildren (4) Rs 480 is divided equally among x children. Ifthe number of sum find theneach would have got Rs 12 less. Find x. the Hence is 300? 30,45.... term of IS, (3) 37x+26 2. (4) Which the Arithmetic progression the termsof the Arithmetic progression.

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